/* ecc.c
 *
 * Copyright (C) 2006-2016 wolfSSL Inc.
 *
 * This file is part of wolfSSL.
 *
 * wolfSSL is free software; you can redistribute it and/or modify
 * it under the terms of the GNU General Public License as published by
 * the Free Software Foundation; either version 2 of the License, or
 * (at your option) any later version.
 *
 * wolfSSL is distributed in the hope that it will be useful,
 * but WITHOUT ANY WARRANTY; without even the implied warranty of
 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
 * GNU General Public License for more details.
 *
 * You should have received a copy of the GNU General Public License
 * along with this program; if not, write to the Free Software
 * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1335, USA
 */



#ifdef HAVE_CONFIG_H
    #include <config.h>
#endif

/* in case user set HAVE_ECC there */
#include <wolfssl/wolfcrypt/settings.h>

/*
Possible ECC enable options:
 * HAVE_ECC:            Overall control of ECC                  default: on
 * HAVE_ECC_ENCRYPT:    ECC encrypt/decrypt w/AES and HKDF      default: off
 * HAVE_ECC_SIGN:       ECC sign                                default: on
 * HAVE_ECC_VERIFY:     ECC verify                              default: on
 * HAVE_ECC_DHE:        ECC build shared secret                 default: on
 * HAVE_ECC_CDH:        ECC cofactor DH shared secret           default: off
 * HAVE_ECC_KEY_IMPORT: ECC Key import                          default: on
 * HAVE_ECC_KEY_EXPORT: ECC Key export                          default: on
 * ECC_SHAMIR:          Enables Shamir calc method              default: on
 * HAVE_COMP_KEY:       Enables compressed key                  default: off
 * WOLFSSL_VALIDATE_ECC_IMPORT: Validate ECC key on import      default: off
 * WOLFSSL_VALIDATE_ECC_KEYGEN: Validate ECC key gen            default: off
 * WOLFSSL_CUSTOM_CURVES: Allow non-standard curves.            default: off
 *                        Includes the curve "a" variable in calculation
 * ECC_DUMP_OID:        Enables dump of OID encoding and sum    default: off
 * ECC_CACHE_CURVE:     Enables cache of curve info to improve perofrmance
                                                                default: off
 * FP_ECC:              ECC Fixed Point Cache                   default: off
 * USE_ECC_B_PARAM:     Enable ECC curve B param                default: off
                         (on for HAVE_COMP_KEY)
 */

/*
ECC Curve Types:
 * NO_ECC_SECP          Disables SECP curves                    default: off (not defined)
 * HAVE_ECC_SECPR2      Enables SECP R2 curves                  default: off
 * HAVE_ECC_SECPR3      Enables SECP R3 curves                  default: off
 * HAVE_ECC_BRAINPOOL   Enables Brainpool curves                default: off
 * HAVE_ECC_KOBLITZ     Enables Koblitz curves                  default: off
 */

/*
ECC Curve Sizes:
 * ECC_USER_CURVES: Allows custom combination of key sizes below
 * HAVE_ALL_CURVES: Enable all key sizes (on unless ECC_USER_CURVES is defined)
 * HAVE_ECC112: 112 bit key
 * HAVE_ECC128: 128 bit key
 * HAVE_ECC160: 160 bit key
 * HAVE_ECC192: 192 bit key
 * HAVE_ECC224: 224 bit key
 * HAVE_ECC239: 239 bit key
 * NO_ECC256: Disables 256 bit key (on by default)
 * HAVE_ECC320: 320 bit key
 * HAVE_ECC384: 384 bit key
 * HAVE_ECC512: 512 bit key
 * HAVE_ECC521: 521 bit key
 */


#ifdef HAVE_ECC

/* Make sure custom curves is enabled for Brainpool or Koblitz curve types */
#if (defined(HAVE_ECC_BRAINPOOL) || defined(HAVE_ECC_KOBLITZ)) &&\
    !defined(WOLFSSL_CUSTOM_CURVES)
    #error Brainpool and Koblitz curves requires WOLFSSL_CUSTOM_CURVES
#endif

/* Make sure ASN is enabled for ECC sign/verify */
#if (defined(HAVE_ECC_SIGN) || defined(HAVE_ECC_VERIFY)) && defined(NO_ASN)
    #error ASN must be enabled for ECC sign/verify
#endif


#include <wolfssl/wolfcrypt/ecc.h>
#include <wolfssl/wolfcrypt/asn.h>
#include <wolfssl/wolfcrypt/error-crypt.h>
#include <wolfssl/wolfcrypt/logging.h>

#ifdef HAVE_ECC_ENCRYPT
    #include <wolfssl/wolfcrypt/hmac.h>
    #include <wolfssl/wolfcrypt/aes.h>
#endif

#ifdef HAVE_X963_KDF
    #include <wolfssl/wolfcrypt/hash.h>
#endif

#ifdef NO_INLINE
    #include <wolfssl/wolfcrypt/misc.h>
#else
    #define WOLFSSL_MISC_INCLUDED
    #include <wolfcrypt/src/misc.c>
#endif

#if defined(FREESCALE_LTC_ECC)
    #include <wolfssl/wolfcrypt/port/nxp/ksdk_port.h>
#endif

#ifdef USE_FAST_MATH
    #define GEN_MEM_ERR FP_MEM
#else
    #define GEN_MEM_ERR MP_MEM
#endif


/* internal ECC states */
enum {
    ECC_STATE_NONE = 0,

    ECC_STATE_SHARED_SEC_GEN,
    ECC_STATE_SHARED_SEC_RES,

    ECC_STATE_SIGN_DO,
    ECC_STATE_SIGN_ENCODE,

    ECC_STATE_VERIFY_DECODE,
    ECC_STATE_VERIFY_DO,
    ECC_STATE_VERIFY_RES,
};


/* map
   ptmul -> mulmod
*/

/* 256-bit curve on by default whether user curves or not */
#if defined(HAVE_ECC112) || defined(HAVE_ALL_CURVES)
    #define ECC112
#endif
#if defined(HAVE_ECC128) || defined(HAVE_ALL_CURVES)
    #define ECC128
#endif
#if defined(HAVE_ECC160) || defined(HAVE_ALL_CURVES)
    #define ECC160
#endif
#if defined(HAVE_ECC192) || defined(HAVE_ALL_CURVES)
    #define ECC192
#endif
#if defined(HAVE_ECC224) || defined(HAVE_ALL_CURVES)
    #define ECC224
#endif
#if defined(HAVE_ECC239) || defined(HAVE_ALL_CURVES)
    #define ECC239
#endif
#if !defined(NO_ECC256)  || defined(HAVE_ALL_CURVES)
    #define ECC256
#endif
#if defined(HAVE_ECC320) || defined(HAVE_ALL_CURVES)
    #define ECC320
#endif
#if defined(HAVE_ECC384) || defined(HAVE_ALL_CURVES)
    #define ECC384
#endif
#if defined(HAVE_ECC512) || defined(HAVE_ALL_CURVES)
    #define ECC512
#endif
#if defined(HAVE_ECC521) || defined(HAVE_ALL_CURVES)
    #define ECC521
#endif


/* The encoded OID's for ECC curves */
#ifdef ECC112
    #ifndef NO_ECC_SECP
        static const ecc_oid_t ecc_oid_secp112r1[] = {
        #ifdef HAVE_OID_ENCODING
            1,3,132,0,6
        #else
            0x2B,0x81,0x04,0x00,0x06
        #endif
        };
    #endif /* !NO_ECC_SECP */
    #ifdef HAVE_ECC_SECPR2
        static const ecc_oid_t ecc_oid_secp112r2[] = {
        #ifdef HAVE_OID_ENCODING
            1,3,132,0,7
        #else
            0x2B,0x81,0x04,0x00,0x07
        #endif
        };
    #endif /* HAVE_ECC_SECPR2 */
#endif /* ECC112 */
#ifdef ECC128
    #ifndef NO_ECC_SECP
        static const ecc_oid_t ecc_oid_secp128r1[] = {
        #ifdef HAVE_OID_ENCODING
            1,3,132,0,28
        #else
            0x2B,0x81,0x04,0x00,0x1C
        #endif
        };
    #endif /* !NO_ECC_SECP */
    #ifdef HAVE_ECC_SECPR2
        static const ecc_oid_t ecc_oid_secp128r2[] = {
        #ifdef HAVE_OID_ENCODING
            1,3,132,0,29
        #else
            0x2B,0x81,0x04,0x00,0x1D
        #endif
        };
    #endif /* HAVE_ECC_SECPR2 */
#endif /* ECC128 */
#ifdef ECC160
    #ifndef NO_ECC_SECP
        static const ecc_oid_t ecc_oid_secp160r1[] = {
        #ifdef HAVE_OID_ENCODING
            1,3,132,0,8
        #else
            0x2B,0x81,0x04,0x00,0x08
        #endif
        };
    #endif /* !NO_ECC_SECP */
    #ifdef HAVE_ECC_SECPR2
        static const ecc_oid_t ecc_oid_secp160r2[] = {
        #ifdef HAVE_OID_ENCODING
            1,3,132,0,30
        #else
            0x2B,0x81,0x04,0x00,0x1E
        #endif
        };
    #endif /* HAVE_ECC_SECPR2 */
    #ifdef HAVE_ECC_KOBLITZ
        static const ecc_oid_t ecc_oid_secp160k1[] = {
        #ifdef HAVE_OID_ENCODING
            1,3,132,0,9
        #else
            0x2B,0x81,0x04,0x00,0x09
        #endif
        };
    #endif /* HAVE_ECC_KOBLITZ */
    #ifdef HAVE_ECC_BRAINPOOL
        static const ecc_oid_t ecc_oid_brainpoolp160r1[] = {
        #ifdef HAVE_OID_ENCODING
            1,3,36,3,3,2,8,1,1,1
        #else
            0x2B,0x24,0x03,0x03,0x02,0x08,0x01,0x01,0x01
        #endif
        };
    #endif /* HAVE_ECC_BRAINPOOL */
#endif /* ECC160 */
#ifdef ECC192
    #ifndef NO_ECC_SECP
        static const ecc_oid_t ecc_oid_secp192r1[] = {
        #ifdef HAVE_OID_ENCODING
            1,2,840,10045,3,1,1
        #else
            0x2A,0x86,0x48,0xCE,0x3D,0x03,0x01,0x01
        #endif
        };
    #endif /* !NO_ECC_SECP */
    #ifdef HAVE_ECC_SECPR2
        static const ecc_oid_t ecc_oid_prime192v2[] = {
        #ifdef HAVE_OID_ENCODING
            1,2,840,10045,3,1,2
        #else
            0x2A,0x86,0x48,0xCE,0x3D,0x03,0x01,0x02
        #endif
        };
    #endif /* HAVE_ECC_SECPR2 */
    #ifdef HAVE_ECC_SECPR3
        static const ecc_oid_t ecc_oid_prime192v3[] = {
        #ifdef HAVE_OID_ENCODING
            1,2,840,10045,3,1,3
        #else
            0x2A,0x86,0x48,0xCE,0x3D,0x03,0x01,0x03
        #endif
        };
    #endif /* HAVE_ECC_SECPR3 */
    #ifdef HAVE_ECC_KOBLITZ
        static const ecc_oid_t ecc_oid_secp192k1[] = {
        #ifdef HAVE_OID_ENCODING
            1,3,132,0,31
        #else
            0x2B,0x81,0x04,0x00,0x1F
        #endif
        };
    #endif /* HAVE_ECC_KOBLITZ */
    #ifdef HAVE_ECC_BRAINPOOL
        static const ecc_oid_t ecc_oid_brainpoolp192r1[] = {
        #ifdef HAVE_OID_ENCODING
            1,3,36,3,3,2,8,1,1,3
        #else
            0x2B,0x24,0x03,0x03,0x02,0x08,0x01,0x01,0x03
        #endif
        };
    #endif /* HAVE_ECC_BRAINPOOL */
#endif /* ECC192 */
#ifdef ECC224
    #ifndef NO_ECC_SECP
        static const ecc_oid_t ecc_oid_secp224r1[] = {
        #ifdef HAVE_OID_ENCODING
            1,3,132,0,33
        #else
            0x2B,0x81,0x04,0x00,0x21
        #endif
        };
    #endif /* !NO_ECC_SECP */
    #ifdef HAVE_ECC_KOBLITZ
        static const ecc_oid_t ecc_oid_secp224k1[] = {
        #ifdef HAVE_OID_ENCODING
            1,3,132,0,32
        #else
            0x2B,0x81,0x04,0x00,0x20
        #endif
        };
    #endif /* HAVE_ECC_KOBLITZ */
    #ifdef HAVE_ECC_BRAINPOOL
        static const ecc_oid_t ecc_oid_brainpoolp224r1[] = {
        #ifdef HAVE_OID_ENCODING
            1,3,36,3,3,2,8,1,1,5
        #else
            0x2B,0x24,0x03,0x03,0x02,0x08,0x01,0x01,0x05
        #endif
        };
    #endif /* HAVE_ECC_BRAINPOOL */
#endif /* ECC224 */
#ifdef ECC239
    #ifndef NO_ECC_SECP
        static const ecc_oid_t ecc_oid_prime239v1[] = {
        #ifdef HAVE_OID_ENCODING
            1,2,840,10045,3,1,4
        #else
            0x2A,0x86,0x48,0xCE,0x3D,0x03,0x01,0x04
        #endif
        };
    #endif /* !NO_ECC_SECP */
    #ifdef HAVE_ECC_SECPR2
        static const ecc_oid_t ecc_oid_prime239v2[] = {
        #ifdef HAVE_OID_ENCODING
            1,2,840,10045,3,1,5
        #else
            0x2A,0x86,0x48,0xCE,0x3D,0x03,0x01,0x05
        #endif
        };
    #endif /* HAVE_ECC_SECPR2 */
    #ifdef HAVE_ECC_SECPR3
        static const ecc_oid_t ecc_oid_prime239v3[] = {
        #ifdef HAVE_OID_ENCODING
            1,2,840,10045,3,1,6
        #else
            0x2A,0x86,0x48,0xCE,0x3D,0x03,0x01,0x06
        #endif
        };
    #endif /* HAVE_ECC_SECPR3 */
#endif /* ECC239 */
#ifdef ECC256
    #ifndef NO_ECC_SECP
        static const ecc_oid_t ecc_oid_secp256r1[] = {
        #ifdef HAVE_OID_ENCODING
            1,2,840,10045,3,1,7
        #else
            0x2A,0x86,0x48,0xCE,0x3D,0x03,0x01,0x07
        #endif
        };
    #endif /* !NO_ECC_SECP */
    #ifdef HAVE_ECC_KOBLITZ
        static const ecc_oid_t ecc_oid_secp256k1[] = {
        #ifdef HAVE_OID_ENCODING
            1,3,132,0,10
        #else
            0x2B,0x81,0x04,0x00,0x0A
        #endif
        };
    #endif /* HAVE_ECC_KOBLITZ */
    #ifdef HAVE_ECC_BRAINPOOL
        static const ecc_oid_t ecc_oid_brainpoolp256r1[] = {
        #ifdef HAVE_OID_ENCODING
            1,3,36,3,3,2,8,1,1,7
        #else
            0x2B,0x24,0x03,0x03,0x02,0x08,0x01,0x01,0x07
        #endif
        };
    #endif /* HAVE_ECC_BRAINPOOL */
#endif /* ECC256 */
#ifdef ECC320
    #ifdef HAVE_ECC_BRAINPOOL
        static const ecc_oid_t ecc_oid_brainpoolp320r1[] = {
        #ifdef HAVE_OID_ENCODING
            1,3,36,3,3,2,8,1,1,9
        #else
            0x2B,0x24,0x03,0x03,0x02,0x08,0x01,0x01,0x09
        #endif
        };
    #endif /* HAVE_ECC_BRAINPOOL */
#endif /* ECC320 */
#ifdef ECC384
    #ifndef NO_ECC_SECP
        static const ecc_oid_t ecc_oid_secp384r1[] = {
        #ifdef HAVE_OID_ENCODING
            1,3,132,0,34
        #else
            0x2B,0x81,0x04,0x00,0x22
        #endif
        };
    #endif /* !NO_ECC_SECP */
    #ifdef HAVE_ECC_BRAINPOOL
        static const ecc_oid_t ecc_oid_brainpoolp384r1[] = {
        #ifdef HAVE_OID_ENCODING
            1,3,36,3,3,2,8,1,1,11
        #else
            0x2B,0x24,0x03,0x03,0x02,0x08,0x01,0x01,0x0B
        #endif
        };
    #endif /* HAVE_ECC_BRAINPOOL */
#endif /* ECC384 */
#ifdef ECC512
    #ifdef HAVE_ECC_BRAINPOOL
        static const ecc_oid_t ecc_oid_brainpoolp512r1[] = {
        #ifdef HAVE_OID_ENCODING
            1,3,36,3,3,2,8,1,1,13
        #else
            0x2B,0x24,0x03,0x03,0x02,0x08,0x01,0x01,0x0D
        #endif
        };
    #endif /* HAVE_ECC_BRAINPOOL */
#endif /* ECC512 */
#ifdef ECC521
    #ifndef NO_ECC_SECP
        static const ecc_oid_t ecc_oid_secp521r1[] = {
        #ifdef HAVE_OID_ENCODING
            1,3,132,0,35
        #else
            0x2B,0x81,0x04,0x00,0x23
        #endif
        };
    #endif /* !NO_ECC_SECP */
#endif /* ECC521 */


/* This holds the key settings.
   ***MUST*** be organized by size from smallest to largest. */

const ecc_set_type ecc_sets[] = {
#ifdef ECC112
    #ifndef NO_ECC_SECP
    {
        14,                             /* size/bytes */
        ECC_SECP112R1,                  /* ID         */
        "SECP112R1",                    /* curve name */
        "DB7C2ABF62E35E668076BEAD208B", /* prime      */
        "DB7C2ABF62E35E668076BEAD2088", /* A          */
        "659EF8BA043916EEDE8911702B22", /* B          */
        "DB7C2ABF62E35E7628DFAC6561C5", /* order      */
        "9487239995A5EE76B55F9C2F098",  /* Gx         */
        "A89CE5AF8724C0A23E0E0FF77500", /* Gy         */
        ecc_oid_secp112r1,              /* oid/oidSz  */
        sizeof(ecc_oid_secp112r1) / sizeof(ecc_oid_t),
        ECC_SECP112R1_OID,              /* oid sum    */
        1,                              /* cofactor   */
    },
    #endif /* !NO_ECC_SECP */
    #ifdef HAVE_ECC_SECPR2
    {
        14,                             /* size/bytes */
        ECC_SECP112R2,                  /* ID         */
        "SECP112R2",                    /* curve name */
        "DB7C2ABF62E35E668076BEAD208B", /* prime      */
        "6127C24C05F38A0AAAF65C0EF02C", /* A          */
        "51DEF1815DB5ED74FCC34C85D709", /* B          */
        "36DF0AAFD8B8D7597CA10520D04B", /* order      */
        "4BA30AB5E892B4E1649DD0928643", /* Gx         */
        "ADCD46F5882E3747DEF36E956E97", /* Gy         */
        ecc_oid_secp112r2,              /* oid/oidSz  */
        sizeof(ecc_oid_secp112r2) / sizeof(ecc_oid_t),
        ECC_SECP112R2_OID,              /* oid sum    */
        4,                              /* cofactor   */
    },
    #endif /* HAVE_ECC_SECPR2 */
#endif /* ECC112 */
#ifdef ECC128
    #ifndef NO_ECC_SECP
    {
        16,                                 /* size/bytes */
        ECC_SECP128R1,                      /* ID         */
        "SECP128R1",                        /* curve name */
        "FFFFFFFDFFFFFFFFFFFFFFFFFFFFFFFF", /* prime      */
        "FFFFFFFDFFFFFFFFFFFFFFFFFFFFFFFC", /* A          */
        "E87579C11079F43DD824993C2CEE5ED3", /* B          */
        "FFFFFFFE0000000075A30D1B9038A115", /* order      */
        "161FF7528B899B2D0C28607CA52C5B86", /* Gx         */
        "CF5AC8395BAFEB13C02DA292DDED7A83", /* Gy         */
        ecc_oid_secp128r1,                  /* oid/oidSz  */
        sizeof(ecc_oid_secp128r1) / sizeof(ecc_oid_t),
        ECC_SECP128R1_OID,                  /* oid sum    */
        1,                                  /* cofactor   */
    },
    #endif /* !NO_ECC_SECP */
    #ifdef HAVE_ECC_SECPR2
    {
        16,                                 /* size/bytes */
        ECC_SECP128R2,                      /* ID         */
        "SECP128R2",                        /* curve name */
        "FFFFFFFDFFFFFFFFFFFFFFFFFFFFFFFF", /* prime      */
        "D6031998D1B3BBFEBF59CC9BBFF9AEE1", /* A          */
        "5EEEFCA380D02919DC2C6558BB6D8A5D", /* B          */
        "3FFFFFFF7FFFFFFFBE0024720613B5A3", /* order      */
        "7B6AA5D85E572983E6FB32A7CDEBC140", /* Gx         */
        "27B6916A894D3AEE7106FE805FC34B44", /* Gy         */
        ecc_oid_secp128r2,                  /* oid/oidSz  */
        sizeof(ecc_oid_secp128r2) / sizeof(ecc_oid_t),
        ECC_SECP128R2_OID,                  /* oid sum    */
        4,                                  /* cofactor   */
    },
    #endif /* HAVE_ECC_SECPR2 */
#endif /* ECC128 */
#ifdef ECC160
    #ifndef NO_ECC_SECP
    {
        20,                                         /* size/bytes */
        ECC_SECP160R1,                              /* ID         */
        "SECP160R1",                                /* curve name */
        "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF7FFFFFFF", /* prime      */
        "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF7FFFFFFC", /* A          */
        "1C97BEFC54BD7A8B65ACF89F81D4D4ADC565FA45", /* B          */
        "100000000000000000001F4C8F927AED3CA752257",/* order      */
        "4A96B5688EF573284664698968C38BB913CBFC82", /* Gx         */
        "23A628553168947D59DCC912042351377AC5FB32", /* Gy         */
        ecc_oid_secp160r1,                          /* oid/oidSz  */
        sizeof(ecc_oid_secp160r1) / sizeof(ecc_oid_t),
        ECC_SECP160R1_OID,                          /* oid sum    */
        1,                                          /* cofactor   */
    },
    #endif /* !NO_ECC_SECP */
    #ifdef HAVE_ECC_SECPR2
    {
        20,                                         /* size/bytes */
        ECC_SECP160R2,                              /* ID         */
        "SECP160R2",                                /* curve name */
        "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFAC73", /* prime      */
        "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFAC70", /* A          */
        "B4E134D3FB59EB8BAB57274904664D5AF50388BA", /* B          */
        "100000000000000000000351EE786A818F3A1A16B",/* order      */
        "52DCB034293A117E1F4FF11B30F7199D3144CE6D", /* Gx         */
        "FEAFFEF2E331F296E071FA0DF9982CFEA7D43F2E", /* Gy         */
        ecc_oid_secp160r2,                          /* oid/oidSz  */
        sizeof(ecc_oid_secp160r2) / sizeof(ecc_oid_t),
        ECC_SECP160R2_OID,                          /* oid sum    */
        1,                                          /* cofactor   */
    },
    #endif /* HAVE_ECC_SECPR2 */
    #ifdef HAVE_ECC_KOBLITZ
    {
        20,                                         /* size/bytes */
        ECC_SECP160K1,                              /* ID         */
        "SECP160K1",                                /* curve name */
        "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFAC73", /* prime      */
        "0000000000000000000000000000000000000000", /* A          */
        "0000000000000000000000000000000000000007", /* B          */
        "100000000000000000001B8FA16DFAB9ACA16B6B3",/* order      */
        "3B4C382CE37AA192A4019E763036F4F5DD4D7EBB", /* Gx         */
        "938CF935318FDCED6BC28286531733C3F03C4FEE", /* Gy         */
        ecc_oid_secp160k1,                          /* oid/oidSz  */
        sizeof(ecc_oid_secp160k1) / sizeof(ecc_oid_t),
        ECC_SECP160K1_OID,                          /* oid sum    */
        1,                                          /* cofactor   */
    },
    #endif /* HAVE_ECC_KOBLITZ */
    #ifdef HAVE_ECC_BRAINPOOL
    {
        20,                                         /* size/bytes */
        ECC_BRAINPOOLP160R1,                        /* ID         */
        "BRAINPOOLP160R1",                          /* curve name */
        "E95E4A5F737059DC60DFC7AD95B3D8139515620F", /* prime      */
        "340E7BE2A280EB74E2BE61BADA745D97E8F7C300", /* A          */
        "1E589A8595423412134FAA2DBDEC95C8D8675E58", /* B          */
        "E95E4A5F737059DC60DF5991D45029409E60FC09", /* order      */
        "BED5AF16EA3F6A4F62938C4631EB5AF7BDBCDBC3", /* Gx         */
        "1667CB477A1A8EC338F94741669C976316DA6321", /* Gy         */
        ecc_oid_brainpoolp160r1,                    /* oid/oidSz  */
        sizeof(ecc_oid_brainpoolp160r1) / sizeof(ecc_oid_t),
        ECC_BRAINPOOLP160R1_OID,                    /* oid sum    */
        1,                                          /* cofactor   */
    },
    #endif /* HAVE_ECC_BRAINPOOL */
#endif /* ECC160 */
#ifdef ECC192
    #ifndef NO_ECC_SECP
    {
        24,                                                 /* size/bytes */
        ECC_SECP192R1,                                      /* ID         */
        "SECP192R1",                                        /* curve name */
        "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFFFFFFFFFFFF", /* prime      */
        "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFFFFFFFFFFFC", /* A          */
        "64210519E59C80E70FA7E9AB72243049FEB8DEECC146B9B1", /* B          */
        "FFFFFFFFFFFFFFFFFFFFFFFF99DEF836146BC9B1B4D22831", /* order      */
        "188DA80EB03090F67CBF20EB43A18800F4FF0AFD82FF1012", /* Gx         */
        "7192B95FFC8DA78631011ED6B24CDD573F977A11E794811",  /* Gy         */
        ecc_oid_secp192r1,                                  /* oid/oidSz  */
        sizeof(ecc_oid_secp192r1) / sizeof(ecc_oid_t),
        ECC_SECP192R1_OID,                                  /* oid sum    */
        1,                                                  /* cofactor   */
    },
    #endif /* !NO_ECC_SECP */
    #ifdef HAVE_ECC_SECPR2
    {
        24,                                                 /* size/bytes */
        ECC_PRIME192V2,                                     /* ID         */
        "PRIME192V2",                                       /* curve name */
        "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFFFFFFFFFFFF", /* prime      */
        "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFFFFFFFFFFFC", /* A          */
        "CC22D6DFB95C6B25E49C0D6364A4E5980C393AA21668D953", /* B          */
        "FFFFFFFFFFFFFFFFFFFFFFFE5FB1A724DC80418648D8DD31", /* order      */
        "EEA2BAE7E1497842F2DE7769CFE9C989C072AD696F48034A", /* Gx         */
        "6574D11D69B6EC7A672BB82A083DF2F2B0847DE970B2DE15", /* Gy         */
        ecc_oid_prime192v2,                                 /* oid/oidSz  */
        sizeof(ecc_oid_prime192v2) / sizeof(ecc_oid_t),
        ECC_PRIME192V2_OID,                                 /* oid sum    */
        1,                                                  /* cofactor   */
    },
    #endif /* HAVE_ECC_SECPR2 */
    #ifdef HAVE_ECC_SECPR3
    {
        24,                                                 /* size/bytes */
        ECC_PRIME192V3,                                     /* ID         */
        "PRIME192V3",                                       /* curve name */
        "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFFFFFFFFFFFF", /* prime      */
        "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFFFFFFFFFFFC", /* A          */
        "22123DC2395A05CAA7423DAECCC94760A7D462256BD56916", /* B          */
        "FFFFFFFFFFFFFFFFFFFFFFFF7A62D031C83F4294F640EC13", /* order      */
        "7D29778100C65A1DA1783716588DCE2B8B4AEE8E228F1896", /* Gx         */
        "38A90F22637337334B49DCB66A6DC8F9978ACA7648A943B0", /* Gy         */
        ecc_oid_prime192v3,                                 /* oid/oidSz  */
        sizeof(ecc_oid_prime192v3) / sizeof(ecc_oid_t),
        ECC_PRIME192V3_OID,                                 /* oid sum    */
        1,                                                  /* cofactor   */
    },
    #endif /* HAVE_ECC_SECPR3 */
    #ifdef HAVE_ECC_KOBLITZ
    {
        24,                                                 /* size/bytes */
        ECC_SECP192K1,                                      /* ID         */
        "SECP192K1",                                        /* curve name */
        "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFEE37", /* prime      */
        "000000000000000000000000000000000000000000000000", /* A          */
        "000000000000000000000000000000000000000000000003", /* B          */
        "FFFFFFFFFFFFFFFFFFFFFFFE26F2FC170F69466A74DEFD8D", /* order      */
        "DB4FF10EC057E9AE26B07D0280B7F4341DA5D1B1EAE06C7D", /* Gx         */
        "9B2F2F6D9C5628A7844163D015BE86344082AA88D95E2F9D", /* Gy         */
        ecc_oid_secp192k1,                                  /* oid/oidSz  */
        sizeof(ecc_oid_secp192k1) / sizeof(ecc_oid_t),
        ECC_SECP192K1_OID,                                  /* oid sum    */
        1,                                                  /* cofactor   */
    },
    #endif /* HAVE_ECC_KOBLITZ */
    #ifdef HAVE_ECC_BRAINPOOL
    {
        24,                                                 /* size/bytes */
        ECC_BRAINPOOLP192R1,                                /* ID         */
        "BRAINPOOLP192R1",                                  /* curve name */
        "C302F41D932A36CDA7A3463093D18DB78FCE476DE1A86297", /* prime      */
        "6A91174076B1E0E19C39C031FE8685C1CAE040E5C69A28EF", /* A          */
        "469A28EF7C28CCA3DC721D044F4496BCCA7EF4146FBF25C9", /* B          */
        "C302F41D932A36CDA7A3462F9E9E916B5BE8F1029AC4ACC1", /* order      */
        "C0A0647EAAB6A48753B033C56CB0F0900A2F5C4853375FD6", /* Gx         */
        "14B690866ABD5BB88B5F4828C1490002E6773FA2FA299B8F", /* Gy         */
        ecc_oid_brainpoolp192r1,                            /* oid/oidSz  */
        sizeof(ecc_oid_brainpoolp192r1) / sizeof(ecc_oid_t),
        ECC_BRAINPOOLP192R1_OID,                            /* oid sum    */
        1,                                                  /* cofactor   */
    },
    #endif /* HAVE_ECC_BRAINPOOL */
#endif /* ECC192 */
#ifdef ECC224
    #ifndef NO_ECC_SECP
    {
        28,                                                         /* size/bytes */
        ECC_SECP224R1,                                              /* ID         */
        "SECP224R1",                                                /* curve name */
        "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF000000000000000000000001", /* prime      */
        "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFFFFFFFFFFFFFFFFFFFE", /* A          */
        "B4050A850C04B3ABF54132565044B0B7D7BFD8BA270B39432355FFB4", /* B          */
        "FFFFFFFFFFFFFFFFFFFFFFFFFFFF16A2E0B8F03E13DD29455C5C2A3D", /* order      */
        "B70E0CBD6BB4BF7F321390B94A03C1D356C21122343280D6115C1D21", /* Gx         */
        "BD376388B5F723FB4C22DFE6CD4375A05A07476444D5819985007E34", /* Gy         */
        ecc_oid_secp224r1,                                          /* oid/oidSz  */
        sizeof(ecc_oid_secp224r1) / sizeof(ecc_oid_t),
        ECC_SECP224R1_OID,                                          /* oid sum    */
        1,                                                          /* cofactor   */
    },
    #endif /* !NO_ECC_SECP */
    #ifdef HAVE_ECC_KOBLITZ
    {
        28,                                                         /* size/bytes */
        ECC_SECP224K1,                                              /* ID         */
        "SECP224K1",                                                /* curve name */
        "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFE56D", /* prime      */
        "00000000000000000000000000000000000000000000000000000000", /* A          */
        "00000000000000000000000000000000000000000000000000000005", /* B          */
        "10000000000000000000000000001DCE8D2EC6184CAF0A971769FB1F7",/* order      */
        "A1455B334DF099DF30FC28A169A467E9E47075A90F7E650EB6B7A45C", /* Gx         */
        "7E089FED7FBA344282CAFBD6F7E319F7C0B0BD59E2CA4BDB556D61A5", /* Gy         */
        ecc_oid_secp224k1,                                          /* oid/oidSz  */
        sizeof(ecc_oid_secp224k1) / sizeof(ecc_oid_t),
        ECC_SECP224K1_OID,                                          /* oid sum    */
        1,                                                          /* cofactor   */
    },
    #endif /* HAVE_ECC_KOBLITZ */
    #ifdef HAVE_ECC_BRAINPOOL
    {
        28,                                                         /* size/bytes */
        ECC_BRAINPOOLP224R1,                                        /* ID         */
        "BRAINPOOLP224R1",                                          /* curve name */
        "D7C134AA264366862A18302575D1D787B09F075797DA89F57EC8C0FF", /* prime      */
        "68A5E62CA9CE6C1C299803A6C1530B514E182AD8B0042A59CAD29F43", /* A          */
        "2580F63CCFE44138870713B1A92369E33E2135D266DBB372386C400B", /* B          */
        "D7C134AA264366862A18302575D0FB98D116BC4B6DDEBCA3A5A7939F", /* order      */
        "0D9029AD2C7E5CF4340823B2A87DC68C9E4CE3174C1E6EFDEE12C07D", /* Gx         */
        "58AA56F772C0726F24C6B89E4ECDAC24354B9E99CAA3F6D3761402CD", /* Gy         */
        ecc_oid_brainpoolp224r1,                                    /* oid/oidSz  */
        sizeof(ecc_oid_brainpoolp224r1) / sizeof(ecc_oid_t),
        ECC_BRAINPOOLP224R1_OID,                                    /* oid sum    */
        1,                                                          /* cofactor   */
    },
    #endif /* HAVE_ECC_BRAINPOOL */
#endif /* ECC224 */
#ifdef ECC239
    #ifndef NO_ECC_SECP
    {
        30,                                                             /* size/bytes */
        ECC_PRIME239V1,                                                 /* ID         */
        "PRIME239V1",                                                   /* curve name */
        "7FFFFFFFFFFFFFFFFFFFFFFF7FFFFFFFFFFF8000000000007FFFFFFFFFFF", /* prime      */
        "7FFFFFFFFFFFFFFFFFFFFFFF7FFFFFFFFFFF8000000000007FFFFFFFFFFC", /* A          */
        "6B016C3BDCF18941D0D654921475CA71A9DB2FB27D1D37796185C2942C0A", /* B          */
        "7FFFFFFFFFFFFFFFFFFFFFFF7FFFFF9E5E9A9F5D9071FBD1522688909D0B", /* order      */
        "0FFA963CDCA8816CCC33B8642BEDF905C3D358573D3F27FBBD3B3CB9AAAF", /* Gx         */
        "7DEBE8E4E90A5DAE6E4054CA530BA04654B36818CE226B39FCCB7B02F1AE", /* Gy         */
        ecc_oid_prime239v1,                                             /* oid/oidSz  */
        sizeof(ecc_oid_prime239v1) / sizeof(ecc_oid_t),
        ECC_PRIME239V1_OID,                                             /* oid sum    */
        1,                                                              /* cofactor   */
    },
    #endif /* !NO_ECC_SECP */
    #ifdef HAVE_ECC_SECPR2
    {
        30,                                                             /* size/bytes */
        ECC_PRIME239V2,                                                 /* ID         */
        "PRIME239V2",                                                   /* curve name */
        "7FFFFFFFFFFFFFFFFFFFFFFF7FFFFFFFFFFF8000000000007FFFFFFFFFFF", /* prime      */
        "7FFFFFFFFFFFFFFFFFFFFFFF7FFFFFFFFFFF8000000000007FFFFFFFFFFC", /* A          */
        "617FAB6832576CBBFED50D99F0249C3FEE58B94BA0038C7AE84C8C832F2C", /* B          */
        "7FFFFFFFFFFFFFFFFFFFFFFF800000CFA7E8594377D414C03821BC582063", /* order      */
        "38AF09D98727705120C921BB5E9E26296A3CDCF2F35757A0EAFD87B830E7", /* Gx         */
        "5B0125E4DBEA0EC7206DA0FC01D9B081329FB555DE6EF460237DFF8BE4BA", /* Gy         */
        ecc_oid_prime239v2,                                             /* oid/oidSz  */
        sizeof(ecc_oid_prime239v2) / sizeof(ecc_oid_t),
        ECC_PRIME239V2_OID,                                             /* oid sum    */
        1,                                                              /* cofactor   */
    },
    #endif /* HAVE_ECC_SECPR2 */
    #ifdef HAVE_ECC_SECPR3
    {
        30,                                                             /* size/bytes */
        ECC_PRIME239V3,                                                 /* ID         */
        "PRIME239V3",                                                   /* curve name */
        "7FFFFFFFFFFFFFFFFFFFFFFF7FFFFFFFFFFF8000000000007FFFFFFFFFFF", /* prime      */
        "7FFFFFFFFFFFFFFFFFFFFFFF7FFFFFFFFFFF8000000000007FFFFFFFFFFC", /* A          */
        "255705FA2A306654B1F4CB03D6A750A30C250102D4988717D9BA15AB6D3E", /* B          */
        "7FFFFFFFFFFFFFFFFFFFFFFF7FFFFF975DEB41B3A6057C3C432146526551", /* order      */
        "6768AE8E18BB92CFCF005C949AA2C6D94853D0E660BBF854B1C9505FE95A", /* Gx         */
        "1607E6898F390C06BC1D552BAD226F3B6FCFE48B6E818499AF18E3ED6CF3", /* Gy         */
        ecc_oid_prime239v3,                                             /* oid/oidSz  */
        sizeof(ecc_oid_prime239v3) / sizeof(ecc_oid_t),
        ECC_PRIME239V3_OID,                                             /* oid sum    */
        1,                                                              /* cofactor   */
    },
    #endif /* HAVE_ECC_SECPR3 */
#endif /* ECC239 */
#ifdef ECC256
    #ifndef NO_ECC_SECP
    {
        32,                                                                 /* size/bytes */
        ECC_SECP256R1,                                                      /* ID         */
        "SECP256R1",                                                        /* curve name */
        "FFFFFFFF00000001000000000000000000000000FFFFFFFFFFFFFFFFFFFFFFFF", /* prime      */
        "FFFFFFFF00000001000000000000000000000000FFFFFFFFFFFFFFFFFFFFFFFC", /* A          */
        "5AC635D8AA3A93E7B3EBBD55769886BC651D06B0CC53B0F63BCE3C3E27D2604B", /* B          */
        "FFFFFFFF00000000FFFFFFFFFFFFFFFFBCE6FAADA7179E84F3B9CAC2FC632551", /* order      */
        "6B17D1F2E12C4247F8BCE6E563A440F277037D812DEB33A0F4A13945D898C296", /* Gx         */
        "4FE342E2FE1A7F9B8EE7EB4A7C0F9E162BCE33576B315ECECBB6406837BF51F5", /* Gy         */
        ecc_oid_secp256r1,                                                  /* oid/oidSz  */
        sizeof(ecc_oid_secp256r1) / sizeof(ecc_oid_t),
        ECC_SECP256R1_OID,                                                  /* oid sum    */
        1,                                                                  /* cofactor   */
    },
    #endif /* !NO_ECC_SECP */
    #ifdef HAVE_ECC_KOBLITZ
    {
        32,                                                                 /* size/bytes */
        ECC_SECP256K1,                                                      /* ID         */
        "SECP256K1",                                                        /* curve name */
        "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFC2F", /* prime      */
        "0000000000000000000000000000000000000000000000000000000000000000", /* A          */
        "0000000000000000000000000000000000000000000000000000000000000007", /* B          */
        "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEBAAEDCE6AF48A03BBFD25E8CD0364141", /* order      */
        "79BE667EF9DCBBAC55A06295CE870B07029BFCDB2DCE28D959F2815B16F81798", /* Gx         */
        "483ADA7726A3C4655DA4FBFC0E1108A8FD17B448A68554199C47D08FFB10D4B8", /* Gy         */
        ecc_oid_secp256k1,                                                  /* oid/oidSz  */
        sizeof(ecc_oid_secp256k1) / sizeof(ecc_oid_t),
        ECC_SECP256K1_OID,                                                  /* oid sum    */
        1,                                                                  /* cofactor   */
    },
    #endif /* HAVE_ECC_KOBLITZ */
    #ifdef HAVE_ECC_BRAINPOOL
    {
        32,                                                                 /* size/bytes */
        ECC_BRAINPOOLP256R1,                                                /* ID         */
        "BRAINPOOLP256R1",                                                  /* curve name */
        "A9FB57DBA1EEA9BC3E660A909D838D726E3BF623D52620282013481D1F6E5377", /* prime      */
        "7D5A0975FC2C3057EEF67530417AFFE7FB8055C126DC5C6CE94A4B44F330B5D9", /* A          */
        "26DC5C6CE94A4B44F330B5D9BBD77CBF958416295CF7E1CE6BCCDC18FF8C07B6", /* B          */
        "A9FB57DBA1EEA9BC3E660A909D838D718C397AA3B561A6F7901E0E82974856A7", /* order      */
        "8BD2AEB9CB7E57CB2C4B482FFC81B7AFB9DE27E1E3BD23C23A4453BD9ACE3262", /* Gx         */
        "547EF835C3DAC4FD97F8461A14611DC9C27745132DED8E545C1D54C72F046997", /* Gy         */
        ecc_oid_brainpoolp256r1,                                            /* oid/oidSz  */
        sizeof(ecc_oid_brainpoolp256r1) / sizeof(ecc_oid_t),
        ECC_BRAINPOOLP256R1_OID,                                            /* oid sum    */
        1,                                                                  /* cofactor   */
    },
    #endif /* HAVE_ECC_BRAINPOOL */
#endif /* ECC256 */
#ifdef ECC320
    #ifdef HAVE_ECC_BRAINPOOL
    {
        40,                                                                                 /* size/bytes */
        ECC_BRAINPOOLP320R1,                                                                /* ID         */
        "BRAINPOOLP320R1",                                                                  /* curve name */
        "D35E472036BC4FB7E13C785ED201E065F98FCFA6F6F40DEF4F92B9EC7893EC28FCD412B1F1B32E27", /* prime      */
        "3EE30B568FBAB0F883CCEBD46D3F3BB8A2A73513F5EB79DA66190EB085FFA9F492F375A97D860EB4", /* A          */
        "520883949DFDBC42D3AD198640688A6FE13F41349554B49ACC31DCCD884539816F5EB4AC8FB1F1A6", /* B          */
        "D35E472036BC4FB7E13C785ED201E065F98FCFA5B68F12A32D482EC7EE8658E98691555B44C59311", /* order      */
        "43BD7E9AFB53D8B85289BCC48EE5BFE6F20137D10A087EB6E7871E2A10A599C710AF8D0D39E20611", /* Gx         */
        "14FDD05545EC1CC8AB4093247F77275E0743FFED117182EAA9C77877AAAC6AC7D35245D1692E8EE1", /* Gy         */
        ecc_oid_brainpoolp320r1, sizeof(ecc_oid_brainpoolp320r1) / sizeof(ecc_oid_t),       /* oid/oidSz  */
        ECC_BRAINPOOLP320R1_OID,                                                            /* oid sum    */
        1,                                                                                  /* cofactor   */
    },
    #endif /* HAVE_ECC_BRAINPOOL */
#endif /* ECC320 */
#ifdef ECC384
    #ifndef NO_ECC_SECP
    {
        48,                                                                                                 /* size/bytes */
        ECC_SECP384R1,                                                                                      /* ID         */
        "SECP384R1",                                                                                        /* curve name */
        "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFFFF0000000000000000FFFFFFFF", /* prime      */
        "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFFFF0000000000000000FFFFFFFC", /* A          */
        "B3312FA7E23EE7E4988E056BE3F82D19181D9C6EFE8141120314088F5013875AC656398D8A2ED19D2A85C8EDD3EC2AEF", /* B          */
        "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFC7634D81F4372DDF581A0DB248B0A77AECEC196ACCC52973", /* order      */
        "AA87CA22BE8B05378EB1C71EF320AD746E1D3B628BA79B9859F741E082542A385502F25DBF55296C3A545E3872760AB7", /* Gx         */
        "3617DE4A96262C6F5D9E98BF9292DC29F8F41DBD289A147CE9DA3113B5F0B8C00A60B1CE1D7E819D7A431D7C90EA0E5F", /* Gy         */
        ecc_oid_secp384r1, sizeof(ecc_oid_secp384r1) / sizeof(ecc_oid_t),                                   /* oid/oidSz  */
        ECC_SECP384R1_OID,                                                                                  /* oid sum    */
        1,                                                                                                  /* cofactor   */
    },
    #endif /* !NO_ECC_SECP */
    #ifdef HAVE_ECC_BRAINPOOL
    {
        48,                                                                                                 /* size/bytes */
        ECC_BRAINPOOLP384R1,                                                                                /* ID         */
        "BRAINPOOLP384R1",                                                                                  /* curve name */
        "8CB91E82A3386D280F5D6F7E50E641DF152F7109ED5456B412B1DA197FB71123ACD3A729901D1A71874700133107EC53", /* prime      */
        "7BC382C63D8C150C3C72080ACE05AFA0C2BEA28E4FB22787139165EFBA91F90F8AA5814A503AD4EB04A8C7DD22CE2826", /* A          */
        "04A8C7DD22CE28268B39B55416F0447C2FB77DE107DCD2A62E880EA53EEB62D57CB4390295DBC9943AB78696FA504C11", /* B          */
        "8CB91E82A3386D280F5D6F7E50E641DF152F7109ED5456B31F166E6CAC0425A7CF3AB6AF6B7FC3103B883202E9046565", /* order      */
        "1D1C64F068CF45FFA2A63A81B7C13F6B8847A3E77EF14FE3DB7FCAFE0CBD10E8E826E03436D646AAEF87B2E247D4AF1E", /* Gx         */
        "8ABE1D7520F9C2A45CB1EB8E95CFD55262B70B29FEEC5864E19C054FF99129280E4646217791811142820341263C5315", /* Gy         */
        ecc_oid_brainpoolp384r1, sizeof(ecc_oid_brainpoolp384r1) / sizeof(ecc_oid_t),                       /* oid/oidSz  */
        ECC_BRAINPOOLP384R1_OID,                                                                            /* oid sum    */
        1,                                                                                                  /* cofactor   */
    },
    #endif /* HAVE_ECC_BRAINPOOL */
#endif /* ECC384 */
#ifdef ECC512
    #ifdef HAVE_ECC_BRAINPOOL
    {
        64,                                                                                                                                 /* size/bytes */
        ECC_BRAINPOOLP512R1,                                                                                                                /* ID         */
        "BRAINPOOLP512R1",                                                                                                                  /* curve name */
        "AADD9DB8DBE9C48B3FD4E6AE33C9FC07CB308DB3B3C9D20ED6639CCA703308717D4D9B009BC66842AECDA12AE6A380E62881FF2F2D82C68528AA6056583A48F3", /* prime      */
        "7830A3318B603B89E2327145AC234CC594CBDD8D3DF91610A83441CAEA9863BC2DED5D5AA8253AA10A2EF1C98B9AC8B57F1117A72BF2C7B9E7C1AC4D77FC94CA", /* A          */
        "3DF91610A83441CAEA9863BC2DED5D5AA8253AA10A2EF1C98B9AC8B57F1117A72BF2C7B9E7C1AC4D77FC94CADC083E67984050B75EBAE5DD2809BD638016F723", /* B          */
        "AADD9DB8DBE9C48B3FD4E6AE33C9FC07CB308DB3B3C9D20ED6639CCA70330870553E5C414CA92619418661197FAC10471DB1D381085DDADDB58796829CA90069", /* order      */
        "81AEE4BDD82ED9645A21322E9C4C6A9385ED9F70B5D916C1B43B62EEF4D0098EFF3B1F78E2D0D48D50D1687B93B97D5F7C6D5047406A5E688B352209BCB9F822", /* Gx         */
        "7DDE385D566332ECC0EABFA9CF7822FDF209F70024A57B1AA000C55B881F8111B2DCDE494A5F485E5BCA4BD88A2763AED1CA2B2FA8F0540678CD1E0F3AD80892", /* Gy         */
        ecc_oid_brainpoolp512r1, sizeof(ecc_oid_brainpoolp512r1) / sizeof(ecc_oid_t),                                                       /* oid/oidSz  */
        ECC_BRAINPOOLP512R1_OID,                                                                                                            /* oid sum    */
        1,                                                                                                                                  /* cofactor   */
    },
    #endif /* HAVE_ECC_BRAINPOOL */
#endif /* ECC512 */
#ifdef ECC521
    #ifndef NO_ECC_SECP
    {
        66,                                                                                                                                    /* size/bytes */
        ECC_SECP521R1,                                                                                                                         /* ID         */
        "SECP521R1",                                                                                                                           /* curve name */
        "1FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF", /* prime      */
        "1FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFC", /* A          */
        "51953EB9618E1C9A1F929A21A0B68540EEA2DA725B99B315F3B8B489918EF109E156193951EC7E937B1652C0BD3BB1BF073573DF883D2C34F1EF451FD46B503F00",  /* B          */
        "1FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFA51868783BF2F966B7FCC0148F709A5D03BB5C9B8899C47AEBB6FB71E91386409", /* order      */
        "C6858E06B70404E9CD9E3ECB662395B4429C648139053FB521F828AF606B4D3DBAA14B5E77EFE75928FE1DC127A2FFA8DE3348B3C1856A429BF97E7E31C2E5BD66",  /* Gx         */
        "11839296A789A3BC0045C8A5FB42C7D1BD998F54449579B446817AFBD17273E662C97EE72995EF42640C550B9013FAD0761353C7086A272C24088BE94769FD16650", /* Gy         */
        ecc_oid_secp521r1, sizeof(ecc_oid_secp521r1) / sizeof(ecc_oid_t),                                                                      /* oid/oidSz  */
        ECC_SECP521R1_OID,                                                                                                                     /* oid sum    */
        1,                                                                                                                                     /* cofactor   */
    },
    #endif /* !NO_ECC_SECP */
#endif /* ECC521 */
{
   0, -1,
   NULL, NULL, NULL, NULL, NULL, NULL, NULL,
   NULL, 0, 0, 0
}
};
#define ECC_SET_COUNT   (sizeof(ecc_sets)/sizeof(ecc_set_type))

#ifdef HAVE_OID_ENCODING
    /* encoded OID cache */
    typedef struct {
        word32 oidSz;
        byte oid[ECC_MAX_OID_LEN];
    } oid_cache_t;
    static oid_cache_t ecc_oid_cache[ECC_SET_COUNT];
#endif


#ifdef HAVE_COMP_KEY
static int wc_ecc_export_x963_compressed(ecc_key*, byte* out, word32* outLen);
#endif

#ifndef WOLFSSL_ATECC508A

static int ecc_check_pubkey_order(ecc_key* key, mp_int* a, mp_int* prime, mp_int* order);
#ifdef ECC_SHAMIR
static int ecc_mul2add(ecc_point* A, mp_int* kA, ecc_point* B, mp_int* kB,
                       ecc_point* C, mp_int* a, mp_int* modulus, void* heap);
#endif

int mp_jacobi(mp_int* a, mp_int* n, int* c);
int mp_sqrtmod_prime(mp_int* n, mp_int* prime, mp_int* ret);


/* Curve Specs */
typedef struct ecc_curve_spec {
    const ecc_set_type* dp;

    mp_int* prime;
    mp_int* Af;
    #ifdef USE_ECC_B_PARAM
        mp_int* Bf;
    #endif
    mp_int* order;
    mp_int* Gx;
    mp_int* Gy;

#ifdef ECC_CACHE_CURVE
    mp_int prime_lcl;
    mp_int Af_lcl;
    #ifdef USE_ECC_B_PARAM
        mp_int Bf_lcl;
    #endif
    mp_int order_lcl;
    mp_int Gx_lcl;
    mp_int Gy_lcl;
#else
    mp_int* spec_ints;
    word32 spec_count;
    word32 spec_use;
#endif

    byte load_mask;
} ecc_curve_spec;

enum ecc_curve_load_mask {
    ECC_CURVE_FIELD_NONE    = 0x00,
    ECC_CURVE_FIELD_PRIME   = 0x01,
    ECC_CURVE_FIELD_AF      = 0x02,
#ifdef USE_ECC_B_PARAM
    ECC_CURVE_FIELD_BF      = 0x04,
#endif
    ECC_CURVE_FIELD_ORDER   = 0x08,
    ECC_CURVE_FIELD_GX      = 0x10,
    ECC_CURVE_FIELD_GY      = 0x20,
#ifdef USE_ECC_B_PARAM
    ECC_CURVE_FIELD_ALL     = 0x3F,
    ECC_CURVE_FIELD_COUNT   = 6,
#else
    ECC_CURVE_FIELD_ALL     = 0x3B,
    ECC_CURVE_FIELD_COUNT   = 5,
#endif
};

#ifdef ECC_CACHE_CURVE
    /* cache (mp_int) of the curve parameters */
    static ecc_curve_spec* ecc_curve_spec_cache[ECC_SET_COUNT];
    #ifndef SINGLE_THREADED
        static wolfSSL_Mutex ecc_curve_cache_mutex;
    #endif

    #define DECLARE_CURVE_SPECS(intcount) ecc_curve_spec* curve = NULL;
#else
    #define DECLARE_CURVE_SPECS(intcount) \
        mp_int spec_ints[(intcount)]; \
        ecc_curve_spec curve_lcl; \
        ecc_curve_spec* curve = &curve_lcl; \
        XMEMSET(curve, 0, sizeof(ecc_curve_spec)); \
        curve->spec_ints = spec_ints; \
        curve->spec_count = intcount;
#endif /* ECC_CACHE_CURVE */

static void _wc_ecc_curve_free(ecc_curve_spec* curve)
{
    if (curve == NULL) {
        return;
    }

    if (curve->load_mask & ECC_CURVE_FIELD_PRIME)
        mp_clear(curve->prime);
    if (curve->load_mask & ECC_CURVE_FIELD_AF)
        mp_clear(curve->Af);
#ifdef USE_ECC_B_PARAM
    if (curve->load_mask & ECC_CURVE_FIELD_BF)
        mp_clear(curve->Bf);
#endif
    if (curve->load_mask & ECC_CURVE_FIELD_ORDER)
        mp_clear(curve->order);
    if (curve->load_mask & ECC_CURVE_FIELD_GX)
        mp_clear(curve->Gx);
    if (curve->load_mask & ECC_CURVE_FIELD_GY)
        mp_clear(curve->Gy);

    curve->load_mask = 0;
}

static void wc_ecc_curve_free(ecc_curve_spec* curve)
{
    /* don't free cached curves */
#ifndef ECC_CACHE_CURVE
    _wc_ecc_curve_free(curve);
#endif
    (void)curve;
}

static int wc_ecc_curve_load_item(const char* src, mp_int** dst,
    ecc_curve_spec* curve, byte mask)
{
    int err;

#ifndef ECC_CACHE_CURVE
    /* get mp_int from temp */
    if (curve->spec_use >= curve->spec_count) {
        WOLFSSL_MSG("Invalid DECLARE_CURVE_SPECS count");
        return ECC_BAD_ARG_E;
    }
    *dst = &curve->spec_ints[curve->spec_use++];
#endif

    err = mp_init(*dst);
    if (err == MP_OKAY) {
        curve->load_mask |= mask;

        err = mp_read_radix(*dst, src, 16);

    #ifdef HAVE_WOLF_BIGINT
        if (err == MP_OKAY)
            err = wc_mp_to_bigint(*dst, &(*dst)->raw);
    #endif
    }
    return err;
}

static int wc_ecc_curve_load(const ecc_set_type* dp, ecc_curve_spec** pCurve,
    byte load_mask)
{
    int ret = 0, x;
    ecc_curve_spec* curve;
    byte load_items = 0; /* mask of items to load */

    if (dp == NULL || pCurve == NULL)
        return BAD_FUNC_ARG;

#ifdef ECC_CACHE_CURVE
    x = wc_ecc_get_curve_idx(dp->id);
    if (x == ECC_CURVE_INVALID)
        return ECC_BAD_ARG_E;

    /* make sure cache has been allocated */
    if (ecc_curve_spec_cache[x] == NULL) {
        ecc_curve_spec_cache[x] = (ecc_curve_spec*)XMALLOC(
            sizeof(ecc_curve_spec), NULL, DYNAMIC_TYPE_ECC);
        if (ecc_curve_spec_cache[x] == NULL)
            return MEMORY_E;
        XMEMSET(ecc_curve_spec_cache[x], 0, sizeof(ecc_curve_spec));
    }

    /* set curve pointer to cache */
    *pCurve = ecc_curve_spec_cache[x];

#endif /* ECC_CACHE_CURVE */
    curve = *pCurve;

    /* make sure the curve is initialized */
    if (curve->dp != dp) {
        curve->load_mask = 0;

    #ifdef ECC_CACHE_CURVE
        curve->prime = &curve->prime_lcl;
        curve->Af = &curve->Af_lcl;
        #ifdef USE_ECC_B_PARAM
            curve->Bf = &curve->Bf_lcl;
        #endif
        curve->order = &curve->order_lcl;
        curve->Gx = &curve->Gx_lcl;
        curve->Gy = &curve->Gy_lcl;
    #endif
    }
    curve->dp = dp; /* set dp info */

#if defined(ECC_CACHE_CURVE) && !defined(SINGLE_THREADED)
    ret = wc_LockMutex(&ecc_curve_cache_mutex);
    if (ret != 0) {
        return MEMORY_E;
    }
#endif

    /* determine items to load */
    load_items = (~curve->load_mask & load_mask);
    curve->load_mask |= load_items;

    /* load items */
    x = 0;
    if (load_items & ECC_CURVE_FIELD_PRIME)
        x += wc_ecc_curve_load_item(dp->prime, &curve->prime, curve,
            ECC_CURVE_FIELD_PRIME);
    if (load_items & ECC_CURVE_FIELD_AF)
        x += wc_ecc_curve_load_item(dp->Af, &curve->Af, curve,
            ECC_CURVE_FIELD_AF);
#ifdef USE_ECC_B_PARAM
    if (load_items & ECC_CURVE_FIELD_BF)
        x += wc_ecc_curve_load_item(dp->Bf, &curve->Bf, curve,
            ECC_CURVE_FIELD_BF);
#endif
    if (load_items & ECC_CURVE_FIELD_ORDER)
        x += wc_ecc_curve_load_item(dp->order, &curve->order, curve,
            ECC_CURVE_FIELD_ORDER);
    if (load_items & ECC_CURVE_FIELD_GX)
        x += wc_ecc_curve_load_item(dp->Gx, &curve->Gx, curve,
            ECC_CURVE_FIELD_GX);
    if (load_items & ECC_CURVE_FIELD_GY)
        x += wc_ecc_curve_load_item(dp->Gy, &curve->Gy, curve,
            ECC_CURVE_FIELD_GY);

    /* check for error */
    if (x != 0) {
        wc_ecc_curve_free(curve);
        ret = MP_READ_E;
    }

#if defined(ECC_CACHE_CURVE) && !defined(SINGLE_THREADED)
    wc_UnLockMutex(&ecc_curve_cache_mutex);
#endif

    return ret;
}

#ifdef ECC_CACHE_CURVE
int wc_ecc_curve_cache_init(void)
{
    int ret = 0;
#if defined(ECC_CACHE_CURVE) && !defined(SINGLE_THREADED)
    ret = wc_InitMutex(&ecc_curve_cache_mutex);
#endif
    return ret;
}

void wc_ecc_curve_cache_free(void)
{
    int x;

    /* free all ECC curve caches */
    for (x = 0; x < (int)ECC_SET_COUNT; x++) {
        if (ecc_curve_spec_cache[x]) {
            _wc_ecc_curve_free(ecc_curve_spec_cache[x]);
            XFREE(ecc_curve_spec_cache[x], NULL, DYNAMIC_TYPE_ECC);
            ecc_curve_spec_cache[x] = NULL;
        }
    }

#if defined(ECC_CACHE_CURVE) && !defined(SINGLE_THREADED)
    wc_FreeMutex(&ecc_curve_cache_mutex);
#endif
}
#endif /* ECC_CACHE_CURVE */

#endif /* WOLFSSL_ATECC508A */


/* Retrieve the curve name for the ECC curve id.
 *
 * curve_id  The id of the curve.
 * returns the name stored from the curve if available, otherwise NULL.
 */
const char* wc_ecc_get_name(int curve_id)
{
    int curve_idx = wc_ecc_get_curve_idx(curve_id);
    if (curve_idx == ECC_CURVE_INVALID)
        return NULL;
    return ecc_sets[curve_idx].name;
}

int wc_ecc_set_curve(ecc_key* key, int keysize, int curve_id)
{
    if (keysize <= 0 && curve_id <= 0) {
        return BAD_FUNC_ARG;
    }

    if (keysize > ECC_MAXSIZE) {
        return ECC_BAD_ARG_E;
    }

    /* handle custom case */
    if (key->idx != ECC_CUSTOM_IDX) {
        int x;

        /* find ecc_set based on curve_id or key size */
        for (x = 0; ecc_sets[x].size != 0; x++) {
            if (curve_id > ECC_CURVE_DEF) {
                if (curve_id == ecc_sets[x].id)
                  break;
            }
            else if (keysize <= ecc_sets[x].size) {
                break;
            }
        }
        if (ecc_sets[x].size == 0) {
            WOLFSSL_MSG("ECC Curve not found");
            return ECC_CURVE_OID_E;
        }

        key->idx = x;
        key->dp  = &ecc_sets[x];
    }

    return 0;
}

#ifndef WOLFSSL_ATECC508A

/**
   Add two ECC points
   P        The point to add
   Q        The point to add
   R        [out] The destination of the double
   a        ECC curve parameter a
   modulus  The modulus of the field the ECC curve is in
   mp       The "b" value from montgomery_setup()
   return   MP_OKAY on success
*/
int ecc_projective_add_point(ecc_point* P, ecc_point* Q, ecc_point* R,
                             mp_int* a, mp_int* modulus, mp_digit mp)
{
   mp_int t1, t2;
#ifdef ALT_ECC_SIZE
   mp_int rx, ry, rz;
#endif
   mp_int *x, *y, *z;
   int    err;

   if (P == NULL || Q == NULL || R == NULL || modulus == NULL) {
       return ECC_BAD_ARG_E;
   }

   /* if Q == R then swap P and Q, so we don't require a local x,y,z */
   if (Q == R) {
      ecc_point* tPt  = P;
      P = Q;
      Q = tPt;
   }

   if ((err = mp_init_multi(&t1, &t2, NULL, NULL, NULL, NULL)) != MP_OKAY) {
      return err;
   }

   /* should we dbl instead? */
   if (err == MP_OKAY)
       err = mp_sub(modulus, Q->y, &t1);
   if (err == MP_OKAY) {
       if ( (mp_cmp(P->x, Q->x) == MP_EQ) &&
            (get_digit_count(Q->z) && mp_cmp(P->z, Q->z) == MP_EQ) &&
            (mp_cmp(P->y, Q->y) == MP_EQ || mp_cmp(P->y, &t1) == MP_EQ)) {
           mp_clear(&t1);
           mp_clear(&t2);
          return ecc_projective_dbl_point(P, R, a, modulus, mp);
       }
   }

   if (err != MP_OKAY) {
      goto done;
   }

/* If use ALT_ECC_SIZE we need to use local stack variable since
   ecc_point x,y,z is reduced size */
#ifdef ALT_ECC_SIZE
   /* Use local stack variable */
   x = &rx;
   y = &ry;
   z = &rz;

   if ((err = mp_init_multi(x, y, z, NULL, NULL, NULL)) != MP_OKAY) {
      goto done;
   }
#else
   /* Use destination directly */
   x = R->x;
   y = R->y;
   z = R->z;
#endif

   if (err == MP_OKAY)
       err = mp_copy(P->x, x);
   if (err == MP_OKAY)
       err = mp_copy(P->y, y);
   if (err == MP_OKAY)
       err = mp_copy(P->z, z);

   /* if Z is one then these are no-operations */
   if (err == MP_OKAY) {
       if (!mp_iszero(Q->z)) {
           /* T1 = Z' * Z' */
           err = mp_sqr(Q->z, &t1);
           if (err == MP_OKAY)
               err = mp_montgomery_reduce(&t1, modulus, mp);

           /* X = X * T1 */
           if (err == MP_OKAY)
               err = mp_mul(&t1, x, x);
           if (err == MP_OKAY)
               err = mp_montgomery_reduce(x, modulus, mp);

           /* T1 = Z' * T1 */
           if (err == MP_OKAY)
               err = mp_mul(Q->z, &t1, &t1);
           if (err == MP_OKAY)
               err = mp_montgomery_reduce(&t1, modulus, mp);

           /* Y = Y * T1 */
           if (err == MP_OKAY)
               err = mp_mul(&t1, y, y);
           if (err == MP_OKAY)
               err = mp_montgomery_reduce(y, modulus, mp);
       }
   }

   /* T1 = Z*Z */
   if (err == MP_OKAY)
       err = mp_sqr(z, &t1);
   if (err == MP_OKAY)
       err = mp_montgomery_reduce(&t1, modulus, mp);

   /* T2 = X' * T1 */
   if (err == MP_OKAY)
       err = mp_mul(Q->x, &t1, &t2);
   if (err == MP_OKAY)
       err = mp_montgomery_reduce(&t2, modulus, mp);

   /* T1 = Z * T1 */
   if (err == MP_OKAY)
       err = mp_mul(z, &t1, &t1);
   if (err == MP_OKAY)
       err = mp_montgomery_reduce(&t1, modulus, mp);

   /* T1 = Y' * T1 */
   if (err == MP_OKAY)
       err = mp_mul(Q->y, &t1, &t1);
   if (err == MP_OKAY)
       err = mp_montgomery_reduce(&t1, modulus, mp);

   /* Y = Y - T1 */
   if (err == MP_OKAY)
       err = mp_sub(y, &t1, y);
   if (err == MP_OKAY) {
       if (mp_isneg(y))
           err = mp_add(y, modulus, y);
   }
   /* T1 = 2T1 */
   if (err == MP_OKAY)
       err = mp_add(&t1, &t1, &t1);
   if (err == MP_OKAY) {
       if (mp_cmp(&t1, modulus) != MP_LT)
           err = mp_sub(&t1, modulus, &t1);
   }
   /* T1 = Y + T1 */
   if (err == MP_OKAY)
       err = mp_add(&t1, y, &t1);
   if (err == MP_OKAY) {
       if (mp_cmp(&t1, modulus) != MP_LT)
           err = mp_sub(&t1, modulus, &t1);
   }
   /* X = X - T2 */
   if (err == MP_OKAY)
       err = mp_sub(x, &t2, x);
   if (err == MP_OKAY) {
       if (mp_isneg(x))
           err = mp_add(x, modulus, x);
   }
   /* T2 = 2T2 */
   if (err == MP_OKAY)
       err = mp_add(&t2, &t2, &t2);
   if (err == MP_OKAY) {
       if (mp_cmp(&t2, modulus) != MP_LT)
           err = mp_sub(&t2, modulus, &t2);
   }
   /* T2 = X + T2 */
   if (err == MP_OKAY)
       err = mp_add(&t2, x, &t2);
   if (err == MP_OKAY) {
       if (mp_cmp(&t2, modulus) != MP_LT)
           err = mp_sub(&t2, modulus, &t2);
   }

   if (err == MP_OKAY) {
       if (!mp_iszero(Q->z)) {
           /* Z = Z * Z' */
           err = mp_mul(z, Q->z, z);
           if (err == MP_OKAY)
               err = mp_montgomery_reduce(z, modulus, mp);
       }
   }

   /* Z = Z * X */
   if (err == MP_OKAY)
       err = mp_mul(z, x, z);
   if (err == MP_OKAY)
       err = mp_montgomery_reduce(z, modulus, mp);

   /* T1 = T1 * X  */
   if (err == MP_OKAY)
       err = mp_mul(&t1, x, &t1);
   if (err == MP_OKAY)
       err = mp_montgomery_reduce(&t1, modulus, mp);

   /* X = X * X */
   if (err == MP_OKAY)
       err = mp_sqr(x, x);
   if (err == MP_OKAY)
       err = mp_montgomery_reduce(x, modulus, mp);

   /* T2 = T2 * x */
   if (err == MP_OKAY)
       err = mp_mul(&t2, x, &t2);
   if (err == MP_OKAY)
       err = mp_montgomery_reduce(&t2, modulus, mp);

   /* T1 = T1 * X  */
   if (err == MP_OKAY)
       err = mp_mul(&t1, x, &t1);
   if (err == MP_OKAY)
       err = mp_montgomery_reduce(&t1, modulus, mp);

   /* X = Y*Y */
   if (err == MP_OKAY)
       err = mp_sqr(y, x);
   if (err == MP_OKAY)
       err = mp_montgomery_reduce(x, modulus, mp);

   /* X = X - T2 */
   if (err == MP_OKAY)
       err = mp_sub(x, &t2, x);
   if (err == MP_OKAY) {
       if (mp_isneg(x))
           err = mp_add(x, modulus, x);
   }
   /* T2 = T2 - X */
   if (err == MP_OKAY)
       err = mp_sub(&t2, x, &t2);
   if (err == MP_OKAY) {
       if (mp_isneg(&t2))
           err = mp_add(&t2, modulus, &t2);
   }
   /* T2 = T2 - X */
   if (err == MP_OKAY)
       err = mp_sub(&t2, x, &t2);
   if (err == MP_OKAY) {
       if (mp_isneg(&t2))
           err = mp_add(&t2, modulus, &t2);
   }
   /* T2 = T2 * Y */
   if (err == MP_OKAY)
       err = mp_mul(&t2, y, &t2);
   if (err == MP_OKAY)
       err = mp_montgomery_reduce(&t2, modulus, mp);

   /* Y = T2 - T1 */
   if (err == MP_OKAY)
       err = mp_sub(&t2, &t1, y);
   if (err == MP_OKAY) {
       if (mp_isneg(y))
           err = mp_add(y, modulus, y);
   }
   /* Y = Y/2 */
   if (err == MP_OKAY) {
       if (mp_isodd(y) == MP_YES)
           err = mp_add(y, modulus, y);
   }
   if (err == MP_OKAY)
       err = mp_div_2(y, y);

#ifdef ALT_ECC_SIZE
   if (err == MP_OKAY)
       err = mp_copy(x, R->x);
   if (err == MP_OKAY)
       err = mp_copy(y, R->y);
   if (err == MP_OKAY)
       err = mp_copy(z, R->z);
#endif

done:

   /* clean up */
   mp_clear(&t1);
   mp_clear(&t2);

   return err;
}

/* ### Point doubling in Jacobian coordinate system ###
 *
 * let us have a curve:                 y^2 = x^3 + a*x + b
 * in Jacobian coordinates it becomes:  y^2 = x^3 + a*x*z^4 + b*z^6
 *
 * The doubling of P = (Xp, Yp, Zp) is given by R = (Xr, Yr, Zr) where:
 * Xr = M^2 - 2*S
 * Yr = M * (S - Xr) - 8*T
 * Zr = 2 * Yp * Zp
 *
 * M = 3 * Xp^2 + a*Zp^4
 * T = Yp^4
 * S = 4 * Xp * Yp^2
 *
 * SPECIAL CASE: when a == 3 we can compute M as
 * M = 3 * (Xp^2 - Zp^4) = 3 * (Xp + Zp^2) * (Xp - Zp^2)
 */

/**
   Double an ECC point
   P   The point to double
   R   [out] The destination of the double
   a   ECC curve parameter a
   modulus  The modulus of the field the ECC curve is in
   mp       The "b" value from montgomery_setup()
   return   MP_OKAY on success
*/
int ecc_projective_dbl_point(ecc_point *P, ecc_point *R, mp_int* a,
                                       mp_int* modulus, mp_digit mp)
{
   mp_int t1, t2;
#ifdef ALT_ECC_SIZE
   mp_int rx, ry, rz;
#endif
   mp_int *x, *y, *z;
   int    err;

   if (P == NULL || R == NULL || modulus == NULL)
       return ECC_BAD_ARG_E;

   if ((err = mp_init_multi(&t1, &t2, NULL, NULL, NULL, NULL)) != MP_OKAY) {
      return err;
   }

/* If use ALT_ECC_SIZE we need to use local stack variable since
   ecc_point x,y,z is reduced size */
#ifdef ALT_ECC_SIZE
   /* Use local stack variable */
   x = &rx;
   y = &ry;
   z = &rz;

   if ((err = mp_init_multi(x, y, z, NULL, NULL, NULL)) != MP_OKAY) {
       mp_clear(&t1);
       mp_clear(&t2);
       return err;
   }
#else
   /* Use destination directly */
   x = R->x;
   y = R->y;
   z = R->z;
#endif

   if (err == MP_OKAY)
       err = mp_copy(P->x, x);
   if (err == MP_OKAY)
       err = mp_copy(P->y, y);
   if (err == MP_OKAY)
       err = mp_copy(P->z, z);

   /* T1 = Z * Z */
   if (err == MP_OKAY)
       err = mp_sqr(z, &t1);
   if (err == MP_OKAY)
       err = mp_montgomery_reduce(&t1, modulus, mp);

   /* Z = Y * Z */
   if (err == MP_OKAY)
       err = mp_mul(z, y, z);
   if (err == MP_OKAY)
       err = mp_montgomery_reduce(z, modulus, mp);

   /* Z = 2Z */
   if (err == MP_OKAY)
       err = mp_add(z, z, z);
   if (err == MP_OKAY) {
       if (mp_cmp(z, modulus) != MP_LT)
           err = mp_sub(z, modulus, z);
   }

   /* Determine if curve "a" should be used in calc */
#ifdef WOLFSSL_CUSTOM_CURVES
   if (err == MP_OKAY) {
      /* Use a and prime to determine if a == 3 */
      err = mp_submod(modulus, a, modulus, &t2);
   }
   if (err == MP_OKAY && mp_cmp_d(&t2, 3) != MP_EQ) {
      /* use "a" in calc */

      /* T2 = T1 * T1 */
      if (err == MP_OKAY)
          err = mp_sqr(&t1, &t2);
      if (err == MP_OKAY)
          err = mp_montgomery_reduce(&t2, modulus, mp);
      /* T1 = T2 * a */
      if (err == MP_OKAY)
          err = mp_mulmod(&t2, a, modulus, &t1);
      /* T2 = X * X */
      if (err == MP_OKAY)
          err = mp_sqr(x, &t2);
      if (err == MP_OKAY)
          err = mp_montgomery_reduce(&t2, modulus, mp);
      /* T1 = T2 + T1 */
      if (err == MP_OKAY)
          err = mp_add(&t1, &t2, &t1);
      if (err == MP_OKAY) {
         if (mp_cmp(&t1, modulus) != MP_LT)
            err = mp_sub(&t1, modulus, &t1);
      }
      /* T1 = T2 + T1 */
      if (err == MP_OKAY)
          err = mp_add(&t1, &t2, &t1);
      if (err == MP_OKAY) {
          if (mp_cmp(&t1, modulus) != MP_LT)
              err = mp_sub(&t1, modulus, &t1);
      }
      /* T1 = T2 + T1 */
      if (err == MP_OKAY)
          err = mp_add(&t1, &t2, &t1);
      if (err == MP_OKAY) {
         if (mp_cmp(&t1, modulus) != MP_LT)
            err = mp_sub(&t1, modulus, &t1);
      }
   }
   else
#endif /* WOLFSSL_CUSTOM_CURVES */
   {
      /* assumes "a" == 3 */
      (void)a;

      /* T2 = X - T1 */
      if (err == MP_OKAY)
          err = mp_sub(x, &t1, &t2);
      if (err == MP_OKAY) {
          if (mp_isneg(&t2))
              err = mp_add(&t2, modulus, &t2);
      }
      /* T1 = X + T1 */
      if (err == MP_OKAY)
          err = mp_add(&t1, x, &t1);
      if (err == MP_OKAY) {
          if (mp_cmp(&t1, modulus) != MP_LT)
              err = mp_sub(&t1, modulus, &t1);
      }
      /* T2 = T1 * T2 */
      if (err == MP_OKAY)
          err = mp_mul(&t1, &t2, &t2);
      if (err == MP_OKAY)
          err = mp_montgomery_reduce(&t2, modulus, mp);

      /* T1 = 2T2 */
      if (err == MP_OKAY)
          err = mp_add(&t2, &t2, &t1);
      if (err == MP_OKAY) {
          if (mp_cmp(&t1, modulus) != MP_LT)
              err = mp_sub(&t1, modulus, &t1);
      }
      /* T1 = T1 + T2 */
      if (err == MP_OKAY)
          err = mp_add(&t1, &t2, &t1);
      if (err == MP_OKAY) {
          if (mp_cmp(&t1, modulus) != MP_LT)
              err = mp_sub(&t1, modulus, &t1);
      }
   }

   /* Y = 2Y */
   if (err == MP_OKAY)
       err = mp_add(y, y, y);
   if (err == MP_OKAY) {
       if (mp_cmp(y, modulus) != MP_LT)
           err = mp_sub(y, modulus, y);
   }
   /* Y = Y * Y */
   if (err == MP_OKAY)
       err = mp_sqr(y, y);
   if (err == MP_OKAY)
       err = mp_montgomery_reduce(y, modulus, mp);

   /* T2 = Y * Y */
   if (err == MP_OKAY)
       err = mp_sqr(y, &t2);
   if (err == MP_OKAY)
       err = mp_montgomery_reduce(&t2, modulus, mp);

   /* T2 = T2/2 */
   if (err == MP_OKAY) {
       if (mp_isodd(&t2) == MP_YES)
           err = mp_add(&t2, modulus, &t2);
   }
   if (err == MP_OKAY)
       err = mp_div_2(&t2, &t2);

   /* Y = Y * X */
   if (err == MP_OKAY)
       err = mp_mul(y, x, y);
   if (err == MP_OKAY)
       err = mp_montgomery_reduce(y, modulus, mp);

   /* X = T1 * T1 */
   if (err == MP_OKAY)
       err = mp_sqr(&t1, x);
   if (err == MP_OKAY)
       err = mp_montgomery_reduce(x, modulus, mp);

   /* X = X - Y */
   if (err == MP_OKAY)
       err = mp_sub(x, y, x);
   if (err == MP_OKAY) {
       if (mp_isneg(x))
           err = mp_add(x, modulus, x);
   }
   /* X = X - Y */
   if (err == MP_OKAY)
       err = mp_sub(x, y, x);
   if (err == MP_OKAY) {
       if (mp_isneg(x))
           err = mp_add(x, modulus, x);
   }

   /* Y = Y - X */
   if (err == MP_OKAY)
       err = mp_sub(y, x, y);
   if (err == MP_OKAY) {
       if (mp_isneg(y))
           err = mp_add(y, modulus, y);
   }
   /* Y = Y * T1 */
   if (err == MP_OKAY)
       err = mp_mul(y, &t1, y);
   if (err == MP_OKAY)
       err = mp_montgomery_reduce(y, modulus, mp);

   /* Y = Y - T2 */
   if (err == MP_OKAY)
       err = mp_sub(y, &t2, y);
   if (err == MP_OKAY) {
       if (mp_isneg(y))
           err = mp_add(y, modulus, y);
   }

#ifdef ALT_ECC_SIZE
   if (err == MP_OKAY)
       err = mp_copy(x, R->x);
   if (err == MP_OKAY)
       err = mp_copy(y, R->y);
   if (err == MP_OKAY)
       err = mp_copy(z, R->z);
#endif

   /* clean up */
   mp_clear(&t1);
   mp_clear(&t2);

   return err;
}


/**
  Map a projective jacbobian point back to affine space
  P        [in/out] The point to map
  modulus  The modulus of the field the ECC curve is in
  mp       The "b" value from montgomery_setup()
  return   MP_OKAY on success
*/
int ecc_map(ecc_point* P, mp_int* modulus, mp_digit mp)
{
   mp_int t1, t2;
#ifdef ALT_ECC_SIZE
   mp_int rx, ry, rz;
#endif
   mp_int *x, *y, *z;
   int    err;

   if (P == NULL || modulus == NULL)
       return ECC_BAD_ARG_E;

   /* special case for point at infinity */
   if (mp_cmp_d(P->z, 0) == MP_EQ) {
       err = mp_set(P->x, 0);
       if (err == MP_OKAY)
           err = mp_set(P->y, 0);
       if (err == MP_OKAY)
           err = mp_set(P->z, 1);
       return err;
   }

   if ((err = mp_init_multi(&t1, &t2, NULL, NULL, NULL, NULL)) != MP_OKAY) {
      return MEMORY_E;
   }

#ifdef ALT_ECC_SIZE
   /* Use local stack variable */
   x = &rx;
   y = &ry;
   z = &rz;

   if ((err = mp_init_multi(x, y, z, NULL, NULL, NULL)) != MP_OKAY) {
       goto done;
   }

   if (err == MP_OKAY)
       err = mp_copy(P->x, x);
   if (err == MP_OKAY)
       err = mp_copy(P->y, y);
   if (err == MP_OKAY)
       err = mp_copy(P->z, z);

   if (err != MP_OKAY) {
      goto done;
   }
#else
   /* Use destination directly */
   x = P->x;
   y = P->y;
   z = P->z;
#endif

   /* first map z back to normal */
   err = mp_montgomery_reduce(z, modulus, mp);

   /* get 1/z */
   if (err == MP_OKAY)
       err = mp_invmod(z, modulus, &t1);

   /* get 1/z^2 and 1/z^3 */
   if (err == MP_OKAY)
       err = mp_sqr(&t1, &t2);
   if (err == MP_OKAY)
       err = mp_mod(&t2, modulus, &t2);
   if (err == MP_OKAY)
       err = mp_mul(&t1, &t2, &t1);
   if (err == MP_OKAY)
       err = mp_mod(&t1, modulus, &t1);

   /* multiply against x/y */
   if (err == MP_OKAY)
       err = mp_mul(x, &t2, x);
   if (err == MP_OKAY)
       err = mp_montgomery_reduce(x, modulus, mp);
   if (err == MP_OKAY)
       err = mp_mul(y, &t1, y);
   if (err == MP_OKAY)
       err = mp_montgomery_reduce(y, modulus, mp);

   if (err == MP_OKAY)
       err = mp_set(z, 1);

#ifdef ALT_ECC_SIZE
   /* return result */
   if (err == MP_OKAY)
      err = mp_copy(x, P->x);
   if (err == MP_OKAY)
      err = mp_copy(y, P->y);
   if (err == MP_OKAY)
      err = mp_copy(z, P->z);

done:
#endif

   /* clean up */
   mp_clear(&t1);
   mp_clear(&t2);

   return err;
}

#if !defined(FREESCALE_LTC_ECC)

#ifndef WC_NO_CACHE_RESISTANT
#if defined(TFM_TIMING_RESISTANT) && defined(USE_FAST_MATH) && \
    !defined(__cplusplus)
    /* let's use the one we already have */
    extern const wolfssl_word wc_off_on_addr[2];
#else
    static const wolfssl_word wc_off_on_addr[2] =
    {
    #if defined(WC_64BIT_CPU)
        W64LIT(0x0000000000000000),
        W64LIT(0xffffffffffffffff)
    #elif defined(WC_16BIT_CPU)
        0x0000U,
        0xffffU
    #else
        /* 32 bit */
        0x00000000U,
        0xffffffffU
    #endif
    };
#endif /* TFM_TIMING_RESISTANT && USE_FAST_MATH */
#endif /* WC_NO_CACHE_RESISTANT */

/**
   Perform a point multiplication
   k    The scalar to multiply by
   G    The base point
   R    [out] Destination for kG
   a    ECC curve parameter a
   modulus  The modulus of the field the ECC curve is in
   map      Boolean whether to map back to affine or not
                (1==map, 0 == leave in projective)
   return MP_OKAY on success
*/
#ifdef FP_ECC
static int normal_ecc_mulmod(mp_int* k, ecc_point *G, ecc_point *R,
                  mp_int* a, mp_int* modulus, int map,
                  void* heap)
#else
int wc_ecc_mulmod_ex(mp_int* k, ecc_point *G, ecc_point *R,
                  mp_int* a, mp_int* modulus, int map,
                  void* heap)
#endif
{
#ifndef ECC_TIMING_RESISTANT
   /* size of sliding window, don't change this! */
   #define WINSIZE  4
   #define M_POINTS 8
   int           first = 1, bitbuf = 0, bitcpy = 0, j;
#else
   #define M_POINTS 3
#endif

   ecc_point     *tG, *M[M_POINTS];
   int           i, err;
   mp_int        mu;
   mp_digit      mp;
   mp_digit      buf;
   int           bitcnt = 0, mode = 0, digidx = 0;

   if (k == NULL || G == NULL || R == NULL || modulus == NULL) {
       return ECC_BAD_ARG_E;
   }

   /* init variables */
   tG = NULL;
   XMEMSET(M, 0, sizeof(M));

   /* init montgomery reduction */
   if ((err = mp_montgomery_setup(modulus, &mp)) != MP_OKAY) {
       return err;
   }

   if ((err = mp_init(&mu)) != MP_OKAY) {
       return err;
   }
   if ((err = mp_montgomery_calc_normalization(&mu, modulus)) != MP_OKAY) {
       mp_clear(&mu);
       return err;
   }

  /* alloc ram for window temps */
  for (i = 0; i < M_POINTS; i++) {
      M[i] = wc_ecc_new_point_h(heap);
      if (M[i] == NULL) {
         mp_clear(&mu);
         err = MEMORY_E; goto exit;
      }
  }

   /* make a copy of G in case R==G */
   tG = wc_ecc_new_point_h(heap);
   if (tG == NULL)
       err = MEMORY_E;

   /* tG = G  and convert to montgomery */
   if (err == MP_OKAY) {
       if (mp_cmp_d(&mu, 1) == MP_EQ) {
           err = mp_copy(G->x, tG->x);
           if (err == MP_OKAY)
               err = mp_copy(G->y, tG->y);
           if (err == MP_OKAY)
               err = mp_copy(G->z, tG->z);
       } else {
           err = mp_mulmod(G->x, &mu, modulus, tG->x);
           if (err == MP_OKAY)
               err = mp_mulmod(G->y, &mu, modulus, tG->y);
           if (err == MP_OKAY)
               err = mp_mulmod(G->z, &mu, modulus, tG->z);
       }
   }

   /* done with mu */
   mp_clear(&mu);

#ifndef ECC_TIMING_RESISTANT

   /* calc the M tab, which holds kG for k==8..15 */
   /* M[0] == 8G */
   if (err == MP_OKAY)
       err = ecc_projective_dbl_point(tG, M[0], a, modulus, mp);
   if (err == MP_OKAY)
       err = ecc_projective_dbl_point(M[0], M[0], a, modulus, mp);
   if (err == MP_OKAY)
       err = ecc_projective_dbl_point(M[0], M[0], a, modulus, mp);

   /* now find (8+k)G for k=1..7 */
   if (err == MP_OKAY)
       for (j = 9; j < 16; j++) {
           err = ecc_projective_add_point(M[j-9], tG, M[j-M_POINTS], a,
                                                                modulus, mp);
           if (err != MP_OKAY) break;
       }

   /* setup sliding window */
   if (err == MP_OKAY) {
       mode   = 0;
       bitcnt = 1;
       buf    = 0;
       digidx = get_digit_count(k) - 1;
       bitcpy = bitbuf = 0;
       first  = 1;

       /* perform ops */
       for (;;) {
           /* grab next digit as required */
           if (--bitcnt == 0) {
               if (digidx == -1) {
                   break;
               }
               buf    = get_digit(k, digidx);
               bitcnt = (int) DIGIT_BIT;
               --digidx;
           }

           /* grab the next msb from the ltiplicand */
           i = (int)(buf >> (DIGIT_BIT - 1)) & 1;
           buf <<= 1;

           /* skip leading zero bits */
           if (mode == 0 && i == 0)
               continue;

           /* if the bit is zero and mode == 1 then we double */
           if (mode == 1 && i == 0) {
               err = ecc_projective_dbl_point(R, R, a, modulus, mp);
               if (err != MP_OKAY) break;
               continue;
           }

           /* else we add it to the window */
           bitbuf |= (i << (WINSIZE - ++bitcpy));
           mode = 2;

           if (bitcpy == WINSIZE) {
               /* if this is the first window we do a simple copy */
               if (first == 1) {
                   /* R = kG [k = first window] */
                   err = mp_copy(M[bitbuf-M_POINTS]->x, R->x);
                   if (err != MP_OKAY) break;

                   err = mp_copy(M[bitbuf-M_POINTS]->y, R->y);
                   if (err != MP_OKAY) break;

                   err = mp_copy(M[bitbuf-M_POINTS]->z, R->z);
                   first = 0;
               } else {
                   /* normal window */
                   /* ok window is filled so double as required and add  */
                   /* double first */
                   for (j = 0; j < WINSIZE; j++) {
                       err = ecc_projective_dbl_point(R, R, a, modulus, mp);
                       if (err != MP_OKAY) break;
                   }
                   if (err != MP_OKAY) break;  /* out of first for(;;) */

                   /* then add, bitbuf will be 8..15 [8..2^WINSIZE] guaranteed */
                   err = ecc_projective_add_point(R, M[bitbuf-M_POINTS], R, a,
                                                               modulus, mp);
               }
               if (err != MP_OKAY) break;
               /* empty window and reset */
               bitcpy = bitbuf = 0;
               mode = 1;
           }
       }
   }

   /* if bits remain then double/add */
   if (err == MP_OKAY) {
       if (mode == 2 && bitcpy > 0) {
           /* double then add */
           for (j = 0; j < bitcpy; j++) {
               /* only double if we have had at least one add first */
               if (first == 0) {
                   err = ecc_projective_dbl_point(R, R, a, modulus, mp);
                   if (err != MP_OKAY) break;
               }

               bitbuf <<= 1;
               if ((bitbuf & (1 << WINSIZE)) != 0) {
                   if (first == 1) {
                       /* first add, so copy */
                       err = mp_copy(tG->x, R->x);
                       if (err != MP_OKAY) break;

                       err = mp_copy(tG->y, R->y);
                       if (err != MP_OKAY) break;

                       err = mp_copy(tG->z, R->z);
                       if (err != MP_OKAY) break;
                       first = 0;
                   } else {
                       /* then add */
                       err = ecc_projective_add_point(R, tG, R, a, modulus,
                                                                       mp);
                       if (err != MP_OKAY) break;
                   }
               }
           }
       }
   }

   #undef WINSIZE

#else /* ECC_TIMING_RESISTANT */

   /* calc the M tab */
   /* M[0] == G */
   if (err == MP_OKAY)
       err = mp_copy(tG->x, M[0]->x);
   if (err == MP_OKAY)
       err = mp_copy(tG->y, M[0]->y);
   if (err == MP_OKAY)
       err = mp_copy(tG->z, M[0]->z);

   /* M[1] == 2G */
   if (err == MP_OKAY)
       err = ecc_projective_dbl_point(tG, M[1], a, modulus, mp);

   /* setup sliding window */
   mode   = 0;
   bitcnt = 1;
   buf    = 0;
   digidx = get_digit_count(k) - 1;

   /* perform ops */
   if (err == MP_OKAY) {
       for (;;) {
           /* grab next digit as required */
           if (--bitcnt == 0) {
               if (digidx == -1) {
                   break;
               }
               buf = get_digit(k, digidx);
               bitcnt = (int)DIGIT_BIT;
               --digidx;
           }

           /* grab the next msb from the multiplicand */
           i = (buf >> (DIGIT_BIT - 1)) & 1;
           buf <<= 1;

           if (mode == 0 && i == 0) {
               /* timing resistant - dummy operations */
               if (err == MP_OKAY)
                   err = ecc_projective_add_point(M[0], M[1], M[2], a, modulus,
                                                  mp);
               if (err == MP_OKAY)
                   err = ecc_projective_dbl_point(M[1], M[2], a, modulus, mp);
               if (err == MP_OKAY)
                   continue;
           }

           if (mode == 0 && i == 1) {
               mode = 1;
               /* timing resistant - dummy operations */
               if (err == MP_OKAY)
                   err = ecc_projective_add_point(M[0], M[1], M[2], a, modulus,
                                                  mp);
               if (err == MP_OKAY)
                   err = ecc_projective_dbl_point(M[1], M[2], a, modulus, mp);
               if (err == MP_OKAY)
                   continue;
           }

           if (err == MP_OKAY)
               err = ecc_projective_add_point(M[0], M[1], M[i^1], a, modulus,
                                                                       mp);
#ifdef WC_NO_CACHE_RESISTANT
           if (err == MP_OKAY)
               err = ecc_projective_dbl_point(M[i], M[i], a, modulus, mp);
#else
            /* instead of using M[i] for double, which leaks key bit to cache
             * monitor, use M[2] as temp, make sure address calc is constant,
             * keep M[0] and M[1] in cache */
           if (err == MP_OKAY)
               err = mp_copy((mp_int*)
                             ( ((wolfssl_word)M[0]->x & wc_off_on_addr[i^1]) +
                               ((wolfssl_word)M[1]->x & wc_off_on_addr[i])),
                             M[2]->x);
           if (err == MP_OKAY)
               err = mp_copy((mp_int*)
                             ( ((wolfssl_word)M[0]->y & wc_off_on_addr[i^1]) +
                               ((wolfssl_word)M[1]->y & wc_off_on_addr[i])),
                             M[2]->y);
           if (err == MP_OKAY)
               err = mp_copy((mp_int*)
                             ( ((wolfssl_word)M[0]->z & wc_off_on_addr[i^1]) +
                               ((wolfssl_word)M[1]->z & wc_off_on_addr[i])),
                             M[2]->z);
           if (err == MP_OKAY)
               err = ecc_projective_dbl_point(M[2], M[2], a, modulus, mp);
           /* copy M[2] back to M[i] */
           if (err == MP_OKAY)
               err = mp_copy(M[2]->x,
                             (mp_int*)
                             ( ((wolfssl_word)M[0]->x & wc_off_on_addr[i^1]) +
                               ((wolfssl_word)M[1]->x & wc_off_on_addr[i])) );
           if (err == MP_OKAY)
               err = mp_copy(M[2]->y,
                             (mp_int*)
                             ( ((wolfssl_word)M[0]->y & wc_off_on_addr[i^1]) +
                               ((wolfssl_word)M[1]->y & wc_off_on_addr[i])) );
           if (err == MP_OKAY)
               err = mp_copy(M[2]->z,
                             (mp_int*)
                             ( ((wolfssl_word)M[0]->z & wc_off_on_addr[i^1]) +
                               ((wolfssl_word)M[1]->z & wc_off_on_addr[i])) );
           if (err != MP_OKAY)
               break;
#endif /* WC_NO_CACHE_RESISTANT */
       } /* end for */
   }

   /* copy result out */
   if (err == MP_OKAY)
       err = mp_copy(M[0]->x, R->x);
   if (err == MP_OKAY)
       err = mp_copy(M[0]->y, R->y);
   if (err == MP_OKAY)
       err = mp_copy(M[0]->z, R->z);

#endif /* ECC_TIMING_RESISTANT */

   /* map R back from projective space */
   if (err == MP_OKAY && map)
       err = ecc_map(R, modulus, mp);

exit:

   /* done */
   wc_ecc_del_point_h(tG, heap);
   for (i = 0; i < M_POINTS; i++) {
       wc_ecc_del_point_h(M[i], heap);
   }

   return err;
}

/** ECC Fixed Point mulmod global
    k        The multiplicand
    G        Base point to multiply
    R        [out] Destination of product
    a        ECC curve parameter a
    modulus  The modulus for the curve
    map      [boolean] If non-zero maps the point back to affine co-ordinates,
             otherwise it's left in jacobian-montgomery form
    return MP_OKAY if successful
*/
int wc_ecc_mulmod(mp_int* k, ecc_point *G, ecc_point *R, mp_int* a,
                  mp_int* modulus, int map)
{
    return wc_ecc_mulmod_ex(k, G, R, a, modulus, map, NULL);
}

#endif /* !FREESCALE_LTC_ECC */


#ifdef ALT_ECC_SIZE

static void alt_fp_init(fp_int* a)
{
    a->size = FP_SIZE_ECC;
    fp_zero(a);
}

#endif /* ALT_ECC_SIZE */


/**
 * use a heap hint when creating new ecc_point
 * return an allocated point on success or NULL on failure
 */
ecc_point* wc_ecc_new_point_h(void* heap)
{
   ecc_point* p;

   p = (ecc_point*)XMALLOC(sizeof(ecc_point), heap, DYNAMIC_TYPE_ECC);
   if (p == NULL) {
      return NULL;
   }
   XMEMSET(p, 0, sizeof(ecc_point));

#ifndef ALT_ECC_SIZE
   if (mp_init_multi(p->x, p->y, p->z, NULL, NULL, NULL) != MP_OKAY) {
      XFREE(p, heap, DYNAMIC_TYPE_ECC);
      return NULL;
   }
#else
   p->x = (mp_int*)&p->xyz[0];
   p->y = (mp_int*)&p->xyz[1];
   p->z = (mp_int*)&p->xyz[2];
   alt_fp_init(p->x);
   alt_fp_init(p->y);
   alt_fp_init(p->z);
#endif

   return p;
}


/**
   Allocate a new ECC point
   return A newly allocated point or NULL on error
*/
ecc_point* wc_ecc_new_point(void)
{
  return wc_ecc_new_point_h(NULL);
}


void wc_ecc_del_point_h(ecc_point* p, void* heap)
{
   /* prevents free'ing null arguments */
   if (p != NULL) {
      mp_clear(p->x);
      mp_clear(p->y);
      mp_clear(p->z);
      XFREE(p, heap, DYNAMIC_TYPE_ECC);
   }
   (void)heap;
}


/** Free an ECC point from memory
  p   The point to free
*/
void wc_ecc_del_point(ecc_point* p)
{
    wc_ecc_del_point_h(p, NULL);
}


/** Copy the value of a point to an other one
  p    The point to copy
  r    The created point
*/
int wc_ecc_copy_point(ecc_point* p, ecc_point *r)
{
    int ret;

    /* prevents null arguments */
    if (p == NULL || r == NULL)
        return ECC_BAD_ARG_E;

    ret = mp_copy(p->x, r->x);
    if (ret != MP_OKAY)
        return ret;
    ret = mp_copy(p->y, r->y);
    if (ret != MP_OKAY)
        return ret;
    ret = mp_copy(p->z, r->z);
    if (ret != MP_OKAY)
        return ret;

    return MP_OKAY;
}

/** Compare the value of a point with an other one
 a    The point to compare
 b    The other point to compare

 return MP_EQ if equal, MP_LT/MP_GT if not, < 0 in case of error
 */
int wc_ecc_cmp_point(ecc_point* a, ecc_point *b)
{
    int ret;

    /* prevents null arguments */
    if (a == NULL || b == NULL)
        return BAD_FUNC_ARG;

    ret = mp_cmp(a->x, b->x);
    if (ret != MP_EQ)
        return ret;
    ret = mp_cmp(a->y, b->y);
    if (ret != MP_EQ)
        return ret;
    ret = mp_cmp(a->z, b->z);
    if (ret != MP_EQ)
        return ret;

    return MP_EQ;
}

#endif /* !WOLFSSL_ATECC508A */


/** Returns whether an ECC idx is valid or not
  n      The idx number to check
  return 1 if valid, 0 if not
*/
int wc_ecc_is_valid_idx(int n)
{
   int x;

   for (x = 0; ecc_sets[x].size != 0; x++)
       ;
   /* -1 is a valid index --- indicating that the domain params
      were supplied by the user */
   if ((n >= ECC_CUSTOM_IDX) && (n < x)) {
      return 1;
   }

   return 0;
}

int wc_ecc_get_curve_idx(int curve_id)
{
    int curve_idx;
    for (curve_idx = 0; ecc_sets[curve_idx].size != 0; curve_idx++) {
        if (curve_id == ecc_sets[curve_idx].id)
            break;
    }
    if (ecc_sets[curve_idx].size == 0) {
        return ECC_CURVE_INVALID;
    }
    return curve_idx;
}

int wc_ecc_get_curve_id(int curve_idx)
{
    if (wc_ecc_is_valid_idx(curve_idx)) {
        return ecc_sets[curve_idx].id;
    }
    return ECC_CURVE_INVALID;
}

/* Returns the curve size that corresponds to a given ecc_curve_id identifier
 *
 * id      curve id, from ecc_curve_id enum in ecc.h
 * return  curve size, from ecc_sets[] on success, negative on error
 */
int wc_ecc_get_curve_size_from_id(int curve_id)
{
    int curve_idx = wc_ecc_get_curve_idx(curve_id);
    if (curve_idx == ECC_CURVE_INVALID)
        return ECC_BAD_ARG_E;
    return ecc_sets[curve_idx].size;
}

/* Returns the curve index that corresponds to a given curve name in
 * ecc_sets[] of ecc.c
 *
 * name    curve name, from ecc_sets[].name in ecc.c
 * return  curve index in ecc_sets[] on success, negative on error
 */
int wc_ecc_get_curve_idx_from_name(const char* curveName)
{
    int curve_idx;
    word32 len;

    if (curveName == NULL)
        return BAD_FUNC_ARG;

    len = (word32)XSTRLEN(curveName);

    for (curve_idx = 0; ecc_sets[curve_idx].size != 0; curve_idx++) {
        if (XSTRNCASECMP(ecc_sets[curve_idx].name, curveName, len) == 0) {
            break;
        }
    }
    if (ecc_sets[curve_idx].size == 0) {
        WOLFSSL_MSG("ecc_set curve name not found");
        return ECC_CURVE_INVALID;
    }
    return curve_idx;
}

/* Returns the curve size that corresponds to a given curve name,
 * as listed in ecc_sets[] of ecc.c.
 *
 * name    curve name, from ecc_sets[].name in ecc.c
 * return  curve size, from ecc_sets[] on success, negative on error
 */
int wc_ecc_get_curve_size_from_name(const char* curveName)
{
    int curve_idx;

    if (curveName == NULL)
        return BAD_FUNC_ARG;

    curve_idx = wc_ecc_get_curve_idx_from_name(curveName);
    if (curve_idx < 0)
        return curve_idx;

    return ecc_sets[curve_idx].size;
}

/* Returns the curve id that corresponds to a given curve name,
 * as listed in ecc_sets[] of ecc.c.
 *
 * name   curve name, from ecc_sets[].name in ecc.c
 * return curve id, from ecc_sets[] on success, negative on error
 */
int wc_ecc_get_curve_id_from_name(const char* curveName)
{
    int curve_idx;

    if (curveName == NULL)
        return BAD_FUNC_ARG;

    curve_idx = wc_ecc_get_curve_idx_from_name(curveName);
    if (curve_idx < 0)
        return curve_idx;

    return ecc_sets[curve_idx].id;
}

/* Compares a curve parameter (hex, from ecc_sets[]) to given input
 * parameter (byte array) for equality.
 *
 * Returns MP_EQ on success, negative on error */
static int wc_ecc_cmp_param(const char* curveParam,
                            const byte* param, word32 paramSz)
{
    int err = MP_OKAY;
    mp_int a, b;

    if (param == NULL || curveParam == NULL)
        return BAD_FUNC_ARG;

    if ((err = mp_init_multi(&a, &b, NULL, NULL, NULL, NULL)) != MP_OKAY)
        return err;

    if (err == MP_OKAY)
        err = mp_read_unsigned_bin(&a, param, paramSz);

    if (err == MP_OKAY)
        err = mp_read_radix(&b, curveParam, 16);

    if (err == MP_OKAY) {
        if (mp_cmp(&a, &b) != MP_EQ) {
            err = -1;
        } else {
            err = MP_EQ;
        }
    }

#ifndef USE_FAST_MATH
    mp_clear(&a);
    mp_clear(&b);
#endif

    return err;
}

/* Returns the curve id in ecc_sets[] that corresponds to a given set of
 * curve parameters.
 *
 * fieldSize  the field size in bits
 * prime      prime of the finite field
 * primeSz    size of prime in octets
 * Af         first coefficient a of the curve
 * AfSz       size of Af in octets
 * Bf         second coefficient b of the curve
 * BfSz       size of Bf in octets
 * order      curve order
 * orderSz    size of curve in octets
 * Gx         affine x coordinate of base point
 * GxSz       size of Gx in octets
 * Gy         affine y coordinate of base point
 * GySz       size of Gy in octets
 * cofactor   curve cofactor
 *
 * return curve id, from ecc_sets[] on success, negative on error
 */
int wc_ecc_get_curve_id_from_params(int fieldSize,
        const byte* prime, word32 primeSz, const byte* Af, word32 AfSz,
        const byte* Bf, word32 BfSz, const byte* order, word32 orderSz,
        const byte* Gx, word32 GxSz, const byte* Gy, word32 GySz, int cofactor)
{
    int idx;
    int curveSz;

    if (prime == NULL || Af == NULL || Bf == NULL || order == NULL ||
        Gx == NULL || Gy == NULL)
        return BAD_FUNC_ARG;

    curveSz = (fieldSize + 1) / 8;    /* round up */

    for (idx = 0; ecc_sets[idx].size != 0; idx++) {
        if (curveSz == ecc_sets[idx].size) {
            if ((wc_ecc_cmp_param(ecc_sets[idx].prime, prime,
                            primeSz) == MP_EQ) &&
                (wc_ecc_cmp_param(ecc_sets[idx].Af, Af, AfSz) == MP_EQ) &&
                (wc_ecc_cmp_param(ecc_sets[idx].Bf, Bf, BfSz) == MP_EQ) &&
                (wc_ecc_cmp_param(ecc_sets[idx].order, order,
                                  orderSz) == MP_EQ) &&
                (wc_ecc_cmp_param(ecc_sets[idx].Gx, Gx, GxSz) == MP_EQ) &&
                (wc_ecc_cmp_param(ecc_sets[idx].Gy, Gy, GySz) == MP_EQ) &&
                (cofactor == ecc_sets[idx].cofactor)) {
                    break;
            }
        }
    }

    if (ecc_sets[idx].size == 0)
        return ECC_CURVE_INVALID;

    return ecc_sets[idx].id;
}


#ifdef HAVE_ECC_DHE
/**
  Create an ECC shared secret between two keys
  private_key      The private ECC key (heap hint based off of private key)
  public_key       The public key
  out              [out] Destination of the shared secret
                         Conforms to EC-DH from ANSI X9.63
  outlen           [in/out] The max size and resulting size of the shared secret
  return           MP_OKAY if successful
*/
int wc_ecc_shared_secret(ecc_key* private_key, ecc_key* public_key, byte* out,
                      word32* outlen)
{
   int err;

   if (private_key == NULL || public_key == NULL || out == NULL ||
                                                            outlen == NULL) {
       return BAD_FUNC_ARG;
   }

   /* type valid? */
   if (private_key->type != ECC_PRIVATEKEY) {
      return ECC_BAD_ARG_E;
   }

   /* Verify domain params supplied */
   if (wc_ecc_is_valid_idx(private_key->idx) == 0 ||
       wc_ecc_is_valid_idx(public_key->idx)  == 0) {
      return ECC_BAD_ARG_E;
   }

   /* Verify curve id matches */
   if (private_key->dp->id != public_key->dp->id) {
      return ECC_BAD_ARG_E;
   }

#ifdef WOLFSSL_ATECC508A
   err = atcatls_ecdh(private_key->slot, public_key->pubkey, out);
   if (err != ATCA_SUCCESS) {
      err = BAD_COND_E;
   }
   *outlen = private_key->dp->size;
#else
   err = wc_ecc_shared_secret_ex(private_key, &public_key->pubkey, out, outlen);
#endif /* WOLFSSL_ATECC508A */

   return err;
}


#ifndef WOLFSSL_ATECC508A

static int wc_ecc_shared_secret_gen_sync(ecc_key* private_key, ecc_point* point,
                             byte* out, word32 *outlen, ecc_curve_spec* curve)
{
    int err;
    ecc_point* result = NULL;
    word32 x = 0;
    mp_int* k = &private_key->k;
#ifdef HAVE_ECC_CDH
    mp_int k_lcl;

    /* if cofactor flag has been set */
    if (private_key->flags & WC_ECC_FLAG_COFACTOR) {
        mp_digit cofactor = (mp_digit)private_key->dp->cofactor;
        /* only perform cofactor calc if not equal to 1 */
        if (cofactor != 1) {
            k = &k_lcl;
            if (mp_init(k) != MP_OKAY)
                return MEMORY_E;
            /* multiply cofactor times private key "k" */
            err = mp_mul_d(&private_key->k, cofactor, k);
            if (err != MP_OKAY) {
                mp_clear(k);
                return err;
            }
        }
    }
#endif

    /* make new point */
    result = wc_ecc_new_point_h(private_key->heap);
    if (result == NULL) {
#ifdef HAVE_ECC_CDH
        if (k == &k_lcl)
            mp_clear(k);
#endif
        return MEMORY_E;
    }

    err = wc_ecc_mulmod_ex(k, point, result,
        curve->Af, curve->prime, 1, private_key->heap);
    if (err == MP_OKAY) {
        x = mp_unsigned_bin_size(curve->prime);
        if (*outlen < x) {
            err = BUFFER_E;
        }
    }

    if (err == MP_OKAY) {
        XMEMSET(out, 0, x);
        err = mp_to_unsigned_bin(result->x,out +
                                 (x - mp_unsigned_bin_size(result->x)));
    }
    *outlen = x;

    wc_ecc_del_point_h(result, private_key->heap);
#ifdef HAVE_ECC_CDH
    if (k == &k_lcl)
        mp_clear(k);
#endif

    return err;
}

#if defined(WOLFSSL_ASYNC_CRYPT) && defined(WC_ASYNC_ENABLE_ECC)
static int wc_ecc_shared_secret_gen_async(ecc_key* private_key,
            ecc_point* point, byte* out, word32 *outlen,
            ecc_curve_spec* curve)
{
    int err;

#ifdef HAVE_CAVIUM
    /* TODO: Not implemented - use software for now */
    err = wc_ecc_shared_secret_gen_sync(private_key, point, out, outlen, curve);

#elif defined(HAVE_INTEL_QA)
    /* sync public key x/y */
    err = wc_ecc_curve_load(private_key->dp, &curve, ECC_CURVE_FIELD_BF);
    if (err == MP_OKAY)
        err = wc_mp_to_bigint(&private_key->k, &private_key->k.raw);
    if (err == MP_OKAY)
        err = wc_mp_to_bigint(point->x, &point->x->raw);
    if (err == MP_OKAY)
        err = wc_mp_to_bigint(point->y, &point->y->raw);
    if (err == MP_OKAY)
        err = IntelQaEcdh(&private_key->asyncDev,
            &private_key->k.raw, &point->x->raw, &point->y->raw,
            out, outlen,
            &curve->Af->raw, &curve->Bf->raw, &curve->prime->raw,
            private_key->dp->cofactor);
#else /* WOLFSSL_ASYNC_CRYPT_TEST */
    WC_ASYNC_TEST* testDev = &private_key->asyncDev.test;
    if (testDev->type == ASYNC_TEST_NONE) {
        testDev->type = ASYNC_TEST_ECC_SHARED_SEC;
        testDev->eccSharedSec.private_key = private_key;
        testDev->eccSharedSec.public_point = point;
        testDev->eccSharedSec.out = out;
        testDev->eccSharedSec.outLen = outlen;
        return WC_PENDING_E;
    }
    err = wc_ecc_shared_secret_gen_sync(private_key, point, out, outlen, curve);
#endif

    return err;
}
#endif /* WOLFSSL_ASYNC_CRYPT */

int wc_ecc_shared_secret_gen(ecc_key* private_key, ecc_point* point,
                                                    byte* out, word32 *outlen)
{
    int err;
    DECLARE_CURVE_SPECS(2)

    if (private_key == NULL || point == NULL || out == NULL ||
                                                            outlen == NULL) {
        return BAD_FUNC_ARG;
    }

    /* load curve info */
    err = wc_ecc_curve_load(private_key->dp, &curve,
        (ECC_CURVE_FIELD_PRIME | ECC_CURVE_FIELD_AF));
    if (err != MP_OKAY)
        return err;

#if defined(WOLFSSL_ASYNC_CRYPT) && defined(WC_ASYNC_ENABLE_ECC)
    if (private_key->asyncDev.marker == WOLFSSL_ASYNC_MARKER_ECC) {
        err = wc_ecc_shared_secret_gen_async(private_key, point,
            out, outlen, curve);
    }
    else
#endif
    {
        err = wc_ecc_shared_secret_gen_sync(private_key, point,
            out, outlen, curve);
    }

    wc_ecc_curve_free(curve);

    return err;
}

/**
 Create an ECC shared secret between private key and public point
 private_key      The private ECC key (heap hint based on private key)
 point            The point to use (public key)
 out              [out] Destination of the shared secret
                        Conforms to EC-DH from ANSI X9.63
 outlen           [in/out] The max size and resulting size of the shared secret
 return           MP_OKAY if successful
*/
int wc_ecc_shared_secret_ex(ecc_key* private_key, ecc_point* point,
                            byte* out, word32 *outlen)
{
    int err;

    if (private_key == NULL || point == NULL || out == NULL ||
                                                            outlen == NULL) {
        return BAD_FUNC_ARG;
    }

    /* type valid? */
    if (private_key->type != ECC_PRIVATEKEY) {
        return ECC_BAD_ARG_E;
    }

    /* Verify domain params supplied */
    if (wc_ecc_is_valid_idx(private_key->idx) == 0)
        return ECC_BAD_ARG_E;

    switch(private_key->state) {
        case ECC_STATE_NONE:
        case ECC_STATE_SHARED_SEC_GEN:
            private_key->state = ECC_STATE_SHARED_SEC_GEN;

            err = wc_ecc_shared_secret_gen(private_key, point, out, outlen);
            if (err < 0) {
                break;
            }

            /* fall through */
        case ECC_STATE_SHARED_SEC_RES:
            private_key->state = ECC_STATE_SHARED_SEC_RES;
            err = 0;
        #if defined(WOLFSSL_ASYNC_CRYPT) && defined(WC_ASYNC_ENABLE_ECC)
            if (private_key->asyncDev.marker == WOLFSSL_ASYNC_MARKER_ECC) {
            #if defined(HAVE_CAVIUM) || defined(HAVE_INTEL_QA)
                err = private_key->asyncDev.event.ret;
            #endif
            }
        #endif
            break;

        default:
            err = BAD_STATE_E;
    } /* switch */

    /* if async pending then return and skip done cleanup below */
    if (err == WC_PENDING_E) {
        private_key->state++;
        return err;
    }

    private_key->state = ECC_STATE_NONE;

    return err;
}
#endif /* !WOLFSSL_ATECC508A */
#endif /* HAVE_ECC_DHE */


#ifndef WOLFSSL_ATECC508A
/* return 1 if point is at infinity, 0 if not, < 0 on error */
int wc_ecc_point_is_at_infinity(ecc_point* p)
{
    if (p == NULL)
        return BAD_FUNC_ARG;

    if (get_digit_count(p->x) == 0 && get_digit_count(p->y) == 0)
        return 1;

    return 0;
}

/* generate random and ensure its greater than 0 and less than order */
static int wc_ecc_gen_k(WC_RNG* rng, int size, mp_int* k, mp_int* order)
{
    int err;
#ifdef WOLFSSL_SMALL_STACK
    byte* buf;
#else
    byte  buf[ECC_MAXSIZE_GEN];
#endif

#ifdef WOLFSSL_SMALL_STACK
    buf = (byte*)XMALLOC(ECC_MAXSIZE_GEN, NULL, DYNAMIC_TYPE_TMP_BUFFER);
    if (buf == NULL)
        return MEMORY_E;
#endif

    /*generate 8 extra bytes to mitigate bias from the modulo operation below*/
    /*see section A.1.2 in 'Suite B Implementor's Guide to FIPS 186-3 (ECDSA)'*/
    size += 8;

    /* make up random string */
    err = wc_RNG_GenerateBlock(rng, buf, size);

    /* load random buffer data into k */
    if (err == 0)
        err = mp_read_unsigned_bin(k, (byte*)buf, size);

    /* quick sanity check to make sure we're not dealing with a 0 key */
    if (err == MP_OKAY) {
        if (mp_iszero(k) == MP_YES)
          err = MP_ZERO_E;
    }

    /* the key should be smaller than the order of base point */
    if (err == MP_OKAY) {
        if (mp_cmp(k, order) != MP_LT) {
            err = mp_mod(k, order, k);
        }
    }

    ForceZero(buf, ECC_MAXSIZE);
#ifdef WOLFSSL_SMALL_STACK
    XFREE(buf, NULL, DYNAMIC_TYPE_TMP_BUFFER);
#endif

    return err;
}
#endif /* !WOLFSSL_ATECC508A */

int wc_ecc_make_key_ex(WC_RNG* rng, int keysize, ecc_key* key, int curve_id)
{
    int            err;
#ifndef WOLFSSL_ATECC508A
    ecc_point*     base = NULL;
    DECLARE_CURVE_SPECS(ECC_CURVE_FIELD_COUNT)
#endif

    if (key == NULL || rng == NULL) {
        return BAD_FUNC_ARG;
    }

    /* make sure required key variables are reset */
    key->state = ECC_STATE_NONE;
    key->idx = 0;
    key->dp = NULL;

    err = wc_ecc_set_curve(key, keysize, curve_id);
    if (err != 0) {
        return err;
    }

#if defined(WOLFSSL_ASYNC_CRYPT) && defined(WC_ASYNC_ENABLE_ECC)
    if (key->asyncDev.marker == WOLFSSL_ASYNC_MARKER_ECC) {
    #ifdef HAVE_CAVIUM
        /* TODO: Not implemented */
    #elif defined(HAVE_INTEL_QA)
        /* TODO: Not implemented */
    #else
        WC_ASYNC_TEST* testDev = &key->asyncDev.test;
        if (testDev->type == ASYNC_TEST_NONE) {
            testDev->type = ASYNC_TEST_ECC_MAKE;
            testDev->eccMake.rng = rng;
            testDev->eccMake.key = key;
            testDev->eccMake.size = keysize;
            testDev->eccMake.curve_id = curve_id;
            return WC_PENDING_E;
        }
    #endif
    }
#endif /* WOLFSSL_ASYNC_CRYPT */

#ifdef WOLFSSL_ATECC508A
   key->type = ECC_PRIVATEKEY;
   err = atcatls_create_key(key->slot, key->pubkey);
   if (err != ATCA_SUCCESS) {
      err = BAD_COND_E;
   }

#else

    /* setup the key variables */
    err = mp_init(&key->k);
    if (err == MP_OKAY) {
    #ifndef ALT_ECC_SIZE
        err = mp_init_multi(key->pubkey.x, key->pubkey.y, key->pubkey.z,
                                                        NULL, NULL, NULL);
    #else
        key->pubkey.x = (mp_int*)&key->pubkey.xyz[0];
        key->pubkey.y = (mp_int*)&key->pubkey.xyz[1];
        key->pubkey.z = (mp_int*)&key->pubkey.xyz[2];
        alt_fp_init(key->pubkey.x);
        alt_fp_init(key->pubkey.y);
        alt_fp_init(key->pubkey.z);
    #endif
    }

    if (err == MP_OKAY) {
        base = wc_ecc_new_point_h(key->heap);
        if (base == NULL)
            err = MEMORY_E;
    }

    /* load curve info */
    if (err == MP_OKAY)
        err = wc_ecc_curve_load(key->dp, &curve, ECC_CURVE_FIELD_ALL);

    /* read in the x/y for this key */
    if (err == MP_OKAY)
        err = mp_copy(curve->Gx, base->x);
    if (err == MP_OKAY)
        err = mp_copy(curve->Gy, base->y);
    if (err == MP_OKAY)
        err = mp_set(base->z, 1);

    /* generate k */
    if (err == MP_OKAY)
        err = wc_ecc_gen_k(rng, key->dp->size, &key->k, curve->order);

    /* make the public key */
    if (err == MP_OKAY)
        err = wc_ecc_mulmod_ex(&key->k, base, &key->pubkey,
            curve->Af, curve->prime, 1, key->heap);

#ifdef WOLFSSL_VALIDATE_ECC_KEYGEN
    /* validate the public key, order * pubkey = point at infinity */
    if (err == MP_OKAY)
        err = ecc_check_pubkey_order(key, curve->Af, curve->prime, curve->order);
#endif /* WOLFSSL_VALIDATE_KEYGEN */

    if (err == MP_OKAY)
        key->type = ECC_PRIVATEKEY;

    /* cleanup these on failure case only */
    if (err != MP_OKAY) {
        /* clean up */
    #ifndef ALT_ECC_SIZE
        mp_clear(key->pubkey.x);
        mp_clear(key->pubkey.y);
        mp_clear(key->pubkey.z);
    #endif
        mp_forcezero(&key->k);
    }

    /* cleanup allocations */
    wc_ecc_del_point_h(base, key->heap);
    wc_ecc_curve_free(curve);

#endif /* WOLFSSL_ATECC508A */

    return err;
}

#ifdef ECC_DUMP_OID
/* Optional dump of encoded OID for adding new curves */
static int mOidDumpDone;
static void wc_ecc_dump_oids(void)
{
    int x;

    if (mOidDumpDone) {
        return;
    }

    /* find matching OID sum (based on encoded value) */
    for (x = 0; ecc_sets[x].size != 0; x++) {
        int i;
        byte* oid;
        word32 oidSz, sum = 0;

        printf("ECC %s (%d):\n", ecc_sets[x].name, x);

    #ifdef HAVE_OID_ENCODING
        byte oidEnc[ECC_MAX_OID_LEN];

        oid = oidEnc;
        oidSz = ECC_MAX_OID_LEN;

        printf("OID: ");
        for (i = 0; i < (int)ecc_sets[x].oidSz; i++) {
            printf("%d.", ecc_sets[x].oid[i]);
        }
        printf("\n");

        EncodeObjectId(ecc_sets[x].oid, ecc_sets[x].oidSz, oidEnc, &oidSz);
    #else
        oid = (byte*)ecc_sets[x].oid;
        oidSz = ecc_sets[x].oidSz;
    #endif

        printf("OID Encoded: ");
        for (i = 0; i < (int)oidSz; i++) {
            printf("0x%02X,", oid[i]);
        }
        printf("\n");

        for (i = 0; i < (int)oidSz; i++) {
            sum += oid[i];
        }
        printf("Sum: %d\n", sum);

        /* validate sum */
        if (ecc_sets[x].oidSum != sum) {
            printf("  Sum %d Not Valid!\n", ecc_sets[x].oidSum);
        }
    }
    mOidDumpDone = 1;
}
#endif /* ECC_DUMP_OID */

/**
 Make a new ECC key
 rng          An active RNG state
 keysize      The keysize for the new key (in octets from 20 to 65 bytes)
 key          [out] Destination of the newly created key
 return       MP_OKAY if successful,
 upon error all allocated memory will be freed
 */
int wc_ecc_make_key(WC_RNG* rng, int keysize, ecc_key* key)
{
    return wc_ecc_make_key_ex(rng, keysize, key, ECC_CURVE_DEF);
}

static INLINE int wc_ecc_alloc_rs(ecc_key* key, mp_int** r, mp_int** s)
{
    int err = 0;

#ifndef WOLFSSL_ASYNC_CRYPT
    (void)key;
#endif

    if (*r == NULL) {
    #ifdef WOLFSSL_ASYNC_CRYPT
        *r = (mp_int*)XMALLOC(sizeof(mp_int), key->heap, DYNAMIC_TYPE_BIGINT);
        if (*r == NULL) {
            return MEMORY_E;
        }
        key->r = *r;
    #endif
    }
    if (*s == NULL) {
    #ifdef WOLFSSL_ASYNC_CRYPT
        *s = (mp_int*)XMALLOC(sizeof(mp_int), key->heap, DYNAMIC_TYPE_BIGINT);
        if (*s == NULL) {
            XFREE(*r, key->heap, DYNAMIC_TYPE_BIGINT);
            return MEMORY_E;
        }
        key->s = *s;
    #endif
    }

    /* initialize mp_int */
    if (*r)
        XMEMSET(*r, 0, sizeof(mp_int));
    if (*s)
        XMEMSET(*s, 0, sizeof(mp_int));

    return err;
}

static INLINE void wc_ecc_free_rs(ecc_key* key, mp_int** r, mp_int** s)
{
    if (*r) {
        mp_clear(*r);

    #ifdef WOLFSSL_ASYNC_CRYPT
        XFREE(*r, key->heap, DYNAMIC_TYPE_BIGINT);
        key->r = NULL;
    #endif
        *r = NULL;
    }
    if (*s) {
        mp_clear(*s);

    #ifdef WOLFSSL_ASYNC_CRYPT
        XFREE(*s, key->heap, DYNAMIC_TYPE_BIGINT);
        key->s = NULL;
    #endif
        *s = NULL;
    }
    (void)key;
}

/* Setup dynamic pointers if using normal math for proper freeing */
int wc_ecc_init_ex(ecc_key* key, void* heap, int devId)
{
    int ret = 0;

    if (key == NULL) {
        return BAD_FUNC_ARG;
    }

#ifdef ECC_DUMP_OID
    wc_ecc_dump_oids();
#endif

    XMEMSET(key, 0, sizeof(ecc_key));
    key->state = ECC_STATE_NONE;

#ifdef WOLFSSL_ATECC508A
    key->slot = atmel_ecc_alloc();
    if (key->slot == ATECC_INVALID_SLOT) {
        return ECC_BAD_ARG_E;
    }
#else
#ifdef ALT_ECC_SIZE
    key->pubkey.x = (mp_int*)&key->pubkey.xyz[0];
    key->pubkey.y = (mp_int*)&key->pubkey.xyz[1];
    key->pubkey.z = (mp_int*)&key->pubkey.xyz[2];
    alt_fp_init(key->pubkey.x);
    alt_fp_init(key->pubkey.y);
    alt_fp_init(key->pubkey.z);
    ret = mp_init(&key->k);
#else
    ret = mp_init_multi(&key->k, key->pubkey.x, key->pubkey.y, key->pubkey.z,
                                                                    NULL, NULL);
#endif /* ALT_ECC_SIZE */
    if (ret != MP_OKAY) {
        return MEMORY_E;
    }
#endif /* WOLFSSL_ATECC508A */

#ifdef WOLFSSL_HEAP_TEST
    key->heap = (void*)WOLFSSL_HEAP_TEST;
#else
    key->heap = heap;
#endif

#if defined(WOLFSSL_ASYNC_CRYPT) && defined(WC_ASYNC_ENABLE_ECC)
    /* handle as async */
    ret = wolfAsync_DevCtxInit(&key->asyncDev, WOLFSSL_ASYNC_MARKER_ECC,
                                                            key->heap, devId);
#else
    (void)devId;
#endif

    return ret;
}

int wc_ecc_init(ecc_key* key)
{
    return wc_ecc_init_ex(key, NULL, INVALID_DEVID);
}

int wc_ecc_set_flags(ecc_key* key, word32 flags)
{
    if (key == NULL) {
        return BAD_FUNC_ARG;
    }
    key->flags |= flags;
    return 0;
}

#ifdef HAVE_ECC_SIGN

#ifndef NO_ASN
/**
 Sign a message digest
 in        The message digest to sign
 inlen     The length of the digest
 out       [out] The destination for the signature
 outlen    [in/out] The max size and resulting size of the signature
 key       A private ECC key
 return    MP_OKAY if successful
 */
int wc_ecc_sign_hash(const byte* in, word32 inlen, byte* out, word32 *outlen,
                     WC_RNG* rng, ecc_key* key)
{
    int err;
    mp_int *r = NULL, *s = NULL;
#ifndef WOLFSSL_ASYNC_CRYPT
    mp_int r_lcl, s_lcl;
    r = &r_lcl;
    s = &s_lcl;
#endif

    if (in == NULL || out == NULL || outlen == NULL || key == NULL ||
                                                                rng == NULL) {
        return ECC_BAD_ARG_E;
    }

    switch(key->state) {
        case ECC_STATE_NONE:
        case ECC_STATE_SIGN_DO:
            key->state = ECC_STATE_SIGN_DO;

            err = wc_ecc_alloc_rs(key, &r, &s);
            if (err != 0)
                break;

            if ((err = mp_init_multi(r, s, NULL, NULL, NULL, NULL)) != MP_OKAY){
                break;
            }

        #ifdef WOLFSSL_ATECC508A
            /* Check args */
            if (inlen != ATECC_KEY_SIZE || *outlen < SIGN_RSP_SIZE) {
                return ECC_BAD_ARG_E;
            }

            /* Sign: Result is 32-bytes of R then 32-bytes of S */
            err = atcatls_sign(key->slot, in, out);
            if (err != ATCA_SUCCESS) {
               return BAD_COND_E;
           }

            /* Load R and S */
            err = mp_read_unsigned_bin(r, &out[0], ATECC_KEY_SIZE);
            if (err != MP_OKAY) {
                return err;
            }
            err = mp_read_unsigned_bin(s, &out[ATECC_KEY_SIZE], ATECC_KEY_SIZE);
            if (err != MP_OKAY) {
                return err;
            }

            /* Check for zeros */
            if (mp_iszero(r) || mp_iszero(s)) {
                return MP_ZERO_E;
            }

        #else

            err = wc_ecc_sign_hash_ex(in, inlen, rng, key, r, s);
            if (err < 0) {
                break;
            }

        #endif /* WOLFSSL_ATECC508A */

            /* fall through */
        case ECC_STATE_SIGN_ENCODE:
            key->state = ECC_STATE_SIGN_ENCODE;

        #if defined(WOLFSSL_ASYNC_CRYPT) && defined(WC_ASYNC_ENABLE_ECC)
            /* restore r/s */
            r = key->r;
            s = key->s;

            if (key->asyncDev.marker == WOLFSSL_ASYNC_MARKER_ECC) {
                /* only do this if not simulator, since it overwrites result */
                #ifndef WOLFSSL_ASYNC_CRYPT_TEST
                    wc_bigint_to_mp(&r->raw, r);
                    wc_bigint_to_mp(&s->raw, s);
                #endif
            }
        #endif /* WOLFSSL_ASYNC_CRYPT */

            /* encoded with DSA header */
            err = StoreECC_DSA_Sig(out, outlen, r, s);

            /* always free r/s */
            mp_clear(r);
            mp_clear(s);
            break;

        default:
            err = BAD_STATE_E;
    }

    /* if async pending then return and skip done cleanup below */
    if (err == WC_PENDING_E) {
        key->state++;
        return err;
    }

    /* cleanup */
    wc_ecc_free_rs(key, &r, &s);
    key->state = ECC_STATE_NONE;

    return err;
}
#endif /* !NO_ASN */

#ifndef WOLFSSL_ATECC508A
/**
  Sign a message digest
  in        The message digest to sign
  inlen     The length of the digest
  key       A private ECC key
  r         [out] The destination for r component of the signature
  s         [out] The destination for s component of the signature
  return    MP_OKAY if successful
*/
int wc_ecc_sign_hash_ex(const byte* in, word32 inlen, WC_RNG* rng,
                     ecc_key* key, mp_int *r, mp_int *s)
{
   int    err;
   mp_int e;
   DECLARE_CURVE_SPECS(1)

   if (in == NULL || r == NULL || s == NULL || key == NULL || rng == NULL)
       return ECC_BAD_ARG_E;

   /* is this a private key? */
   if (key->type != ECC_PRIVATEKEY) {
      return ECC_BAD_ARG_E;
   }

   /* is the IDX valid ?  */
   if (wc_ecc_is_valid_idx(key->idx) != 1) {
      return ECC_BAD_ARG_E;
   }

#if defined(WOLFSSL_ASYNC_CRYPT) && defined(WC_ASYNC_ENABLE_ECC) && \
       defined(WOLFSSL_ASYNC_CRYPT_TEST)
    if (key->asyncDev.marker == WOLFSSL_ASYNC_MARKER_ECC) {
        WC_ASYNC_TEST* testDev = &key->asyncDev.test;
        if (testDev->type == ASYNC_TEST_NONE) {
            testDev->type = ASYNC_TEST_ECC_SIGN;
            testDev->eccSign.in = in;
            testDev->eccSign.inSz = inlen;
            testDev->eccSign.rng = rng;
            testDev->eccSign.key = key;
            testDev->eccSign.r = r;
            testDev->eccSign.s = s;
            return WC_PENDING_E;
        }
    }
#endif

   /* get the hash and load it as a bignum into 'e' */
   /* init the bignums */
   if ((err = mp_init(&e)) != MP_OKAY) {
      return err;
   }

   /* load curve info */
   err = wc_ecc_curve_load(key->dp, &curve, ECC_CURVE_FIELD_ORDER);

   /* load digest into e */
   if (err == MP_OKAY) {
       /* we may need to truncate if hash is longer than key size */
       word32 orderBits = mp_count_bits(curve->order);

       /* truncate down to byte size, may be all that's needed */
       if ((WOLFSSL_BIT_SIZE * inlen) > orderBits)
           inlen = (orderBits + WOLFSSL_BIT_SIZE - 1) / WOLFSSL_BIT_SIZE;
       err = mp_read_unsigned_bin(&e, (byte*)in, inlen);

       /* may still need bit truncation too */
       if (err == MP_OKAY && (WOLFSSL_BIT_SIZE * inlen) > orderBits)
           mp_rshb(&e, WOLFSSL_BIT_SIZE - (orderBits & 0x7));
   }

   /* make up a key and export the public copy */
   if (err == MP_OKAY) {
       int loop_check = 0;
       ecc_key pubkey;

   #if defined(WOLFSSL_ASYNC_CRYPT) && defined(WC_ASYNC_ENABLE_ECC)
        if (key->asyncDev.marker == WOLFSSL_ASYNC_MARKER_ECC) {
        #ifdef HAVE_CAVIUM
            /* TODO: Not implemented */
        #elif defined(HAVE_INTEL_QA)
           mp_int k;

           err = mp_init(&k);
           /* make sure r and s are allocated */
           if (err == MP_OKAY)
               err = wc_bigint_alloc(&key->r->raw, key->dp->size);
           if (err == MP_OKAY)
               err = wc_bigint_alloc(&key->s->raw, key->dp->size);
           /* load e and k */
           if (err == MP_OKAY)
               err = wc_mp_to_bigint(&e, &e.raw);
           if (err == MP_OKAY)
               err = wc_mp_to_bigint(&key->k, &key->k.raw);
           if (err == MP_OKAY)
               err = wc_ecc_curve_load(key->dp, &curve, ECC_CURVE_FIELD_ALL);
           if (err == MP_OKAY)
               err = wc_ecc_gen_k(rng, key->dp->size, &k, curve->order);
           if (err == MP_OKAY)
               err = wc_mp_to_bigint(&k, &k.raw);
           if (err == MP_OKAY)
               err = IntelQaEcdsaSign(&key->asyncDev, &e.raw, &key->k.raw,
                  &k.raw, &r->raw, &s->raw, &curve->Af->raw, &curve->Bf->raw,
                  &curve->prime->raw, &curve->order->raw, &curve->Gx->raw,
                  &curve->Gy->raw);

           mp_clear(&e);
           mp_clear(&k);
           wc_ecc_curve_free(curve);

           return err;
       #endif
       }
   #endif /* WOLFSSL_ASYNC_CRYPT */

       /* don't use async for key, since we don't support async return here */
       if (wc_ecc_init_ex(&pubkey, key->heap, INVALID_DEVID) == MP_OKAY) {
           for (;;) {
               if (++loop_check > 64) {
                    err = RNG_FAILURE_E;
                    break;
               }
               err = wc_ecc_make_key_ex(rng, key->dp->size, &pubkey,
                                                              key->dp->id);
               if (err != MP_OKAY) break;

               /* find r = x1 mod n */
               err = mp_mod(pubkey.pubkey.x, curve->order, r);
               if (err != MP_OKAY) break;

               if (mp_iszero(r) == MP_YES) {
                #ifndef ALT_ECC_SIZE
                   mp_clear(pubkey.pubkey.x);
                   mp_clear(pubkey.pubkey.y);
                   mp_clear(pubkey.pubkey.z);
                #endif
                   mp_forcezero(&pubkey.k);
               }
               else {
                   /* find s = (e + xr)/k */
                   err = mp_invmod(&pubkey.k, curve->order, &pubkey.k);
                   if (err != MP_OKAY) break;

                   /* s = xr */
                   err = mp_mulmod(&key->k, r, curve->order, s);
                   if (err != MP_OKAY) break;

                   /* s = e +  xr */
                   err = mp_add(&e, s, s);
                   if (err != MP_OKAY) break;

                   /* s = e +  xr */
                   err = mp_mod(s, curve->order, s);
                   if (err != MP_OKAY) break;

                   /* s = (e + xr)/k */
                   err = mp_mulmod(s, &pubkey.k, curve->order, s);

                   if (mp_iszero(s) == MP_NO)
                       break;
                }
           }
           wc_ecc_free(&pubkey);
       }
   }

   mp_clear(&e);
   wc_ecc_curve_free(curve);

   return err;
}
#endif /* WOLFSSL_ATECC508A */
#endif /* HAVE_ECC_SIGN */

/**
  Free an ECC key from memory
  key   The key you wish to free
*/
void wc_ecc_free(ecc_key* key)
{
    if (key == NULL) {
        return;
    }

#if defined(WOLFSSL_ASYNC_CRYPT) && defined(WC_ASYNC_ENABLE_ECC)
    wolfAsync_DevCtxFree(&key->asyncDev, WOLFSSL_ASYNC_MARKER_ECC);
    wc_ecc_free_rs(key, &key->r, &key->s);
#endif

#ifdef WOLFSSL_ATECC508A
   atmel_ecc_free(key->slot);
   key->slot = -1;
#else

    mp_clear(key->pubkey.x);
    mp_clear(key->pubkey.y);
    mp_clear(key->pubkey.z);

    mp_forcezero(&key->k);
#endif /* WOLFSSL_ATECC508A */
}

#ifdef ECC_SHAMIR

/** Computes kA*A + kB*B = C using Shamir's Trick
  A        First point to multiply
  kA       What to multiple A by
  B        Second point to multiply
  kB       What to multiple B by
  C        [out] Destination point (can overlap with A or B)
  a        ECC curve parameter a
  modulus  Modulus for curve
  return MP_OKAY on success
*/
#ifdef FP_ECC
static int normal_ecc_mul2add(ecc_point* A, mp_int* kA,
                             ecc_point* B, mp_int* kB,
                             ecc_point* C, mp_int* a, mp_int* modulus,
                             void* heap)
#else
static int ecc_mul2add(ecc_point* A, mp_int* kA,
                    ecc_point* B, mp_int* kB,
                    ecc_point* C, mp_int* a, mp_int* modulus,
                    void* heap)
#endif
{
  ecc_point*     precomp[16];
  unsigned       bitbufA, bitbufB, lenA, lenB, len, nA, nB, nibble;
  unsigned char* tA;
  unsigned char* tB;
  int            err = MP_OKAY, first, x, y;
  mp_digit mp;

  /* argchks */
  if (A == NULL || kA == NULL || B == NULL || kB == NULL || C == NULL ||
                                                         modulus == NULL) {
     return ECC_BAD_ARG_E;
  }

  /* allocate memory */
  tA = (unsigned char*)XMALLOC(ECC_BUFSIZE, heap, DYNAMIC_TYPE_TMP_BUFFER);
  if (tA == NULL) {
     return GEN_MEM_ERR;
  }
  tB = (unsigned char*)XMALLOC(ECC_BUFSIZE, heap, DYNAMIC_TYPE_TMP_BUFFER);
  if (tB == NULL) {
     XFREE(tA, heap, DYNAMIC_TYPE_TMP_BUFFER);
     return GEN_MEM_ERR;
  }

  /* init variables */
  XMEMSET(tA, 0, ECC_BUFSIZE);
  XMEMSET(tB, 0, ECC_BUFSIZE);
  XMEMSET(precomp, 0, sizeof(precomp));

  /* get sizes */
  lenA = mp_unsigned_bin_size(kA);
  lenB = mp_unsigned_bin_size(kB);
  len  = MAX(lenA, lenB);

  /* sanity check */
  if ((lenA > ECC_BUFSIZE) || (lenB > ECC_BUFSIZE)) {
    err = BAD_FUNC_ARG;
  }

  if (err == MP_OKAY) {
    /* extract and justify kA */
    err = mp_to_unsigned_bin(kA, (len - lenA) + tA);

    /* extract and justify kB */
    if (err == MP_OKAY)
        err = mp_to_unsigned_bin(kB, (len - lenB) + tB);

    /* allocate the table */
    if (err == MP_OKAY) {
        for (x = 0; x < 16; x++) {
            precomp[x] = wc_ecc_new_point_h(heap);
            if (precomp[x] == NULL) {
                err = GEN_MEM_ERR;
                break;
            }
        }
    }
  }

  if (err == MP_OKAY)
    /* init montgomery reduction */
    err = mp_montgomery_setup(modulus, &mp);

  if (err == MP_OKAY) {
    mp_int mu;
    err = mp_init(&mu);
    if (err == MP_OKAY) {
      err = mp_montgomery_calc_normalization(&mu, modulus);

      if (err == MP_OKAY)
        /* copy ones ... */
        err = mp_mulmod(A->x, &mu, modulus, precomp[1]->x);

      if (err == MP_OKAY)
        err = mp_mulmod(A->y, &mu, modulus, precomp[1]->y);
      if (err == MP_OKAY)
        err = mp_mulmod(A->z, &mu, modulus, precomp[1]->z);

      if (err == MP_OKAY)
        err = mp_mulmod(B->x, &mu, modulus, precomp[1<<2]->x);
      if (err == MP_OKAY)
        err = mp_mulmod(B->y, &mu, modulus, precomp[1<<2]->y);
      if (err == MP_OKAY)
        err = mp_mulmod(B->z, &mu, modulus, precomp[1<<2]->z);

      /* done with mu */
      mp_clear(&mu);
    }
  }

  if (err == MP_OKAY)
    /* precomp [i,0](A + B) table */
    err = ecc_projective_dbl_point(precomp[1], precomp[2], a, modulus, mp);

  if (err == MP_OKAY)
    err = ecc_projective_add_point(precomp[1], precomp[2], precomp[3],
                                   a, modulus, mp);
  if (err == MP_OKAY)
    /* precomp [0,i](A + B) table */
    err = ecc_projective_dbl_point(precomp[1<<2], precomp[2<<2], a, modulus, mp);

  if (err == MP_OKAY)
    err = ecc_projective_add_point(precomp[1<<2], precomp[2<<2], precomp[3<<2],
                                   a, modulus, mp);

  if (err == MP_OKAY) {
    /* precomp [i,j](A + B) table (i != 0, j != 0) */
    for (x = 1; x < 4; x++) {
        for (y = 1; y < 4; y++) {
            if (err == MP_OKAY)
                err = ecc_projective_add_point(precomp[x], precomp[(y<<2)],
                                               precomp[x+(y<<2)], a, modulus, mp);
        }
    }
  }

  if (err == MP_OKAY) {
    nibble  = 3;
    first   = 1;
    bitbufA = tA[0];
    bitbufB = tB[0];

    /* for every byte of the multiplicands */
    for (x = 0;; ) {
        /* grab a nibble */
        if (++nibble == 4) {
            if (x == (int)len) break;
            bitbufA = tA[x];
            bitbufB = tB[x];
            nibble  = 0;
            x++;
        }

        /* extract two bits from both, shift/update */
        nA = (bitbufA >> 6) & 0x03;
        nB = (bitbufB >> 6) & 0x03;
        bitbufA = (bitbufA << 2) & 0xFF;
        bitbufB = (bitbufB << 2) & 0xFF;

        /* if both zero, if first, continue */
        if ((nA == 0) && (nB == 0) && (first == 1)) {
            continue;
        }

        /* double twice, only if this isn't the first */
        if (first == 0) {
            /* double twice */
            if (err == MP_OKAY)
                err = ecc_projective_dbl_point(C, C, a, modulus, mp);
            if (err == MP_OKAY)
                err = ecc_projective_dbl_point(C, C, a, modulus, mp);
            else
                break;
        }

        /* if not both zero */
        if ((nA != 0) || (nB != 0)) {
            if (first == 1) {
                /* if first, copy from table */
                first = 0;
                if (err == MP_OKAY)
                    err = mp_copy(precomp[nA + (nB<<2)]->x, C->x);

                if (err == MP_OKAY)
                    err = mp_copy(precomp[nA + (nB<<2)]->y, C->y);

                if (err == MP_OKAY)
                    err = mp_copy(precomp[nA + (nB<<2)]->z, C->z);
                else
                    break;
            } else {
                /* if not first, add from table */
                if (err == MP_OKAY)
                    err = ecc_projective_add_point(C, precomp[nA + (nB<<2)], C,
                                                   a, modulus, mp);
                else
                    break;
            }
        }
    }
  }

  /* reduce to affine */
  if (err == MP_OKAY)
    err = ecc_map(C, modulus, mp);

  /* clean up */
  for (x = 0; x < 16; x++) {
     wc_ecc_del_point_h(precomp[x], heap);
  }

  ForceZero(tA, ECC_BUFSIZE);
  ForceZero(tB, ECC_BUFSIZE);
  XFREE(tA, heap, DYNAMIC_TYPE_TMP_BUFFER);
  XFREE(tB, heap, DYNAMIC_TYPE_TMP_BUFFER);

  return err;
}

#endif /* ECC_SHAMIR */


#ifdef HAVE_ECC_VERIFY
#ifndef NO_ASN
/* verify
 *
 * w  = s^-1 mod n
 * u1 = xw
 * u2 = rw
 * X = u1*G + u2*Q
 * v = X_x1 mod n
 * accept if v == r
 */

/**
 Verify an ECC signature
 sig         The signature to verify
 siglen      The length of the signature (octets)
 hash        The hash (message digest) that was signed
 hashlen     The length of the hash (octets)
 res         Result of signature, 1==valid, 0==invalid
 key         The corresponding public ECC key
 return      MP_OKAY if successful (even if the signature is not valid)
 */
int wc_ecc_verify_hash(const byte* sig, word32 siglen, const byte* hash,
                       word32 hashlen, int* res, ecc_key* key)
{
    int err;
    mp_int *r = NULL, *s = NULL;
#ifndef WOLFSSL_ASYNC_CRYPT
    mp_int r_lcl, s_lcl;
    r = &r_lcl;
    s = &s_lcl;
#endif

    if (sig == NULL || hash == NULL || res == NULL || key == NULL) {
        return ECC_BAD_ARG_E;
    }

    switch(key->state) {
        case ECC_STATE_NONE:
        case ECC_STATE_VERIFY_DECODE:
            key->state = ECC_STATE_VERIFY_DECODE;

            /* default to invalid signature */
            *res = 0;

            /* Note, DecodeECC_DSA_Sig() calls mp_init() on r and s.
             * If either of those don't allocate correctly, none of
             * the rest of this function will execute, and everything
             * gets cleaned up at the end. */
            err = wc_ecc_alloc_rs(key, &r, &s);
            if (err != 0)
                break;

            /* decode DSA header */
            err = DecodeECC_DSA_Sig(sig, siglen, r, s);
            if (err < 0) {
                break;
            }

            /* fall through */
        case ECC_STATE_VERIFY_DO:
            key->state = ECC_STATE_VERIFY_DO;

            err = wc_ecc_verify_hash_ex(r, s, hash, hashlen, res, key);
            if (err < 0) {
                break;
            }

            /* fall through */
        case ECC_STATE_VERIFY_RES:
            key->state = ECC_STATE_VERIFY_RES;
            err = 0;

        #ifdef WOLFSSL_ASYNC_CRYPT
            /* restore r/s */
            r = key->r;
            s = key->s;
        #endif

            /* done with R/S */
            mp_clear(r);
            mp_clear(s);
            break;

        default:
            err = BAD_STATE_E;
    }

    /* if async pending then return and skip done cleanup below */
    if (err == WC_PENDING_E) {
        key->state++;
        return err;
    }

    /* cleanup */
    wc_ecc_free_rs(key, &r, &s);
    key->state = ECC_STATE_NONE;

    return err;
}
#endif /* !NO_ASN */


/**
   Verify an ECC signature
   r           The signature R component to verify
   s           The signature S component to verify
   hash        The hash (message digest) that was signed
   hashlen     The length of the hash (octets)
   res         Result of signature, 1==valid, 0==invalid
   key         The corresponding public ECC key
   return      MP_OKAY if successful (even if the signature is not valid)
*/
int wc_ecc_verify_hash_ex(mp_int *r, mp_int *s, const byte* hash,
                    word32 hashlen, int* res, ecc_key* key)
{
   int           err;
#ifndef WOLFSSL_ATECC508A
   int          did_init = 0;
   ecc_point    *mG = NULL, *mQ = NULL;
   mp_int        v;
   mp_int        w;
   mp_int        u1;
   mp_int        u2;
   mp_int        e;
   DECLARE_CURVE_SPECS(ECC_CURVE_FIELD_COUNT)
#else
   byte sigRS[ATECC_KEY_SIZE*2];
#endif

   if (r == NULL || s == NULL || hash == NULL || res == NULL || key == NULL)
       return ECC_BAD_ARG_E;

   /* default to invalid signature */
   *res = 0;

   /* is the IDX valid ?  */
   if (wc_ecc_is_valid_idx(key->idx) != 1) {
      return ECC_BAD_ARG_E;
   }

#if defined(WOLFSSL_ASYNC_CRYPT) && defined(WC_ASYNC_ENABLE_ECC) && \
       defined(WOLFSSL_ASYNC_CRYPT_TEST)
    if (key->asyncDev.marker == WOLFSSL_ASYNC_MARKER_ECC) {
        WC_ASYNC_TEST* testDev = &key->asyncDev.test;
        if (testDev->type == ASYNC_TEST_NONE) {
            testDev->type = ASYNC_TEST_ECC_VERIFY;
            testDev->eccVerify.r = r;
            testDev->eccVerify.s = s;
            testDev->eccVerify.hash = hash;
            testDev->eccVerify.hashlen = hashlen;
            testDev->eccVerify.stat = res;
            testDev->eccVerify.key = key;
            return WC_PENDING_E;
        }
    }
#endif

#ifdef WOLFSSL_ATECC508A
    /* Extract R and S */
    err = mp_to_unsigned_bin(r, &sigRS[0]);
    if (err != MP_OKAY) {
        return err;
    }
    err = mp_to_unsigned_bin(s, &sigRS[ATECC_KEY_SIZE]);
    if (err != MP_OKAY) {
        return err;
    }

    err = atcatls_verify(hash, sigRS, key->pubkey, (bool*)res);
    if (err != ATCA_SUCCESS) {
       return BAD_COND_E;
   }

#else

   err = mp_init(&e);
   if (err != MP_OKAY)
      return MEMORY_E;

   /* read in the specs for this curve */
   err = wc_ecc_curve_load(key->dp, &curve, ECC_CURVE_FIELD_ALL);

   /* check for zero */
   if (err == MP_OKAY) {
       if (mp_iszero(r) == MP_YES || mp_iszero(s) == MP_YES ||
           mp_cmp(r, curve->order) != MP_LT ||
           mp_cmp(s, curve->order) != MP_LT) {
           err = MP_ZERO_E;
       }
   }

   /* read hash */
   if (err == MP_OKAY) {
       /* we may need to truncate if hash is longer than key size */
       unsigned int orderBits = mp_count_bits(curve->order);

       /* truncate down to byte size, may be all that's needed */
       if ( (WOLFSSL_BIT_SIZE * hashlen) > orderBits)
           hashlen = (orderBits + WOLFSSL_BIT_SIZE - 1) / WOLFSSL_BIT_SIZE;
       err = mp_read_unsigned_bin(&e, hash, hashlen);

       /* may still need bit truncation too */
       if (err == MP_OKAY && (WOLFSSL_BIT_SIZE * hashlen) > orderBits)
           mp_rshb(&e, WOLFSSL_BIT_SIZE - (orderBits & 0x7));
   }

   /* check for async hardware acceleration */
#if defined(WOLFSSL_ASYNC_CRYPT) && defined(WC_ASYNC_ENABLE_ECC)
   if (key->asyncDev.marker == WOLFSSL_ASYNC_MARKER_ECC) {
   #ifdef HAVE_CAVIUM
      /* TODO: Not implemented */
   #elif defined(HAVE_INTEL_QA)
      err = wc_mp_to_bigint(&e, &e.raw);
      if (err == MP_OKAY)
          err = wc_mp_to_bigint(key->pubkey.x, &key->pubkey.x->raw);
      if (err == MP_OKAY)
          err = wc_mp_to_bigint(key->pubkey.y, &key->pubkey.y->raw);
      if (err == MP_OKAY)
          err = IntelQaEcdsaVerify(&key->asyncDev, &e.raw, &key->pubkey.x->raw,
                &key->pubkey.y->raw, &r->raw, &s->raw, &curve->Af->raw,
                &curve->Bf->raw, &curve->prime->raw, &curve->order->raw,
                &curve->Gx->raw, &curve->Gy->raw, res);

      mp_clear(&e);

      wc_ecc_curve_free(curve);

      return err;
   #endif
   }
#endif /* WOLFSSL_ASYNC_CRYPT */

   /* allocate ints */
   if (err == MP_OKAY) {
       if ((err = mp_init_multi(&v, &w, &u1, &u2, NULL, NULL)) != MP_OKAY) {
          err = MEMORY_E;
       }
       did_init = 1;
   }

   /* allocate points */
   if (err == MP_OKAY) {
       mG = wc_ecc_new_point_h(key->heap);
       mQ = wc_ecc_new_point_h(key->heap);
       if (mQ  == NULL || mG == NULL)
          err = MEMORY_E;
   }

   /*  w  = s^-1 mod n */
   if (err == MP_OKAY)
       err = mp_invmod(s, curve->order, &w);

   /* u1 = ew */
   if (err == MP_OKAY)
       err = mp_mulmod(&e, &w, curve->order, &u1);

   /* u2 = rw */
   if (err == MP_OKAY)
       err = mp_mulmod(r, &w, curve->order, &u2);

   /* find mG and mQ */
   if (err == MP_OKAY)
       err = mp_copy(curve->Gx, mG->x);
   if (err == MP_OKAY)
       err = mp_copy(curve->Gy, mG->y);
   if (err == MP_OKAY)
       err = mp_set(mG->z, 1);

   if (err == MP_OKAY)
       err = mp_copy(key->pubkey.x, mQ->x);
   if (err == MP_OKAY)
       err = mp_copy(key->pubkey.y, mQ->y);
   if (err == MP_OKAY)
       err = mp_copy(key->pubkey.z, mQ->z);

#ifdef FREESCALE_LTC_ECC
   /* use PKHA to compute u1*mG + u2*mQ */
   if (err == MP_OKAY)
       err = wc_ecc_mulmod_ex(&u1, mG, mG, curve->Af, curve->prime, 0, key->heap);
   if (err == MP_OKAY)
       err = wc_ecc_mulmod_ex(&u2, mQ, mQ, curve->Af, curve->prime, 0, key->heap);
   if (err == MP_OKAY)
       err = wc_ecc_point_add(mG, mQ, mG, curve->prime);
#else /* FREESCALE_LTC_ECC */
#ifndef ECC_SHAMIR
    {
       mp_digit      mp;

       /* compute u1*mG + u2*mQ = mG */
       if (err == MP_OKAY)
           err = wc_ecc_mulmod_ex(&u1, mG, mG, curve->Af, curve->prime, 0, key->heap);
       if (err == MP_OKAY)
           err = wc_ecc_mulmod_ex(&u2, mQ, mQ, curve->Af, curve->prime, 0, key->heap);

       /* find the montgomery mp */
       if (err == MP_OKAY)
           err = mp_montgomery_setup(curve->prime, &mp);

       /* add them */
       if (err == MP_OKAY)
           err = ecc_projective_add_point(mQ, mG, mG, curve->Af,
                                                            curve->prime, mp);

       /* reduce */
       if (err == MP_OKAY)
           err = ecc_map(mG, curve->prime, mp);
    }
#else
       /* use Shamir's trick to compute u1*mG + u2*mQ using half the doubles */
       if (err == MP_OKAY)
           err = ecc_mul2add(mG, &u1, mQ, &u2, mG, curve->Af, curve->prime,
                                                                    key->heap);
#endif /* ECC_SHAMIR */
#endif /* FREESCALE_LTC_ECC */
   /* v = X_x1 mod n */
   if (err == MP_OKAY)
       err = mp_mod(mG->x, curve->order, &v);

   /* does v == r */
   if (err == MP_OKAY) {
       if (mp_cmp(&v, r) == MP_EQ)
           *res = 1;
   }

   /* cleanup */
   wc_ecc_del_point_h(mG, key->heap);
   wc_ecc_del_point_h(mQ, key->heap);

   mp_clear(&e);
   if (did_init) {
       mp_clear(&v);
       mp_clear(&w);
       mp_clear(&u1);
       mp_clear(&u2);
   }

   wc_ecc_curve_free(curve);

#endif /* WOLFSSL_ATECC508A */

   return err;
}
#endif /* HAVE_ECC_VERIFY */

#ifdef HAVE_ECC_KEY_IMPORT
#ifndef WOLFSSL_ATECC508A
/* import point from der */
int wc_ecc_import_point_der(byte* in, word32 inLen, const int curve_idx,
                            ecc_point* point)
{
    int err = 0;
    int compressed = 0;

    if (in == NULL || point == NULL || (curve_idx < 0) ||
        (wc_ecc_is_valid_idx(curve_idx) == 0))
        return ECC_BAD_ARG_E;

    /* must be odd */
    if ((inLen & 1) == 0) {
        return ECC_BAD_ARG_E;
    }

    /* init point */
#ifdef ALT_ECC_SIZE
    point->x = (mp_int*)&point->xyz[0];
    point->y = (mp_int*)&point->xyz[1];
    point->z = (mp_int*)&point->xyz[2];
    alt_fp_init(point->x);
    alt_fp_init(point->y);
    alt_fp_init(point->z);
#else
    err = mp_init_multi(point->x, point->y, point->z, NULL, NULL, NULL);
#endif
    if (err != MP_OKAY)
        return MEMORY_E;

    /* check for 4, 2, or 3 */
    if (in[0] != 0x04 && in[0] != 0x02 && in[0] != 0x03) {
        err = ASN_PARSE_E;
    }

    if (in[0] == 0x02 || in[0] == 0x03) {
#ifdef HAVE_COMP_KEY
        compressed = 1;
#else
        err = NOT_COMPILED_IN;
#endif
    }

    /* read data */
    if (err == MP_OKAY)
        err = mp_read_unsigned_bin(point->x, (byte*)in+1, (inLen-1)>>1);

#ifdef HAVE_COMP_KEY
    if (err == MP_OKAY && compressed == 1) {   /* build y */
        int did_init = 0;
        mp_int t1, t2;
        DECLARE_CURVE_SPECS(3)

        if (mp_init_multi(&t1, &t2, NULL, NULL, NULL, NULL) != MP_OKAY)
            err = MEMORY_E;
        else
            did_init = 1;

        /* load curve info */
        if (err == MP_OKAY)
            err = wc_ecc_curve_load(&ecc_sets[curve_idx], &curve,
                (ECC_CURVE_FIELD_PRIME | ECC_CURVE_FIELD_AF |
                    ECC_CURVE_FIELD_BF));

        /* compute x^3 */
        if (err == MP_OKAY)
            err = mp_sqr(point->x, &t1);
        if (err == MP_OKAY)
            err = mp_mulmod(&t1, point->x, curve->prime, &t1);

        /* compute x^3 + a*x */
        if (err == MP_OKAY)
            err = mp_mulmod(curve->Af, point->x, curve->prime, &t2);
        if (err == MP_OKAY)
            err = mp_add(&t1, &t2, &t1);

        /* compute x^3 + a*x + b */
        if (err == MP_OKAY)
            err = mp_add(&t1, curve->Bf, &t1);

        /* compute sqrt(x^3 + a*x + b) */
        if (err == MP_OKAY)
            err = mp_sqrtmod_prime(&t1, curve->prime, &t2);

        /* adjust y */
        if (err == MP_OKAY) {
            if ((mp_isodd(&t2) == MP_YES && in[0] == 0x03) ||
                (mp_isodd(&t2) == MP_NO && in[0] == 0x02)) {
                err = mp_mod(&t2, curve->prime, point->y);
            }
            else {
                err = mp_submod(curve->prime, &t2, curve->prime, point->y);
            }
        }

        if (did_init) {
            mp_clear(&t2);
            mp_clear(&t1);
        }

        wc_ecc_curve_free(curve);
    }
#endif

    if (err == MP_OKAY && compressed == 0)
        err = mp_read_unsigned_bin(point->y,
                                   (byte*)in+1+((inLen-1)>>1), (inLen-1)>>1);
    if (err == MP_OKAY)
        err = mp_set(point->z, 1);

    if (err != MP_OKAY) {
        mp_clear(point->x);
        mp_clear(point->y);
        mp_clear(point->z);
    }

    return err;
}
#endif /* !WOLFSSL_ATECC508A */
#endif /* HAVE_ECC_KEY_IMPORT */

#ifdef HAVE_ECC_KEY_EXPORT
/* export point to der */
int wc_ecc_export_point_der(const int curve_idx, ecc_point* point, byte* out,
                            word32* outLen)
{
    int    ret = MP_OKAY;
    word32 numlen;
#ifndef WOLFSSL_ATECC508A
#ifdef WOLFSSL_SMALL_STACK
    byte*  buf;
#else
    byte   buf[ECC_BUFSIZE];
#endif
#endif /* !WOLFSSL_ATECC508A */

    if ((curve_idx < 0) || (wc_ecc_is_valid_idx(curve_idx) == 0))
        return ECC_BAD_ARG_E;

    /* return length needed only */
    if (point != NULL && out == NULL && outLen != NULL) {
        numlen = ecc_sets[curve_idx].size;
        *outLen = 1 + 2*numlen;
        return LENGTH_ONLY_E;
    }

    if (point == NULL || out == NULL || outLen == NULL)
        return ECC_BAD_ARG_E;

    numlen = ecc_sets[curve_idx].size;

    if (*outLen < (1 + 2*numlen)) {
        *outLen = 1 + 2*numlen;
        return BUFFER_E;
    }

#ifdef WOLFSSL_ATECC508A
   /* TODO: Implement equiv call to ATECC508A */
   ret = BAD_COND_E;

#else

    /* store byte 0x04 */
    out[0] = 0x04;

#ifdef WOLFSSL_SMALL_STACK
    buf = (byte*)XMALLOC(ECC_BUFSIZE, NULL, DYNAMIC_TYPE_TMP_BUFFER);
    if (buf == NULL)
        return MEMORY_E;
#endif

    /* pad and store x */
    XMEMSET(buf, 0, ECC_BUFSIZE);
    ret = mp_to_unsigned_bin(point->x, buf +
                                 (numlen - mp_unsigned_bin_size(point->x)));
    if (ret != MP_OKAY)
        goto done;
    XMEMCPY(out+1, buf, numlen);

    /* pad and store y */
    XMEMSET(buf, 0, ECC_BUFSIZE);
    ret = mp_to_unsigned_bin(point->y, buf +
                                 (numlen - mp_unsigned_bin_size(point->y)));
    if (ret != MP_OKAY)
        goto done;
    XMEMCPY(out+1+numlen, buf, numlen);

    *outLen = 1 + 2*numlen;

done:
#ifdef WOLFSSL_SMALL_STACK
    XFREE(buf, NULL, DYNAMIC_TYPE_TMP_BUFFER);
#endif
#endif /* WOLFSSL_ATECC508A */

    return ret;
}


/* export public ECC key in ANSI X9.63 format */
int wc_ecc_export_x963(ecc_key* key, byte* out, word32* outLen)
{
   int    ret = MP_OKAY;
   word32 numlen;
#ifndef WOLFSSL_ATECC508A
#ifdef WOLFSSL_SMALL_STACK
   byte*  buf;
#else
   byte   buf[ECC_BUFSIZE];
#endif
   word32 pubxlen, pubylen;
#endif /* WOLFSSL_ATECC508A */

   /* return length needed only */
   if (key != NULL && out == NULL && outLen != NULL) {
      numlen = key->dp->size;
      *outLen = 1 + 2*numlen;
      return LENGTH_ONLY_E;
   }

   if (key == NULL || out == NULL || outLen == NULL)
      return ECC_BAD_ARG_E;

   if (wc_ecc_is_valid_idx(key->idx) == 0) {
      return ECC_BAD_ARG_E;
   }
   numlen = key->dp->size;

    /* verify room in out buffer */
   if (*outLen < (1 + 2*numlen)) {
      *outLen = 1 + 2*numlen;
      return BUFFER_E;
   }

#ifdef WOLFSSL_ATECC508A
   /* TODO: Implement equiv call to ATECC508A */
   ret = BAD_COND_E;

#else

   /* verify public key length is less than key size */
   pubxlen = mp_unsigned_bin_size(key->pubkey.x);
   pubylen = mp_unsigned_bin_size(key->pubkey.y);
   if ((pubxlen > numlen) || (pubylen > numlen)) {
      WOLFSSL_MSG("Public key x/y invalid!");
      return BUFFER_E;
   }

   /* store byte 0x04 */
   out[0] = 0x04;

#ifdef WOLFSSL_SMALL_STACK
   buf = (byte*)XMALLOC(ECC_BUFSIZE, NULL, DYNAMIC_TYPE_TMP_BUFFER);
   if (buf == NULL)
      return MEMORY_E;
#endif

   /* pad and store x */
   XMEMSET(buf, 0, ECC_BUFSIZE);
   ret = mp_to_unsigned_bin(key->pubkey.x, buf + (numlen - pubxlen));
   if (ret != MP_OKAY)
      goto done;
   XMEMCPY(out+1, buf, numlen);

   /* pad and store y */
   XMEMSET(buf, 0, ECC_BUFSIZE);
   ret = mp_to_unsigned_bin(key->pubkey.y, buf + (numlen - pubylen));
   if (ret != MP_OKAY)
      goto done;
   XMEMCPY(out+1+numlen, buf, numlen);

   *outLen = 1 + 2*numlen;

done:
#ifdef WOLFSSL_SMALL_STACK
   XFREE(buf, NULL, DYNAMIC_TYPE_TMP_BUFFER);
#endif
#endif /* WOLFSSL_ATECC508A */

   return ret;
}


/* export public ECC key in ANSI X9.63 format, extended with
 * compression option */
int wc_ecc_export_x963_ex(ecc_key* key, byte* out, word32* outLen,
                          int compressed)
{
    if (compressed == 0)
        return wc_ecc_export_x963(key, out, outLen);
#ifdef HAVE_COMP_KEY
    else
        return wc_ecc_export_x963_compressed(key, out, outLen);
#else
    return NOT_COMPILED_IN;
#endif
}
#endif /* HAVE_ECC_KEY_EXPORT */


#ifndef WOLFSSL_ATECC508A

/* is ecc point on curve described by dp ? */
int wc_ecc_is_point(ecc_point* ecp, mp_int* a, mp_int* b, mp_int* prime)
{
   int err;
   mp_int t1, t2;

   if ((err = mp_init_multi(&t1, &t2, NULL, NULL, NULL, NULL)) != MP_OKAY) {
      return err;
   }

   /* compute y^2 */
   if (err == MP_OKAY)
       err = mp_sqr(ecp->y, &t1);

   /* compute x^3 */
   if (err == MP_OKAY)
       err = mp_sqr(ecp->x, &t2);
   if (err == MP_OKAY)
       err = mp_mod(&t2, prime, &t2);
   if (err == MP_OKAY)
       err = mp_mul(ecp->x, &t2, &t2);

   /* compute y^2 - x^3 */
   if (err == MP_OKAY)
       err = mp_sub(&t1, &t2, &t1);

   /* Determine if curve "a" should be used in calc */
#ifdef WOLFSSL_CUSTOM_CURVES
   if (err == MP_OKAY) {
      /* Use a and prime to determine if a == 3 */
      err = mp_set(&t2, 0);
      if (err == MP_OKAY)
          err = mp_submod(prime, a, prime, &t2);
   }
   if (err == MP_OKAY && mp_cmp_d(&t2, 3) != MP_EQ) {
      /* compute y^2 - x^3 + a*x */
      if (err == MP_OKAY)
          err = mp_mulmod(&t2, ecp->x, prime, &t2);
      if (err == MP_OKAY)
          err = mp_addmod(&t1, &t2, prime, &t1);
   }
   else
#endif /* WOLFSSL_CUSTOM_CURVES */
   {
      /* assumes "a" == 3 */
      (void)a;

      /* compute y^2 - x^3 + 3x */
      if (err == MP_OKAY)
          err = mp_add(&t1, ecp->x, &t1);
      if (err == MP_OKAY)
          err = mp_add(&t1, ecp->x, &t1);
      if (err == MP_OKAY)
          err = mp_add(&t1, ecp->x, &t1);
      if (err == MP_OKAY)
          err = mp_mod(&t1, prime, &t1);
  }

   /* adjust range (0, prime) */
   while (err == MP_OKAY && mp_isneg(&t1)) {
      err = mp_add(&t1, prime, &t1);
   }
   while (err == MP_OKAY && mp_cmp(&t1, prime) != MP_LT) {
      err = mp_sub(&t1, prime, &t1);
   }

   /* compare to b */
   if (err == MP_OKAY) {
       if (mp_cmp(&t1, b) != MP_EQ) {
          err = MP_VAL;
       } else {
          err = MP_OKAY;
       }
   }

   mp_clear(&t1);
   mp_clear(&t2);

   return err;
}


/* validate privkey * generator == pubkey, 0 on success */
static int ecc_check_privkey_gen(ecc_key* key, mp_int* a, mp_int* prime)
{
    int        err = MP_OKAY;
    ecc_point* base = NULL;
    ecc_point* res  = NULL;
    DECLARE_CURVE_SPECS(2)

    if (key == NULL)
        return BAD_FUNC_ARG;

    base = wc_ecc_new_point_h(key->heap);
    if (base == NULL)
        return MEMORY_E;

    /* load curve info */
    err = wc_ecc_curve_load(key->dp, &curve,
                                    (ECC_CURVE_FIELD_GX | ECC_CURVE_FIELD_GY));

    /* set up base generator */
    if (err == MP_OKAY)
        err = mp_copy(curve->Gx, base->x);
    if (err == MP_OKAY)
        err = mp_copy(curve->Gy, base->y);
    if (err == MP_OKAY)
        err = mp_set(base->z, 1);

    if (err == MP_OKAY) {
        res = wc_ecc_new_point_h(key->heap);
        if (res == NULL)
            err = MEMORY_E;
        else {
            err = wc_ecc_mulmod_ex(&key->k, base, res, a, prime, 1, key->heap);
            if (err == MP_OKAY) {
                /* compare result to public key */
                if (mp_cmp(res->x, key->pubkey.x) != MP_EQ ||
                    mp_cmp(res->y, key->pubkey.y) != MP_EQ ||
                    mp_cmp(res->z, key->pubkey.z) != MP_EQ) {
                    /* didn't match */
                    err = ECC_PRIV_KEY_E;
                }
            }
        }
    }

    wc_ecc_curve_free(curve);
    wc_ecc_del_point_h(res, key->heap);
    wc_ecc_del_point_h(base, key->heap);

    return err;
}

#ifdef WOLFSSL_VALIDATE_ECC_IMPORT

/* check privkey generator helper, creates prime needed */
static int ecc_check_privkey_gen_helper(ecc_key* key)
{
    int    err;
#ifndef WOLFSSL_ATECC508A
    DECLARE_CURVE_SPECS(2)
#endif

    if (key == NULL)
        return BAD_FUNC_ARG;

#ifdef WOLFSSL_ATECC508A
    /* TODO: Implement equiv call to ATECC508A */
    err = BAD_COND_E;

#else

    /* load curve info */
    err = wc_ecc_curve_load(key->dp, &curve,
        (ECC_CURVE_FIELD_PRIME | ECC_CURVE_FIELD_AF));

    if (err == MP_OKAY)
        err = ecc_check_privkey_gen(key, curve->Af, curve->prime);

    wc_ecc_curve_free(curve);

#endif /* WOLFSSL_ATECC508A */

    return err;
}

#endif /* WOLFSSL_VALIDATE_ECC_IMPORT */


/* validate order * pubkey = point at infinity, 0 on success */
static int ecc_check_pubkey_order(ecc_key* key, mp_int* a, mp_int* prime,
    mp_int* order)
{
    ecc_point* inf = NULL;
    int        err;

    if (key == NULL)
        return BAD_FUNC_ARG;

    inf = wc_ecc_new_point_h(key->heap);
    if (inf == NULL)
        err = MEMORY_E;
    else {
    	err = wc_ecc_mulmod_ex(order, &key->pubkey, inf, a, prime, 1, key->heap);
        if (err == MP_OKAY && !wc_ecc_point_is_at_infinity(inf))
            err = ECC_INF_E;
    }

    wc_ecc_del_point_h(inf, key->heap);

    return err;
}

#endif /* !WOLFSSL_ATECC508A */


/* perform sanity checks on ecc key validity, 0 on success */
int wc_ecc_check_key(ecc_key* key)
{
    int    err;
#ifndef WOLFSSL_ATECC508A
    mp_int* b;
#ifdef USE_ECC_B_PARAM
    DECLARE_CURVE_SPECS(4)
#else
    mp_int b_lcl;
    DECLARE_CURVE_SPECS(3)
    b = &b_lcl;
    XMEMSET(b, 0, sizeof(mp_int));
#endif
#endif /* WOLFSSL_ATECC508A */

    if (key == NULL)
        return BAD_FUNC_ARG;

#ifdef WOLFSSL_ATECC508A
    /* TODO: Implement equiv call to ATECC508A */
    err = BAD_COND_E;

#else

    /* pubkey point cannot be at infinity */
    if (wc_ecc_point_is_at_infinity(&key->pubkey))
        return ECC_INF_E;

    /* load curve info */
    err = wc_ecc_curve_load(key->dp, &curve, (ECC_CURVE_FIELD_PRIME |
            ECC_CURVE_FIELD_AF | ECC_CURVE_FIELD_ORDER
#ifdef USE_ECC_B_PARAM
            | ECC_CURVE_FIELD_BF
#endif
    ));

#ifndef USE_ECC_B_PARAM
    /* load curve b parameter */
    if (err == MP_OKAY)
        err = mp_init(b);
    if (err == MP_OKAY)
        err = mp_read_radix(b, key->dp->Bf, 16);
#else
    b = curve->Bf;
#endif

    /* Qx must be in the range [0, p-1] */
    if (mp_cmp(key->pubkey.x, curve->prime) != MP_LT)
        err = ECC_OUT_OF_RANGE_E;

    /* Qy must be in the range [0, p-1] */
    if (mp_cmp(key->pubkey.y, curve->prime) != MP_LT)
        err = ECC_OUT_OF_RANGE_E;

    /* make sure point is actually on curve */
    if (err == MP_OKAY)
        err = wc_ecc_is_point(&key->pubkey, curve->Af, b, curve->prime);

    /* pubkey * order must be at infinity */
    if (err == MP_OKAY)
        err = ecc_check_pubkey_order(key, curve->Af, curve->prime, curve->order);

    /* private * base generator must equal pubkey */
    if (err == MP_OKAY && key->type == ECC_PRIVATEKEY)
        err = ecc_check_privkey_gen(key, curve->Af, curve->prime);

    wc_ecc_curve_free(curve);

#ifndef USE_ECC_B_PARAM
    mp_clear(b);
#endif

#endif /* WOLFSSL_ATECC508A */

    return err;
}

#ifdef HAVE_ECC_KEY_IMPORT
/* import public ECC key in ANSI X9.63 format */
int wc_ecc_import_x963_ex(const byte* in, word32 inLen, ecc_key* key,
                          int curve_id)
{
    int err = MP_OKAY;
#ifndef WOLFSSL_ATECC508A
    int compressed = 0;
#endif /* !WOLFSSL_ATECC508A */
    void* heap;

    if (in == NULL || key == NULL)
        return BAD_FUNC_ARG;

    /* must be odd */
    if ((inLen & 1) == 0) {
        return ECC_BAD_ARG_E;
    }

    heap = key->heap; /* save heap */
    XMEMSET(key, 0, sizeof(ecc_key));
    key->heap = heap; /* restore heap */

#ifdef WOLFSSL_ATECC508A
    /* TODO: Implement equiv call to ATECC508A */
    err = BAD_COND_E;

#else

    /* init key */
    #ifdef ALT_ECC_SIZE
        key->pubkey.x = (mp_int*)&key->pubkey.xyz[0];
        key->pubkey.y = (mp_int*)&key->pubkey.xyz[1];
        key->pubkey.z = (mp_int*)&key->pubkey.xyz[2];
        alt_fp_init(key->pubkey.x);
        alt_fp_init(key->pubkey.y);
        alt_fp_init(key->pubkey.z);
        err = mp_init(&key->k);
    #else
        err = mp_init_multi(&key->k,
                    key->pubkey.x, key->pubkey.y, key->pubkey.z, NULL, NULL);
    #endif
    if (err != MP_OKAY)
        return MEMORY_E;

    /* check for 4, 2, or 3 */
    if (in[0] != 0x04 && in[0] != 0x02 && in[0] != 0x03) {
        err = ASN_PARSE_E;
    }

    if (in[0] == 0x02 || in[0] == 0x03) {
    #ifdef HAVE_COMP_KEY
        compressed = 1;
    #else
        err = NOT_COMPILED_IN;
    #endif
    }

    if (err == MP_OKAY) {
        int keysize;
        /* adjust inLen if compressed */
        if (compressed)
            inLen = (inLen-1)*2 + 1;  /* used uncompressed len */

        /* determine key size */
        keysize = ((inLen-1)>>1);
        err = wc_ecc_set_curve(key, keysize, curve_id);
        key->type = ECC_PUBLICKEY;
    }

    /* read data */
    if (err == MP_OKAY)
        err = mp_read_unsigned_bin(key->pubkey.x, (byte*)in+1, (inLen-1)>>1);

#ifdef HAVE_COMP_KEY
    if (err == MP_OKAY && compressed == 1) {   /* build y */
        mp_int t1, t2;
        int did_init = 0;

        DECLARE_CURVE_SPECS(3)

        if (mp_init_multi(&t1, &t2, NULL, NULL, NULL, NULL) != MP_OKAY)
            err = MEMORY_E;
        else
            did_init = 1;

        /* load curve info */
        if (err == MP_OKAY)
            err = wc_ecc_curve_load(key->dp, &curve,
                (ECC_CURVE_FIELD_PRIME | ECC_CURVE_FIELD_AF |
                 ECC_CURVE_FIELD_BF));

        /* compute x^3 */
        if (err == MP_OKAY)
            err = mp_sqr(key->pubkey.x, &t1);
        if (err == MP_OKAY)
            err = mp_mulmod(&t1, key->pubkey.x, curve->prime, &t1);

        /* compute x^3 + a*x */
        if (err == MP_OKAY)
            err = mp_mulmod(curve->Af, key->pubkey.x, curve->prime, &t2);
        if (err == MP_OKAY)
            err = mp_add(&t1, &t2, &t1);

        /* compute x^3 + a*x + b */
        if (err == MP_OKAY)
            err = mp_add(&t1, curve->Bf, &t1);

        /* compute sqrt(x^3 + a*x + b) */
        if (err == MP_OKAY)
            err = mp_sqrtmod_prime(&t1, curve->prime, &t2);

        /* adjust y */
        if (err == MP_OKAY) {
            if ((mp_isodd(&t2) == MP_YES && in[0] == 0x03) ||
                (mp_isodd(&t2) == MP_NO && in[0] == 0x02)) {
                err = mp_mod(&t2, curve->prime, &t2);
            }
            else {
                err = mp_submod(curve->prime, &t2, curve->prime, &t2);
            }
            if (err == MP_OKAY)
                err = mp_copy(&t2, key->pubkey.y);
        }

        if (did_init) {
            mp_clear(&t2);
            mp_clear(&t1);
        }

        wc_ecc_curve_free(curve);
    }
#endif /* HAVE_COMP_KEY */

    if (err == MP_OKAY && compressed == 0)
        err = mp_read_unsigned_bin(key->pubkey.y, (byte*)in+1+((inLen-1)>>1),
                                                                (inLen-1)>>1);
    if (err == MP_OKAY)
        err = mp_set(key->pubkey.z, 1);

#ifdef WOLFSSL_VALIDATE_ECC_IMPORT
    if (err == MP_OKAY)
        err = wc_ecc_check_key(key);
#endif

    if (err != MP_OKAY) {
        mp_clear(key->pubkey.x);
        mp_clear(key->pubkey.y);
        mp_clear(key->pubkey.z);
        mp_clear(&key->k);
    }
#endif /* WOLFSSL_ATECC508A */

    return err;
}

int wc_ecc_import_x963(const byte* in, word32 inLen, ecc_key* key)
{
    return wc_ecc_import_x963_ex(in, inLen, key, ECC_CURVE_DEF);
}
#endif /* HAVE_ECC_KEY_IMPORT */

#ifdef HAVE_ECC_KEY_EXPORT
/* export ecc private key only raw, outLen is in/out size
   return MP_OKAY on success */
int wc_ecc_export_private_only(ecc_key* key, byte* out, word32* outLen)
{
    word32 numlen;

    if (key == NULL || out == NULL || outLen == NULL) {
        return BAD_FUNC_ARG;
    }

    if (wc_ecc_is_valid_idx(key->idx) == 0) {
        return ECC_BAD_ARG_E;
    }
    numlen = key->dp->size;

    if (*outLen < numlen) {
        *outLen = numlen;
        return BUFFER_E;
    }
    *outLen = numlen;
    XMEMSET(out, 0, *outLen);

#ifdef WOLFSSL_ATECC508A
   /* TODO: Implement equiv call to ATECC508A */
   return BAD_COND_E;

#else

    return mp_to_unsigned_bin(&key->k, out + (numlen -
                                           mp_unsigned_bin_size(&key->k)));
#endif /* WOLFSSL_ATECC508A */
}


/* export ecc key to component form, d is optional if only exporting public
 * return MP_OKAY on success */
static int wc_ecc_export_raw(ecc_key* key, byte* qx, word32* qxLen,
                             byte* qy, word32* qyLen, byte* d, word32* dLen)
{
    int  err;
    byte exportPriv = 0;
    word32 numLen;

    if (key == NULL || qx == NULL || qxLen == NULL || qy == NULL ||
        qyLen == NULL) {
        return BAD_FUNC_ARG;
    }

    if (wc_ecc_is_valid_idx(key->idx) == 0) {
        return ECC_BAD_ARG_E;
    }
    numLen = key->dp->size;

    if (d != NULL) {
        if (dLen == NULL || key->type != ECC_PRIVATEKEY)
            return BAD_FUNC_ARG;
        exportPriv = 1;
    }

    /* check public buffer sizes */
    if ((*qxLen < numLen) || (*qyLen < numLen)) {
        *qxLen = numLen;
        *qyLen = numLen;
        return BUFFER_E;
    }

    *qxLen = numLen;
    *qyLen = numLen;

    XMEMSET(qx, 0, *qxLen);
    XMEMSET(qy, 0, *qyLen);

    /* private d component */
    if (exportPriv == 1) {

        /* check private buffer size */
        if (*dLen < numLen) {
            *dLen = numLen;
            return BUFFER_E;
        }

        *dLen = numLen;
        XMEMSET(d, 0, *dLen);

        /* private key, d */
        err = mp_to_unsigned_bin(&key->k, d +
                            (numLen - mp_unsigned_bin_size(&key->k)));
        if (err != MP_OKAY)
            return err;
    }

    /* public x component */
    err = mp_to_unsigned_bin(key->pubkey.x, qx +
                            (numLen - mp_unsigned_bin_size(key->pubkey.x)));
    if (err != MP_OKAY)
        return err;

    /* public y component */
    err = mp_to_unsigned_bin(key->pubkey.y, qy +
                            (numLen - mp_unsigned_bin_size(key->pubkey.y)));
    if (err != MP_OKAY)
        return err;

    return 0;
}


/* export public key to raw elements including public (Qx,Qy)
 * return MP_OKAY on success, negative on error */
int wc_ecc_export_public_raw(ecc_key* key, byte* qx, word32* qxLen,
                             byte* qy, word32* qyLen)
{
    return wc_ecc_export_raw(key, qx, qxLen, qy, qyLen, NULL, NULL);
}


/* export ecc key to raw elements including public (Qx,Qy) and private (d)
 * return MP_OKAY on success, negative on error */
int wc_ecc_export_private_raw(ecc_key* key, byte* qx, word32* qxLen,
                              byte* qy, word32* qyLen, byte* d, word32* dLen)
{
    /* sanitize d and dLen, other args are checked later */
    if (d == NULL || dLen == NULL)
        return BAD_FUNC_ARG;

    return wc_ecc_export_raw(key, qx, qxLen, qy, qyLen, d, dLen);
}

#endif /* HAVE_ECC_KEY_EXPORT */

#ifdef HAVE_ECC_KEY_IMPORT
/* import private key, public part optional if (pub) passed as NULL */
int wc_ecc_import_private_key_ex(const byte* priv, word32 privSz,
                                 const byte* pub, word32 pubSz, ecc_key* key,
                                 int curve_id)
{
    int ret;

    /* public optional, NULL if only importing private */
    if (pub != NULL) {

        ret = wc_ecc_import_x963_ex(pub, pubSz, key, curve_id);

    } else {

        if (key == NULL || priv == NULL)
            return BAD_FUNC_ARG;

        /* make sure required key variables are reset */
        key->state = ECC_STATE_NONE;
        key->idx = 0;
        key->dp = NULL;

        /* set key size */
        ret = wc_ecc_set_curve(key, privSz, curve_id);
    }

    if (ret != 0)
        return ret;

    key->type = ECC_PRIVATEKEY;

#ifdef WOLFSSL_ATECC508A
    /* TODO: Implement equiv call to ATECC508A */
    return BAD_COND_E;

#else

    ret = mp_read_unsigned_bin(&key->k, priv, privSz);

#endif /* WOLFSSL_ATECC508A */

#ifdef WOLFSSL_VALIDATE_ECC_IMPORT
    if (ret == MP_OKAY)
        ret = ecc_check_privkey_gen_helper(key);
#endif

    return ret;
}

/* ecc private key import, public key in ANSI X9.63 format, private raw */
int wc_ecc_import_private_key(const byte* priv, word32 privSz, const byte* pub,
                           word32 pubSz, ecc_key* key)
{
    return wc_ecc_import_private_key_ex(priv, privSz, pub, pubSz, key,
                                                                ECC_CURVE_DEF);
}
#endif /* HAVE_ECC_KEY_IMPORT */

#ifndef NO_ASN
/**
   Convert ECC R,S to signature
   r       R component of signature
   s       S component of signature
   out     DER-encoded ECDSA signature
   outlen  [in/out] output buffer size, output signature size
   return  MP_OKAY on success
*/
int wc_ecc_rs_to_sig(const char* r, const char* s, byte* out, word32* outlen)
{
    int err;
    mp_int rtmp;
    mp_int stmp;

    if (r == NULL || s == NULL || out == NULL || outlen == NULL)
        return ECC_BAD_ARG_E;

    err = mp_init_multi(&rtmp, &stmp, NULL, NULL, NULL, NULL);
    if (err != MP_OKAY)
        return err;

    err = mp_read_radix(&rtmp, r, 16);
    if (err == MP_OKAY)
        err = mp_read_radix(&stmp, s, 16);

    /* convert mp_ints to ECDSA sig, initializes rtmp and stmp internally */
    if (err == MP_OKAY)
        err = StoreECC_DSA_Sig(out, outlen, &rtmp, &stmp);

    if (err == MP_OKAY) {
        if (mp_iszero(&rtmp) == MP_YES || mp_iszero(&stmp) == MP_YES)
            err = MP_ZERO_E;
    }

    mp_clear(&rtmp);
    mp_clear(&stmp);

    return err;
}


/**
   Convert ECC signature to R,S
   sig     DER-encoded ECDSA signature
   sigLen  length of signature in octets
   r       R component of signature
   rLen    [in/out] output "r" buffer size, output "r" size
   s       S component of signature
   sLen    [in/out] output "s" buffer size, output "s" size
   return  MP_OKAY on success, negative on error
*/
int wc_ecc_sig_to_rs(const byte* sig, word32 sigLen, byte* r, word32* rLen,
                     byte* s, word32* sLen)
{
    int err;
    word32 x = 0;
    mp_int rtmp;
    mp_int stmp;

    if (sig == NULL || r == NULL || rLen == NULL || s == NULL || sLen == NULL)
        return ECC_BAD_ARG_E;

    err = DecodeECC_DSA_Sig(sig, sigLen, &rtmp, &stmp);

    /* extract r */
    if (err == MP_OKAY) {
        x = mp_unsigned_bin_size(&rtmp);
        if (*rLen < x)
            err = BUFFER_E;

        if (err == MP_OKAY) {
            *rLen = x;
            err = mp_to_unsigned_bin(&rtmp, r);
        }
    }

    /* extract s */
    if (err == MP_OKAY) {
        x = mp_unsigned_bin_size(&stmp);
        if (*sLen < x)
            err = BUFFER_E;

        if (err == MP_OKAY) {
            *sLen = x;
            err = mp_to_unsigned_bin(&stmp, s);
        }
    }

    mp_clear(&rtmp);
    mp_clear(&stmp);

    return err;
}
#endif /* !NO_ASN */

#ifdef HAVE_ECC_KEY_IMPORT
static int wc_ecc_import_raw_private(ecc_key* key, const char* qx,
          const char* qy, const char* d, int curve_id)
{
    int err = MP_OKAY;
    void* heap;

    /* if d is NULL, only import as public key using Qx,Qy */
    if (key == NULL || qx == NULL || qy == NULL) {
        return BAD_FUNC_ARG;
    }

    heap = key->heap; /* save heap */
    XMEMSET(key, 0, sizeof(ecc_key));
    key->heap = heap; /* restore heap */

    /* set curve type and index */
    err = wc_ecc_set_curve(key, 0, curve_id);
    if (err != 0) {
        return err;
    }

#ifdef WOLFSSL_ATECC508A
    /* TODO: Implement equiv call to ATECC508A */
    err = BAD_COND_E;

#else

    /* init key */
#ifdef ALT_ECC_SIZE
    key->pubkey.x = (mp_int*)&key->pubkey.xyz[0];
    key->pubkey.y = (mp_int*)&key->pubkey.xyz[1];
    key->pubkey.z = (mp_int*)&key->pubkey.xyz[2];
    alt_fp_init(key->pubkey.x);
    alt_fp_init(key->pubkey.y);
    alt_fp_init(key->pubkey.z);
    err = mp_init(&key->k);
#else
    err = mp_init_multi(&key->k, key->pubkey.x, key->pubkey.y, key->pubkey.z,
                                                                  NULL, NULL);
#endif
    if (err != MP_OKAY)
        return MEMORY_E;

    /* read Qx */
    if (err == MP_OKAY)
        err = mp_read_radix(key->pubkey.x, qx, 16);

    /* read Qy */
    if (err == MP_OKAY)
        err = mp_read_radix(key->pubkey.y, qy, 16);

    if (err == MP_OKAY)
        err = mp_set(key->pubkey.z, 1);

    /* import private key */
    if (err == MP_OKAY) {
        if (d != NULL) {
            key->type = ECC_PRIVATEKEY;
            err = mp_read_radix(&key->k, d, 16);
        } else {
            key->type = ECC_PUBLICKEY;
        }
    }

#ifdef WOLFSSL_VALIDATE_ECC_IMPORT
    if (err == MP_OKAY)
        err = wc_ecc_check_key(key);
#endif

    if (err != MP_OKAY) {
        mp_clear(key->pubkey.x);
        mp_clear(key->pubkey.y);
        mp_clear(key->pubkey.z);
        mp_clear(&key->k);
    }
#endif /* WOLFSSL_ATECC508A */

    return err;
}

/**
   Import raw ECC key
   key       The destination ecc_key structure
   qx        x component of the public key, as ASCII hex string
   qy        y component of the public key, as ASCII hex string
   d         private key, as ASCII hex string, optional if importing public
             key only
   dp        Custom ecc_set_type
   return    MP_OKAY on success
*/
int wc_ecc_import_raw_ex(ecc_key* key, const char* qx, const char* qy,
                   const char* d, int curve_id)
{
    return wc_ecc_import_raw_private(key, qx, qy, d, curve_id);

}

/**
   Import raw ECC key
   key       The destination ecc_key structure
   qx        x component of the public key, as ASCII hex string
   qy        y component of the public key, as ASCII hex string
   d         private key, as ASCII hex string, optional if importing public
             key only
   curveName ECC curve name, from ecc_sets[]
   return    MP_OKAY on success
*/
int wc_ecc_import_raw(ecc_key* key, const char* qx, const char* qy,
                   const char* d, const char* curveName)
{
    int err, x;

    /* if d is NULL, only import as public key using Qx,Qy */
    if (key == NULL || qx == NULL || qy == NULL || curveName == NULL) {
        return BAD_FUNC_ARG;
    }

    /* set curve type and index */
    for (x = 0; ecc_sets[x].size != 0; x++) {
        if (XSTRNCMP(ecc_sets[x].name, curveName,
                     XSTRLEN(curveName)) == 0) {
            break;
        }
    }

    if (ecc_sets[x].size == 0) {
        WOLFSSL_MSG("ecc_set curve name not found");
        err = ASN_PARSE_E;
    } else {
        return wc_ecc_import_raw_private(key, qx, qy, d, ecc_sets[x].id);
    }

    return err;
}
#endif /* HAVE_ECC_KEY_IMPORT */

/* key size in octets */
int wc_ecc_size(ecc_key* key)
{
    if (key == NULL) return 0;

    return key->dp->size;
}


/* worst case estimate, check actual return from wc_ecc_sign_hash for actual
   value of signature size in octets */
int wc_ecc_sig_size(ecc_key* key)
{
    int sz = wc_ecc_size(key);
    if (sz <= 0)
        return sz;

    return (sz * 2) + SIG_HEADER_SZ + ECC_MAX_PAD_SZ;
}


#ifdef FP_ECC

/* fixed point ECC cache */
/* number of entries in the cache */
#ifndef FP_ENTRIES
    #define FP_ENTRIES 15
#endif

/* number of bits in LUT */
#ifndef FP_LUT
    #define FP_LUT     8U
#endif

#ifdef ECC_SHAMIR
    /* Sharmir requires a bigger LUT, TAO */
    #if (FP_LUT > 12) || (FP_LUT < 4)
        #error FP_LUT must be between 4 and 12 inclusively
    #endif
#else
    #if (FP_LUT > 12) || (FP_LUT < 2)
        #error FP_LUT must be between 2 and 12 inclusively
    #endif
#endif


/** Our FP cache */
typedef struct {
   ecc_point* g;               /* cached COPY of base point */
   ecc_point* LUT[1U<<FP_LUT]; /* fixed point lookup */
   mp_int     mu;              /* copy of the montgomery constant */
   int        lru_count;       /* amount of times this entry has been used */
   int        lock;            /* flag to indicate cache eviction */
                               /* permitted (0) or not (1) */
} fp_cache_t;

/* if HAVE_THREAD_LS this cache is per thread, no locking needed */
static THREAD_LS_T fp_cache_t fp_cache[FP_ENTRIES];

#ifndef HAVE_THREAD_LS
    static volatile int initMutex = 0;  /* prevent multiple mutex inits */
    static wolfSSL_Mutex ecc_fp_lock;
#endif /* HAVE_THREAD_LS */

/* simple table to help direct the generation of the LUT */
static const struct {
   int ham, terma, termb;
} lut_orders[] = {
   { 0, 0, 0 }, { 1, 0, 0 }, { 1, 0, 0 }, { 2, 1, 2 }, { 1, 0, 0 }, { 2, 1, 4 }, { 2, 2, 4 }, { 3, 3, 4 },
   { 1, 0, 0 }, { 2, 1, 8 }, { 2, 2, 8 }, { 3, 3, 8 }, { 2, 4, 8 }, { 3, 5, 8 }, { 3, 6, 8 }, { 4, 7, 8 },
   { 1, 0, 0 }, { 2, 1, 16 }, { 2, 2, 16 }, { 3, 3, 16 }, { 2, 4, 16 }, { 3, 5, 16 }, { 3, 6, 16 }, { 4, 7, 16 },
   { 2, 8, 16 }, { 3, 9, 16 }, { 3, 10, 16 }, { 4, 11, 16 }, { 3, 12, 16 }, { 4, 13, 16 }, { 4, 14, 16 }, { 5, 15, 16 },
   { 1, 0, 0 }, { 2, 1, 32 }, { 2, 2, 32 }, { 3, 3, 32 }, { 2, 4, 32 }, { 3, 5, 32 }, { 3, 6, 32 }, { 4, 7, 32 },
   { 2, 8, 32 }, { 3, 9, 32 }, { 3, 10, 32 }, { 4, 11, 32 }, { 3, 12, 32 }, { 4, 13, 32 }, { 4, 14, 32 }, { 5, 15, 32 },
   { 2, 16, 32 }, { 3, 17, 32 }, { 3, 18, 32 }, { 4, 19, 32 }, { 3, 20, 32 }, { 4, 21, 32 }, { 4, 22, 32 }, { 5, 23, 32 },
   { 3, 24, 32 }, { 4, 25, 32 }, { 4, 26, 32 }, { 5, 27, 32 }, { 4, 28, 32 }, { 5, 29, 32 }, { 5, 30, 32 }, { 6, 31, 32 },
#if FP_LUT > 6
   { 1, 0, 0 }, { 2, 1, 64 }, { 2, 2, 64 }, { 3, 3, 64 }, { 2, 4, 64 }, { 3, 5, 64 }, { 3, 6, 64 }, { 4, 7, 64 },
   { 2, 8, 64 }, { 3, 9, 64 }, { 3, 10, 64 }, { 4, 11, 64 }, { 3, 12, 64 }, { 4, 13, 64 }, { 4, 14, 64 }, { 5, 15, 64 },
   { 2, 16, 64 }, { 3, 17, 64 }, { 3, 18, 64 }, { 4, 19, 64 }, { 3, 20, 64 }, { 4, 21, 64 }, { 4, 22, 64 }, { 5, 23, 64 },
   { 3, 24, 64 }, { 4, 25, 64 }, { 4, 26, 64 }, { 5, 27, 64 }, { 4, 28, 64 }, { 5, 29, 64 }, { 5, 30, 64 }, { 6, 31, 64 },
   { 2, 32, 64 }, { 3, 33, 64 }, { 3, 34, 64 }, { 4, 35, 64 }, { 3, 36, 64 }, { 4, 37, 64 }, { 4, 38, 64 }, { 5, 39, 64 },
   { 3, 40, 64 }, { 4, 41, 64 }, { 4, 42, 64 }, { 5, 43, 64 }, { 4, 44, 64 }, { 5, 45, 64 }, { 5, 46, 64 }, { 6, 47, 64 },
   { 3, 48, 64 }, { 4, 49, 64 }, { 4, 50, 64 }, { 5, 51, 64 }, { 4, 52, 64 }, { 5, 53, 64 }, { 5, 54, 64 }, { 6, 55, 64 },
   { 4, 56, 64 }, { 5, 57, 64 }, { 5, 58, 64 }, { 6, 59, 64 }, { 5, 60, 64 }, { 6, 61, 64 }, { 6, 62, 64 }, { 7, 63, 64 },
#if FP_LUT > 7
   { 1, 0, 0 }, { 2, 1, 128 }, { 2, 2, 128 }, { 3, 3, 128 }, { 2, 4, 128 }, { 3, 5, 128 }, { 3, 6, 128 }, { 4, 7, 128 },
   { 2, 8, 128 }, { 3, 9, 128 }, { 3, 10, 128 }, { 4, 11, 128 }, { 3, 12, 128 }, { 4, 13, 128 }, { 4, 14, 128 }, { 5, 15, 128 },
   { 2, 16, 128 }, { 3, 17, 128 }, { 3, 18, 128 }, { 4, 19, 128 }, { 3, 20, 128 }, { 4, 21, 128 }, { 4, 22, 128 }, { 5, 23, 128 },
   { 3, 24, 128 }, { 4, 25, 128 }, { 4, 26, 128 }, { 5, 27, 128 }, { 4, 28, 128 }, { 5, 29, 128 }, { 5, 30, 128 }, { 6, 31, 128 },
   { 2, 32, 128 }, { 3, 33, 128 }, { 3, 34, 128 }, { 4, 35, 128 }, { 3, 36, 128 }, { 4, 37, 128 }, { 4, 38, 128 }, { 5, 39, 128 },
   { 3, 40, 128 }, { 4, 41, 128 }, { 4, 42, 128 }, { 5, 43, 128 }, { 4, 44, 128 }, { 5, 45, 128 }, { 5, 46, 128 }, { 6, 47, 128 },
   { 3, 48, 128 }, { 4, 49, 128 }, { 4, 50, 128 }, { 5, 51, 128 }, { 4, 52, 128 }, { 5, 53, 128 }, { 5, 54, 128 }, { 6, 55, 128 },
   { 4, 56, 128 }, { 5, 57, 128 }, { 5, 58, 128 }, { 6, 59, 128 }, { 5, 60, 128 }, { 6, 61, 128 }, { 6, 62, 128 }, { 7, 63, 128 },
   { 2, 64, 128 }, { 3, 65, 128 }, { 3, 66, 128 }, { 4, 67, 128 }, { 3, 68, 128 }, { 4, 69, 128 }, { 4, 70, 128 }, { 5, 71, 128 },
   { 3, 72, 128 }, { 4, 73, 128 }, { 4, 74, 128 }, { 5, 75, 128 }, { 4, 76, 128 }, { 5, 77, 128 }, { 5, 78, 128 }, { 6, 79, 128 },
   { 3, 80, 128 }, { 4, 81, 128 }, { 4, 82, 128 }, { 5, 83, 128 }, { 4, 84, 128 }, { 5, 85, 128 }, { 5, 86, 128 }, { 6, 87, 128 },
   { 4, 88, 128 }, { 5, 89, 128 }, { 5, 90, 128 }, { 6, 91, 128 }, { 5, 92, 128 }, { 6, 93, 128 }, { 6, 94, 128 }, { 7, 95, 128 },
   { 3, 96, 128 }, { 4, 97, 128 }, { 4, 98, 128 }, { 5, 99, 128 }, { 4, 100, 128 }, { 5, 101, 128 }, { 5, 102, 128 }, { 6, 103, 128 },
   { 4, 104, 128 }, { 5, 105, 128 }, { 5, 106, 128 }, { 6, 107, 128 }, { 5, 108, 128 }, { 6, 109, 128 }, { 6, 110, 128 }, { 7, 111, 128 },
   { 4, 112, 128 }, { 5, 113, 128 }, { 5, 114, 128 }, { 6, 115, 128 }, { 5, 116, 128 }, { 6, 117, 128 }, { 6, 118, 128 }, { 7, 119, 128 },
   { 5, 120, 128 }, { 6, 121, 128 }, { 6, 122, 128 }, { 7, 123, 128 }, { 6, 124, 128 }, { 7, 125, 128 }, { 7, 126, 128 }, { 8, 127, 128 },
#if FP_LUT > 8
   { 1, 0, 0 }, { 2, 1, 256 }, { 2, 2, 256 }, { 3, 3, 256 }, { 2, 4, 256 }, { 3, 5, 256 }, { 3, 6, 256 }, { 4, 7, 256 },
   { 2, 8, 256 }, { 3, 9, 256 }, { 3, 10, 256 }, { 4, 11, 256 }, { 3, 12, 256 }, { 4, 13, 256 }, { 4, 14, 256 }, { 5, 15, 256 },
   { 2, 16, 256 }, { 3, 17, 256 }, { 3, 18, 256 }, { 4, 19, 256 }, { 3, 20, 256 }, { 4, 21, 256 }, { 4, 22, 256 }, { 5, 23, 256 },
   { 3, 24, 256 }, { 4, 25, 256 }, { 4, 26, 256 }, { 5, 27, 256 }, { 4, 28, 256 }, { 5, 29, 256 }, { 5, 30, 256 }, { 6, 31, 256 },
   { 2, 32, 256 }, { 3, 33, 256 }, { 3, 34, 256 }, { 4, 35, 256 }, { 3, 36, 256 }, { 4, 37, 256 }, { 4, 38, 256 }, { 5, 39, 256 },
   { 3, 40, 256 }, { 4, 41, 256 }, { 4, 42, 256 }, { 5, 43, 256 }, { 4, 44, 256 }, { 5, 45, 256 }, { 5, 46, 256 }, { 6, 47, 256 },
   { 3, 48, 256 }, { 4, 49, 256 }, { 4, 50, 256 }, { 5, 51, 256 }, { 4, 52, 256 }, { 5, 53, 256 }, { 5, 54, 256 }, { 6, 55, 256 },
   { 4, 56, 256 }, { 5, 57, 256 }, { 5, 58, 256 }, { 6, 59, 256 }, { 5, 60, 256 }, { 6, 61, 256 }, { 6, 62, 256 }, { 7, 63, 256 },
   { 2, 64, 256 }, { 3, 65, 256 }, { 3, 66, 256 }, { 4, 67, 256 }, { 3, 68, 256 }, { 4, 69, 256 }, { 4, 70, 256 }, { 5, 71, 256 },
   { 3, 72, 256 }, { 4, 73, 256 }, { 4, 74, 256 }, { 5, 75, 256 }, { 4, 76, 256 }, { 5, 77, 256 }, { 5, 78, 256 }, { 6, 79, 256 },
   { 3, 80, 256 }, { 4, 81, 256 }, { 4, 82, 256 }, { 5, 83, 256 }, { 4, 84, 256 }, { 5, 85, 256 }, { 5, 86, 256 }, { 6, 87, 256 },
   { 4, 88, 256 }, { 5, 89, 256 }, { 5, 90, 256 }, { 6, 91, 256 }, { 5, 92, 256 }, { 6, 93, 256 }, { 6, 94, 256 }, { 7, 95, 256 },
   { 3, 96, 256 }, { 4, 97, 256 }, { 4, 98, 256 }, { 5, 99, 256 }, { 4, 100, 256 }, { 5, 101, 256 }, { 5, 102, 256 }, { 6, 103, 256 },
   { 4, 104, 256 }, { 5, 105, 256 }, { 5, 106, 256 }, { 6, 107, 256 }, { 5, 108, 256 }, { 6, 109, 256 }, { 6, 110, 256 }, { 7, 111, 256 },
   { 4, 112, 256 }, { 5, 113, 256 }, { 5, 114, 256 }, { 6, 115, 256 }, { 5, 116, 256 }, { 6, 117, 256 }, { 6, 118, 256 }, { 7, 119, 256 },
   { 5, 120, 256 }, { 6, 121, 256 }, { 6, 122, 256 }, { 7, 123, 256 }, { 6, 124, 256 }, { 7, 125, 256 }, { 7, 126, 256 }, { 8, 127, 256 },
   { 2, 128, 256 }, { 3, 129, 256 }, { 3, 130, 256 }, { 4, 131, 256 }, { 3, 132, 256 }, { 4, 133, 256 }, { 4, 134, 256 }, { 5, 135, 256 },
   { 3, 136, 256 }, { 4, 137, 256 }, { 4, 138, 256 }, { 5, 139, 256 }, { 4, 140, 256 }, { 5, 141, 256 }, { 5, 142, 256 }, { 6, 143, 256 },
   { 3, 144, 256 }, { 4, 145, 256 }, { 4, 146, 256 }, { 5, 147, 256 }, { 4, 148, 256 }, { 5, 149, 256 }, { 5, 150, 256 }, { 6, 151, 256 },
   { 4, 152, 256 }, { 5, 153, 256 }, { 5, 154, 256 }, { 6, 155, 256 }, { 5, 156, 256 }, { 6, 157, 256 }, { 6, 158, 256 }, { 7, 159, 256 },
   { 3, 160, 256 }, { 4, 161, 256 }, { 4, 162, 256 }, { 5, 163, 256 }, { 4, 164, 256 }, { 5, 165, 256 }, { 5, 166, 256 }, { 6, 167, 256 },
   { 4, 168, 256 }, { 5, 169, 256 }, { 5, 170, 256 }, { 6, 171, 256 }, { 5, 172, 256 }, { 6, 173, 256 }, { 6, 174, 256 }, { 7, 175, 256 },
   { 4, 176, 256 }, { 5, 177, 256 }, { 5, 178, 256 }, { 6, 179, 256 }, { 5, 180, 256 }, { 6, 181, 256 }, { 6, 182, 256 }, { 7, 183, 256 },
   { 5, 184, 256 }, { 6, 185, 256 }, { 6, 186, 256 }, { 7, 187, 256 }, { 6, 188, 256 }, { 7, 189, 256 }, { 7, 190, 256 }, { 8, 191, 256 },
   { 3, 192, 256 }, { 4, 193, 256 }, { 4, 194, 256 }, { 5, 195, 256 }, { 4, 196, 256 }, { 5, 197, 256 }, { 5, 198, 256 }, { 6, 199, 256 },
   { 4, 200, 256 }, { 5, 201, 256 }, { 5, 202, 256 }, { 6, 203, 256 }, { 5, 204, 256 }, { 6, 205, 256 }, { 6, 206, 256 }, { 7, 207, 256 },
   { 4, 208, 256 }, { 5, 209, 256 }, { 5, 210, 256 }, { 6, 211, 256 }, { 5, 212, 256 }, { 6, 213, 256 }, { 6, 214, 256 }, { 7, 215, 256 },
   { 5, 216, 256 }, { 6, 217, 256 }, { 6, 218, 256 }, { 7, 219, 256 }, { 6, 220, 256 }, { 7, 221, 256 }, { 7, 222, 256 }, { 8, 223, 256 },
   { 4, 224, 256 }, { 5, 225, 256 }, { 5, 226, 256 }, { 6, 227, 256 }, { 5, 228, 256 }, { 6, 229, 256 }, { 6, 230, 256 }, { 7, 231, 256 },
   { 5, 232, 256 }, { 6, 233, 256 }, { 6, 234, 256 }, { 7, 235, 256 }, { 6, 236, 256 }, { 7, 237, 256 }, { 7, 238, 256 }, { 8, 239, 256 },
   { 5, 240, 256 }, { 6, 241, 256 }, { 6, 242, 256 }, { 7, 243, 256 }, { 6, 244, 256 }, { 7, 245, 256 }, { 7, 246, 256 }, { 8, 247, 256 },
   { 6, 248, 256 }, { 7, 249, 256 }, { 7, 250, 256 }, { 8, 251, 256 }, { 7, 252, 256 }, { 8, 253, 256 }, { 8, 254, 256 }, { 9, 255, 256 },
#if FP_LUT > 9
   { 1, 0, 0 }, { 2, 1, 512 }, { 2, 2, 512 }, { 3, 3, 512 }, { 2, 4, 512 }, { 3, 5, 512 }, { 3, 6, 512 }, { 4, 7, 512 },
   { 2, 8, 512 }, { 3, 9, 512 }, { 3, 10, 512 }, { 4, 11, 512 }, { 3, 12, 512 }, { 4, 13, 512 }, { 4, 14, 512 }, { 5, 15, 512 },
   { 2, 16, 512 }, { 3, 17, 512 }, { 3, 18, 512 }, { 4, 19, 512 }, { 3, 20, 512 }, { 4, 21, 512 }, { 4, 22, 512 }, { 5, 23, 512 },
   { 3, 24, 512 }, { 4, 25, 512 }, { 4, 26, 512 }, { 5, 27, 512 }, { 4, 28, 512 }, { 5, 29, 512 }, { 5, 30, 512 }, { 6, 31, 512 },
   { 2, 32, 512 }, { 3, 33, 512 }, { 3, 34, 512 }, { 4, 35, 512 }, { 3, 36, 512 }, { 4, 37, 512 }, { 4, 38, 512 }, { 5, 39, 512 },
   { 3, 40, 512 }, { 4, 41, 512 }, { 4, 42, 512 }, { 5, 43, 512 }, { 4, 44, 512 }, { 5, 45, 512 }, { 5, 46, 512 }, { 6, 47, 512 },
   { 3, 48, 512 }, { 4, 49, 512 }, { 4, 50, 512 }, { 5, 51, 512 }, { 4, 52, 512 }, { 5, 53, 512 }, { 5, 54, 512 }, { 6, 55, 512 },
   { 4, 56, 512 }, { 5, 57, 512 }, { 5, 58, 512 }, { 6, 59, 512 }, { 5, 60, 512 }, { 6, 61, 512 }, { 6, 62, 512 }, { 7, 63, 512 },
   { 2, 64, 512 }, { 3, 65, 512 }, { 3, 66, 512 }, { 4, 67, 512 }, { 3, 68, 512 }, { 4, 69, 512 }, { 4, 70, 512 }, { 5, 71, 512 },
   { 3, 72, 512 }, { 4, 73, 512 }, { 4, 74, 512 }, { 5, 75, 512 }, { 4, 76, 512 }, { 5, 77, 512 }, { 5, 78, 512 }, { 6, 79, 512 },
   { 3, 80, 512 }, { 4, 81, 512 }, { 4, 82, 512 }, { 5, 83, 512 }, { 4, 84, 512 }, { 5, 85, 512 }, { 5, 86, 512 }, { 6, 87, 512 },
   { 4, 88, 512 }, { 5, 89, 512 }, { 5, 90, 512 }, { 6, 91, 512 }, { 5, 92, 512 }, { 6, 93, 512 }, { 6, 94, 512 }, { 7, 95, 512 },
   { 3, 96, 512 }, { 4, 97, 512 }, { 4, 98, 512 }, { 5, 99, 512 }, { 4, 100, 512 }, { 5, 101, 512 }, { 5, 102, 512 }, { 6, 103, 512 },
   { 4, 104, 512 }, { 5, 105, 512 }, { 5, 106, 512 }, { 6, 107, 512 }, { 5, 108, 512 }, { 6, 109, 512 }, { 6, 110, 512 }, { 7, 111, 512 },
   { 4, 112, 512 }, { 5, 113, 512 }, { 5, 114, 512 }, { 6, 115, 512 }, { 5, 116, 512 }, { 6, 117, 512 }, { 6, 118, 512 }, { 7, 119, 512 },
   { 5, 120, 512 }, { 6, 121, 512 }, { 6, 122, 512 }, { 7, 123, 512 }, { 6, 124, 512 }, { 7, 125, 512 }, { 7, 126, 512 }, { 8, 127, 512 },
   { 2, 128, 512 }, { 3, 129, 512 }, { 3, 130, 512 }, { 4, 131, 512 }, { 3, 132, 512 }, { 4, 133, 512 }, { 4, 134, 512 }, { 5, 135, 512 },
   { 3, 136, 512 }, { 4, 137, 512 }, { 4, 138, 512 }, { 5, 139, 512 }, { 4, 140, 512 }, { 5, 141, 512 }, { 5, 142, 512 }, { 6, 143, 512 },
   { 3, 144, 512 }, { 4, 145, 512 }, { 4, 146, 512 }, { 5, 147, 512 }, { 4, 148, 512 }, { 5, 149, 512 }, { 5, 150, 512 }, { 6, 151, 512 },
   { 4, 152, 512 }, { 5, 153, 512 }, { 5, 154, 512 }, { 6, 155, 512 }, { 5, 156, 512 }, { 6, 157, 512 }, { 6, 158, 512 }, { 7, 159, 512 },
   { 3, 160, 512 }, { 4, 161, 512 }, { 4, 162, 512 }, { 5, 163, 512 }, { 4, 164, 512 }, { 5, 165, 512 }, { 5, 166, 512 }, { 6, 167, 512 },
   { 4, 168, 512 }, { 5, 169, 512 }, { 5, 170, 512 }, { 6, 171, 512 }, { 5, 172, 512 }, { 6, 173, 512 }, { 6, 174, 512 }, { 7, 175, 512 },
   { 4, 176, 512 }, { 5, 177, 512 }, { 5, 178, 512 }, { 6, 179, 512 }, { 5, 180, 512 }, { 6, 181, 512 }, { 6, 182, 512 }, { 7, 183, 512 },
   { 5, 184, 512 }, { 6, 185, 512 }, { 6, 186, 512 }, { 7, 187, 512 }, { 6, 188, 512 }, { 7, 189, 512 }, { 7, 190, 512 }, { 8, 191, 512 },
   { 3, 192, 512 }, { 4, 193, 512 }, { 4, 194, 512 }, { 5, 195, 512 }, { 4, 196, 512 }, { 5, 197, 512 }, { 5, 198, 512 }, { 6, 199, 512 },
   { 4, 200, 512 }, { 5, 201, 512 }, { 5, 202, 512 }, { 6, 203, 512 }, { 5, 204, 512 }, { 6, 205, 512 }, { 6, 206, 512 }, { 7, 207, 512 },
   { 4, 208, 512 }, { 5, 209, 512 }, { 5, 210, 512 }, { 6, 211, 512 }, { 5, 212, 512 }, { 6, 213, 512 }, { 6, 214, 512 }, { 7, 215, 512 },
   { 5, 216, 512 }, { 6, 217, 512 }, { 6, 218, 512 }, { 7, 219, 512 }, { 6, 220, 512 }, { 7, 221, 512 }, { 7, 222, 512 }, { 8, 223, 512 },
   { 4, 224, 512 }, { 5, 225, 512 }, { 5, 226, 512 }, { 6, 227, 512 }, { 5, 228, 512 }, { 6, 229, 512 }, { 6, 230, 512 }, { 7, 231, 512 },
   { 5, 232, 512 }, { 6, 233, 512 }, { 6, 234, 512 }, { 7, 235, 512 }, { 6, 236, 512 }, { 7, 237, 512 }, { 7, 238, 512 }, { 8, 239, 512 },
   { 5, 240, 512 }, { 6, 241, 512 }, { 6, 242, 512 }, { 7, 243, 512 }, { 6, 244, 512 }, { 7, 245, 512 }, { 7, 246, 512 }, { 8, 247, 512 },
   { 6, 248, 512 }, { 7, 249, 512 }, { 7, 250, 512 }, { 8, 251, 512 }, { 7, 252, 512 }, { 8, 253, 512 }, { 8, 254, 512 }, { 9, 255, 512 },
   { 2, 256, 512 }, { 3, 257, 512 }, { 3, 258, 512 }, { 4, 259, 512 }, { 3, 260, 512 }, { 4, 261, 512 }, { 4, 262, 512 }, { 5, 263, 512 },
   { 3, 264, 512 }, { 4, 265, 512 }, { 4, 266, 512 }, { 5, 267, 512 }, { 4, 268, 512 }, { 5, 269, 512 }, { 5, 270, 512 }, { 6, 271, 512 },
   { 3, 272, 512 }, { 4, 273, 512 }, { 4, 274, 512 }, { 5, 275, 512 }, { 4, 276, 512 }, { 5, 277, 512 }, { 5, 278, 512 }, { 6, 279, 512 },
   { 4, 280, 512 }, { 5, 281, 512 }, { 5, 282, 512 }, { 6, 283, 512 }, { 5, 284, 512 }, { 6, 285, 512 }, { 6, 286, 512 }, { 7, 287, 512 },
   { 3, 288, 512 }, { 4, 289, 512 }, { 4, 290, 512 }, { 5, 291, 512 }, { 4, 292, 512 }, { 5, 293, 512 }, { 5, 294, 512 }, { 6, 295, 512 },
   { 4, 296, 512 }, { 5, 297, 512 }, { 5, 298, 512 }, { 6, 299, 512 }, { 5, 300, 512 }, { 6, 301, 512 }, { 6, 302, 512 }, { 7, 303, 512 },
   { 4, 304, 512 }, { 5, 305, 512 }, { 5, 306, 512 }, { 6, 307, 512 }, { 5, 308, 512 }, { 6, 309, 512 }, { 6, 310, 512 }, { 7, 311, 512 },
   { 5, 312, 512 }, { 6, 313, 512 }, { 6, 314, 512 }, { 7, 315, 512 }, { 6, 316, 512 }, { 7, 317, 512 }, { 7, 318, 512 }, { 8, 319, 512 },
   { 3, 320, 512 }, { 4, 321, 512 }, { 4, 322, 512 }, { 5, 323, 512 }, { 4, 324, 512 }, { 5, 325, 512 }, { 5, 326, 512 }, { 6, 327, 512 },
   { 4, 328, 512 }, { 5, 329, 512 }, { 5, 330, 512 }, { 6, 331, 512 }, { 5, 332, 512 }, { 6, 333, 512 }, { 6, 334, 512 }, { 7, 335, 512 },
   { 4, 336, 512 }, { 5, 337, 512 }, { 5, 338, 512 }, { 6, 339, 512 }, { 5, 340, 512 }, { 6, 341, 512 }, { 6, 342, 512 }, { 7, 343, 512 },
   { 5, 344, 512 }, { 6, 345, 512 }, { 6, 346, 512 }, { 7, 347, 512 }, { 6, 348, 512 }, { 7, 349, 512 }, { 7, 350, 512 }, { 8, 351, 512 },
   { 4, 352, 512 }, { 5, 353, 512 }, { 5, 354, 512 }, { 6, 355, 512 }, { 5, 356, 512 }, { 6, 357, 512 }, { 6, 358, 512 }, { 7, 359, 512 },
   { 5, 360, 512 }, { 6, 361, 512 }, { 6, 362, 512 }, { 7, 363, 512 }, { 6, 364, 512 }, { 7, 365, 512 }, { 7, 366, 512 }, { 8, 367, 512 },
   { 5, 368, 512 }, { 6, 369, 512 }, { 6, 370, 512 }, { 7, 371, 512 }, { 6, 372, 512 }, { 7, 373, 512 }, { 7, 374, 512 }, { 8, 375, 512 },
   { 6, 376, 512 }, { 7, 377, 512 }, { 7, 378, 512 }, { 8, 379, 512 }, { 7, 380, 512 }, { 8, 381, 512 }, { 8, 382, 512 }, { 9, 383, 512 },
   { 3, 384, 512 }, { 4, 385, 512 }, { 4, 386, 512 }, { 5, 387, 512 }, { 4, 388, 512 }, { 5, 389, 512 }, { 5, 390, 512 }, { 6, 391, 512 },
   { 4, 392, 512 }, { 5, 393, 512 }, { 5, 394, 512 }, { 6, 395, 512 }, { 5, 396, 512 }, { 6, 397, 512 }, { 6, 398, 512 }, { 7, 399, 512 },
   { 4, 400, 512 }, { 5, 401, 512 }, { 5, 402, 512 }, { 6, 403, 512 }, { 5, 404, 512 }, { 6, 405, 512 }, { 6, 406, 512 }, { 7, 407, 512 },
   { 5, 408, 512 }, { 6, 409, 512 }, { 6, 410, 512 }, { 7, 411, 512 }, { 6, 412, 512 }, { 7, 413, 512 }, { 7, 414, 512 }, { 8, 415, 512 },
   { 4, 416, 512 }, { 5, 417, 512 }, { 5, 418, 512 }, { 6, 419, 512 }, { 5, 420, 512 }, { 6, 421, 512 }, { 6, 422, 512 }, { 7, 423, 512 },
   { 5, 424, 512 }, { 6, 425, 512 }, { 6, 426, 512 }, { 7, 427, 512 }, { 6, 428, 512 }, { 7, 429, 512 }, { 7, 430, 512 }, { 8, 431, 512 },
   { 5, 432, 512 }, { 6, 433, 512 }, { 6, 434, 512 }, { 7, 435, 512 }, { 6, 436, 512 }, { 7, 437, 512 }, { 7, 438, 512 }, { 8, 439, 512 },
   { 6, 440, 512 }, { 7, 441, 512 }, { 7, 442, 512 }, { 8, 443, 512 }, { 7, 444, 512 }, { 8, 445, 512 }, { 8, 446, 512 }, { 9, 447, 512 },
   { 4, 448, 512 }, { 5, 449, 512 }, { 5, 450, 512 }, { 6, 451, 512 }, { 5, 452, 512 }, { 6, 453, 512 }, { 6, 454, 512 }, { 7, 455, 512 },
   { 5, 456, 512 }, { 6, 457, 512 }, { 6, 458, 512 }, { 7, 459, 512 }, { 6, 460, 512 }, { 7, 461, 512 }, { 7, 462, 512 }, { 8, 463, 512 },
   { 5, 464, 512 }, { 6, 465, 512 }, { 6, 466, 512 }, { 7, 467, 512 }, { 6, 468, 512 }, { 7, 469, 512 }, { 7, 470, 512 }, { 8, 471, 512 },
   { 6, 472, 512 }, { 7, 473, 512 }, { 7, 474, 512 }, { 8, 475, 512 }, { 7, 476, 512 }, { 8, 477, 512 }, { 8, 478, 512 }, { 9, 479, 512 },
   { 5, 480, 512 }, { 6, 481, 512 }, { 6, 482, 512 }, { 7, 483, 512 }, { 6, 484, 512 }, { 7, 485, 512 }, { 7, 486, 512 }, { 8, 487, 512 },
   { 6, 488, 512 }, { 7, 489, 512 }, { 7, 490, 512 }, { 8, 491, 512 }, { 7, 492, 512 }, { 8, 493, 512 }, { 8, 494, 512 }, { 9, 495, 512 },
   { 6, 496, 512 }, { 7, 497, 512 }, { 7, 498, 512 }, { 8, 499, 512 }, { 7, 500, 512 }, { 8, 501, 512 }, { 8, 502, 512 }, { 9, 503, 512 },
   { 7, 504, 512 }, { 8, 505, 512 }, { 8, 506, 512 }, { 9, 507, 512 }, { 8, 508, 512 }, { 9, 509, 512 }, { 9, 510, 512 }, { 10, 511, 512 },
#if FP_LUT > 10
   { 1, 0, 0 }, { 2, 1, 1024 }, { 2, 2, 1024 }, { 3, 3, 1024 }, { 2, 4, 1024 }, { 3, 5, 1024 }, { 3, 6, 1024 }, { 4, 7, 1024 },
   { 2, 8, 1024 }, { 3, 9, 1024 }, { 3, 10, 1024 }, { 4, 11, 1024 }, { 3, 12, 1024 }, { 4, 13, 1024 }, { 4, 14, 1024 }, { 5, 15, 1024 },
   { 2, 16, 1024 }, { 3, 17, 1024 }, { 3, 18, 1024 }, { 4, 19, 1024 }, { 3, 20, 1024 }, { 4, 21, 1024 }, { 4, 22, 1024 }, { 5, 23, 1024 },
   { 3, 24, 1024 }, { 4, 25, 1024 }, { 4, 26, 1024 }, { 5, 27, 1024 }, { 4, 28, 1024 }, { 5, 29, 1024 }, { 5, 30, 1024 }, { 6, 31, 1024 },
   { 2, 32, 1024 }, { 3, 33, 1024 }, { 3, 34, 1024 }, { 4, 35, 1024 }, { 3, 36, 1024 }, { 4, 37, 1024 }, { 4, 38, 1024 }, { 5, 39, 1024 },
   { 3, 40, 1024 }, { 4, 41, 1024 }, { 4, 42, 1024 }, { 5, 43, 1024 }, { 4, 44, 1024 }, { 5, 45, 1024 }, { 5, 46, 1024 }, { 6, 47, 1024 },
   { 3, 48, 1024 }, { 4, 49, 1024 }, { 4, 50, 1024 }, { 5, 51, 1024 }, { 4, 52, 1024 }, { 5, 53, 1024 }, { 5, 54, 1024 }, { 6, 55, 1024 },
   { 4, 56, 1024 }, { 5, 57, 1024 }, { 5, 58, 1024 }, { 6, 59, 1024 }, { 5, 60, 1024 }, { 6, 61, 1024 }, { 6, 62, 1024 }, { 7, 63, 1024 },
   { 2, 64, 1024 }, { 3, 65, 1024 }, { 3, 66, 1024 }, { 4, 67, 1024 }, { 3, 68, 1024 }, { 4, 69, 1024 }, { 4, 70, 1024 }, { 5, 71, 1024 },
   { 3, 72, 1024 }, { 4, 73, 1024 }, { 4, 74, 1024 }, { 5, 75, 1024 }, { 4, 76, 1024 }, { 5, 77, 1024 }, { 5, 78, 1024 }, { 6, 79, 1024 },
   { 3, 80, 1024 }, { 4, 81, 1024 }, { 4, 82, 1024 }, { 5, 83, 1024 }, { 4, 84, 1024 }, { 5, 85, 1024 }, { 5, 86, 1024 }, { 6, 87, 1024 },
   { 4, 88, 1024 }, { 5, 89, 1024 }, { 5, 90, 1024 }, { 6, 91, 1024 }, { 5, 92, 1024 }, { 6, 93, 1024 }, { 6, 94, 1024 }, { 7, 95, 1024 },
   { 3, 96, 1024 }, { 4, 97, 1024 }, { 4, 98, 1024 }, { 5, 99, 1024 }, { 4, 100, 1024 }, { 5, 101, 1024 }, { 5, 102, 1024 }, { 6, 103, 1024 },
   { 4, 104, 1024 }, { 5, 105, 1024 }, { 5, 106, 1024 }, { 6, 107, 1024 }, { 5, 108, 1024 }, { 6, 109, 1024 }, { 6, 110, 1024 }, { 7, 111, 1024 },
   { 4, 112, 1024 }, { 5, 113, 1024 }, { 5, 114, 1024 }, { 6, 115, 1024 }, { 5, 116, 1024 }, { 6, 117, 1024 }, { 6, 118, 1024 }, { 7, 119, 1024 },
   { 5, 120, 1024 }, { 6, 121, 1024 }, { 6, 122, 1024 }, { 7, 123, 1024 }, { 6, 124, 1024 }, { 7, 125, 1024 }, { 7, 126, 1024 }, { 8, 127, 1024 },
   { 2, 128, 1024 }, { 3, 129, 1024 }, { 3, 130, 1024 }, { 4, 131, 1024 }, { 3, 132, 1024 }, { 4, 133, 1024 }, { 4, 134, 1024 }, { 5, 135, 1024 },
   { 3, 136, 1024 }, { 4, 137, 1024 }, { 4, 138, 1024 }, { 5, 139, 1024 }, { 4, 140, 1024 }, { 5, 141, 1024 }, { 5, 142, 1024 }, { 6, 143, 1024 },
   { 3, 144, 1024 }, { 4, 145, 1024 }, { 4, 146, 1024 }, { 5, 147, 1024 }, { 4, 148, 1024 }, { 5, 149, 1024 }, { 5, 150, 1024 }, { 6, 151, 1024 },
   { 4, 152, 1024 }, { 5, 153, 1024 }, { 5, 154, 1024 }, { 6, 155, 1024 }, { 5, 156, 1024 }, { 6, 157, 1024 }, { 6, 158, 1024 }, { 7, 159, 1024 },
   { 3, 160, 1024 }, { 4, 161, 1024 }, { 4, 162, 1024 }, { 5, 163, 1024 }, { 4, 164, 1024 }, { 5, 165, 1024 }, { 5, 166, 1024 }, { 6, 167, 1024 },
   { 4, 168, 1024 }, { 5, 169, 1024 }, { 5, 170, 1024 }, { 6, 171, 1024 }, { 5, 172, 1024 }, { 6, 173, 1024 }, { 6, 174, 1024 }, { 7, 175, 1024 },
   { 4, 176, 1024 }, { 5, 177, 1024 }, { 5, 178, 1024 }, { 6, 179, 1024 }, { 5, 180, 1024 }, { 6, 181, 1024 }, { 6, 182, 1024 }, { 7, 183, 1024 },
   { 5, 184, 1024 }, { 6, 185, 1024 }, { 6, 186, 1024 }, { 7, 187, 1024 }, { 6, 188, 1024 }, { 7, 189, 1024 }, { 7, 190, 1024 }, { 8, 191, 1024 },
   { 3, 192, 1024 }, { 4, 193, 1024 }, { 4, 194, 1024 }, { 5, 195, 1024 }, { 4, 196, 1024 }, { 5, 197, 1024 }, { 5, 198, 1024 }, { 6, 199, 1024 },
   { 4, 200, 1024 }, { 5, 201, 1024 }, { 5, 202, 1024 }, { 6, 203, 1024 }, { 5, 204, 1024 }, { 6, 205, 1024 }, { 6, 206, 1024 }, { 7, 207, 1024 },
   { 4, 208, 1024 }, { 5, 209, 1024 }, { 5, 210, 1024 }, { 6, 211, 1024 }, { 5, 212, 1024 }, { 6, 213, 1024 }, { 6, 214, 1024 }, { 7, 215, 1024 },
   { 5, 216, 1024 }, { 6, 217, 1024 }, { 6, 218, 1024 }, { 7, 219, 1024 }, { 6, 220, 1024 }, { 7, 221, 1024 }, { 7, 222, 1024 }, { 8, 223, 1024 },
   { 4, 224, 1024 }, { 5, 225, 1024 }, { 5, 226, 1024 }, { 6, 227, 1024 }, { 5, 228, 1024 }, { 6, 229, 1024 }, { 6, 230, 1024 }, { 7, 231, 1024 },
   { 5, 232, 1024 }, { 6, 233, 1024 }, { 6, 234, 1024 }, { 7, 235, 1024 }, { 6, 236, 1024 }, { 7, 237, 1024 }, { 7, 238, 1024 }, { 8, 239, 1024 },
   { 5, 240, 1024 }, { 6, 241, 1024 }, { 6, 242, 1024 }, { 7, 243, 1024 }, { 6, 244, 1024 }, { 7, 245, 1024 }, { 7, 246, 1024 }, { 8, 247, 1024 },
   { 6, 248, 1024 }, { 7, 249, 1024 }, { 7, 250, 1024 }, { 8, 251, 1024 }, { 7, 252, 1024 }, { 8, 253, 1024 }, { 8, 254, 1024 }, { 9, 255, 1024 },
   { 2, 256, 1024 }, { 3, 257, 1024 }, { 3, 258, 1024 }, { 4, 259, 1024 }, { 3, 260, 1024 }, { 4, 261, 1024 }, { 4, 262, 1024 }, { 5, 263, 1024 },
   { 3, 264, 1024 }, { 4, 265, 1024 }, { 4, 266, 1024 }, { 5, 267, 1024 }, { 4, 268, 1024 }, { 5, 269, 1024 }, { 5, 270, 1024 }, { 6, 271, 1024 },
   { 3, 272, 1024 }, { 4, 273, 1024 }, { 4, 274, 1024 }, { 5, 275, 1024 }, { 4, 276, 1024 }, { 5, 277, 1024 }, { 5, 278, 1024 }, { 6, 279, 1024 },
   { 4, 280, 1024 }, { 5, 281, 1024 }, { 5, 282, 1024 }, { 6, 283, 1024 }, { 5, 284, 1024 }, { 6, 285, 1024 }, { 6, 286, 1024 }, { 7, 287, 1024 },
   { 3, 288, 1024 }, { 4, 289, 1024 }, { 4, 290, 1024 }, { 5, 291, 1024 }, { 4, 292, 1024 }, { 5, 293, 1024 }, { 5, 294, 1024 }, { 6, 295, 1024 },
   { 4, 296, 1024 }, { 5, 297, 1024 }, { 5, 298, 1024 }, { 6, 299, 1024 }, { 5, 300, 1024 }, { 6, 301, 1024 }, { 6, 302, 1024 }, { 7, 303, 1024 },
   { 4, 304, 1024 }, { 5, 305, 1024 }, { 5, 306, 1024 }, { 6, 307, 1024 }, { 5, 308, 1024 }, { 6, 309, 1024 }, { 6, 310, 1024 }, { 7, 311, 1024 },
   { 5, 312, 1024 }, { 6, 313, 1024 }, { 6, 314, 1024 }, { 7, 315, 1024 }, { 6, 316, 1024 }, { 7, 317, 1024 }, { 7, 318, 1024 }, { 8, 319, 1024 },
   { 3, 320, 1024 }, { 4, 321, 1024 }, { 4, 322, 1024 }, { 5, 323, 1024 }, { 4, 324, 1024 }, { 5, 325, 1024 }, { 5, 326, 1024 }, { 6, 327, 1024 },
   { 4, 328, 1024 }, { 5, 329, 1024 }, { 5, 330, 1024 }, { 6, 331, 1024 }, { 5, 332, 1024 }, { 6, 333, 1024 }, { 6, 334, 1024 }, { 7, 335, 1024 },
   { 4, 336, 1024 }, { 5, 337, 1024 }, { 5, 338, 1024 }, { 6, 339, 1024 }, { 5, 340, 1024 }, { 6, 341, 1024 }, { 6, 342, 1024 }, { 7, 343, 1024 },
   { 5, 344, 1024 }, { 6, 345, 1024 }, { 6, 346, 1024 }, { 7, 347, 1024 }, { 6, 348, 1024 }, { 7, 349, 1024 }, { 7, 350, 1024 }, { 8, 351, 1024 },
   { 4, 352, 1024 }, { 5, 353, 1024 }, { 5, 354, 1024 }, { 6, 355, 1024 }, { 5, 356, 1024 }, { 6, 357, 1024 }, { 6, 358, 1024 }, { 7, 359, 1024 },
   { 5, 360, 1024 }, { 6, 361, 1024 }, { 6, 362, 1024 }, { 7, 363, 1024 }, { 6, 364, 1024 }, { 7, 365, 1024 }, { 7, 366, 1024 }, { 8, 367, 1024 },
   { 5, 368, 1024 }, { 6, 369, 1024 }, { 6, 370, 1024 }, { 7, 371, 1024 }, { 6, 372, 1024 }, { 7, 373, 1024 }, { 7, 374, 1024 }, { 8, 375, 1024 },
   { 6, 376, 1024 }, { 7, 377, 1024 }, { 7, 378, 1024 }, { 8, 379, 1024 }, { 7, 380, 1024 }, { 8, 381, 1024 }, { 8, 382, 1024 }, { 9, 383, 1024 },
   { 3, 384, 1024 }, { 4, 385, 1024 }, { 4, 386, 1024 }, { 5, 387, 1024 }, { 4, 388, 1024 }, { 5, 389, 1024 }, { 5, 390, 1024 }, { 6, 391, 1024 },
   { 4, 392, 1024 }, { 5, 393, 1024 }, { 5, 394, 1024 }, { 6, 395, 1024 }, { 5, 396, 1024 }, { 6, 397, 1024 }, { 6, 398, 1024 }, { 7, 399, 1024 },
   { 4, 400, 1024 }, { 5, 401, 1024 }, { 5, 402, 1024 }, { 6, 403, 1024 }, { 5, 404, 1024 }, { 6, 405, 1024 }, { 6, 406, 1024 }, { 7, 407, 1024 },
   { 5, 408, 1024 }, { 6, 409, 1024 }, { 6, 410, 1024 }, { 7, 411, 1024 }, { 6, 412, 1024 }, { 7, 413, 1024 }, { 7, 414, 1024 }, { 8, 415, 1024 },
   { 4, 416, 1024 }, { 5, 417, 1024 }, { 5, 418, 1024 }, { 6, 419, 1024 }, { 5, 420, 1024 }, { 6, 421, 1024 }, { 6, 422, 1024 }, { 7, 423, 1024 },
   { 5, 424, 1024 }, { 6, 425, 1024 }, { 6, 426, 1024 }, { 7, 427, 1024 }, { 6, 428, 1024 }, { 7, 429, 1024 }, { 7, 430, 1024 }, { 8, 431, 1024 },
   { 5, 432, 1024 }, { 6, 433, 1024 }, { 6, 434, 1024 }, { 7, 435, 1024 }, { 6, 436, 1024 }, { 7, 437, 1024 }, { 7, 438, 1024 }, { 8, 439, 1024 },
   { 6, 440, 1024 }, { 7, 441, 1024 }, { 7, 442, 1024 }, { 8, 443, 1024 }, { 7, 444, 1024 }, { 8, 445, 1024 }, { 8, 446, 1024 }, { 9, 447, 1024 },
   { 4, 448, 1024 }, { 5, 449, 1024 }, { 5, 450, 1024 }, { 6, 451, 1024 }, { 5, 452, 1024 }, { 6, 453, 1024 }, { 6, 454, 1024 }, { 7, 455, 1024 },
   { 5, 456, 1024 }, { 6, 457, 1024 }, { 6, 458, 1024 }, { 7, 459, 1024 }, { 6, 460, 1024 }, { 7, 461, 1024 }, { 7, 462, 1024 }, { 8, 463, 1024 },
   { 5, 464, 1024 }, { 6, 465, 1024 }, { 6, 466, 1024 }, { 7, 467, 1024 }, { 6, 468, 1024 }, { 7, 469, 1024 }, { 7, 470, 1024 }, { 8, 471, 1024 },
   { 6, 472, 1024 }, { 7, 473, 1024 }, { 7, 474, 1024 }, { 8, 475, 1024 }, { 7, 476, 1024 }, { 8, 477, 1024 }, { 8, 478, 1024 }, { 9, 479, 1024 },
   { 5, 480, 1024 }, { 6, 481, 1024 }, { 6, 482, 1024 }, { 7, 483, 1024 }, { 6, 484, 1024 }, { 7, 485, 1024 }, { 7, 486, 1024 }, { 8, 487, 1024 },
   { 6, 488, 1024 }, { 7, 489, 1024 }, { 7, 490, 1024 }, { 8, 491, 1024 }, { 7, 492, 1024 }, { 8, 493, 1024 }, { 8, 494, 1024 }, { 9, 495, 1024 },
   { 6, 496, 1024 }, { 7, 497, 1024 }, { 7, 498, 1024 }, { 8, 499, 1024 }, { 7, 500, 1024 }, { 8, 501, 1024 }, { 8, 502, 1024 }, { 9, 503, 1024 },
   { 7, 504, 1024 }, { 8, 505, 1024 }, { 8, 506, 1024 }, { 9, 507, 1024 }, { 8, 508, 1024 }, { 9, 509, 1024 }, { 9, 510, 1024 }, { 10, 511, 1024 },
   { 2, 512, 1024 }, { 3, 513, 1024 }, { 3, 514, 1024 }, { 4, 515, 1024 }, { 3, 516, 1024 }, { 4, 517, 1024 }, { 4, 518, 1024 }, { 5, 519, 1024 },
   { 3, 520, 1024 }, { 4, 521, 1024 }, { 4, 522, 1024 }, { 5, 523, 1024 }, { 4, 524, 1024 }, { 5, 525, 1024 }, { 5, 526, 1024 }, { 6, 527, 1024 },
   { 3, 528, 1024 }, { 4, 529, 1024 }, { 4, 530, 1024 }, { 5, 531, 1024 }, { 4, 532, 1024 }, { 5, 533, 1024 }, { 5, 534, 1024 }, { 6, 535, 1024 },
   { 4, 536, 1024 }, { 5, 537, 1024 }, { 5, 538, 1024 }, { 6, 539, 1024 }, { 5, 540, 1024 }, { 6, 541, 1024 }, { 6, 542, 1024 }, { 7, 543, 1024 },
   { 3, 544, 1024 }, { 4, 545, 1024 }, { 4, 546, 1024 }, { 5, 547, 1024 }, { 4, 548, 1024 }, { 5, 549, 1024 }, { 5, 550, 1024 }, { 6, 551, 1024 },
   { 4, 552, 1024 }, { 5, 553, 1024 }, { 5, 554, 1024 }, { 6, 555, 1024 }, { 5, 556, 1024 }, { 6, 557, 1024 }, { 6, 558, 1024 }, { 7, 559, 1024 },
   { 4, 560, 1024 }, { 5, 561, 1024 }, { 5, 562, 1024 }, { 6, 563, 1024 }, { 5, 564, 1024 }, { 6, 565, 1024 }, { 6, 566, 1024 }, { 7, 567, 1024 },
   { 5, 568, 1024 }, { 6, 569, 1024 }, { 6, 570, 1024 }, { 7, 571, 1024 }, { 6, 572, 1024 }, { 7, 573, 1024 }, { 7, 574, 1024 }, { 8, 575, 1024 },
   { 3, 576, 1024 }, { 4, 577, 1024 }, { 4, 578, 1024 }, { 5, 579, 1024 }, { 4, 580, 1024 }, { 5, 581, 1024 }, { 5, 582, 1024 }, { 6, 583, 1024 },
   { 4, 584, 1024 }, { 5, 585, 1024 }, { 5, 586, 1024 }, { 6, 587, 1024 }, { 5, 588, 1024 }, { 6, 589, 1024 }, { 6, 590, 1024 }, { 7, 591, 1024 },
   { 4, 592, 1024 }, { 5, 593, 1024 }, { 5, 594, 1024 }, { 6, 595, 1024 }, { 5, 596, 1024 }, { 6, 597, 1024 }, { 6, 598, 1024 }, { 7, 599, 1024 },
   { 5, 600, 1024 }, { 6, 601, 1024 }, { 6, 602, 1024 }, { 7, 603, 1024 }, { 6, 604, 1024 }, { 7, 605, 1024 }, { 7, 606, 1024 }, { 8, 607, 1024 },
   { 4, 608, 1024 }, { 5, 609, 1024 }, { 5, 610, 1024 }, { 6, 611, 1024 }, { 5, 612, 1024 }, { 6, 613, 1024 }, { 6, 614, 1024 }, { 7, 615, 1024 },
   { 5, 616, 1024 }, { 6, 617, 1024 }, { 6, 618, 1024 }, { 7, 619, 1024 }, { 6, 620, 1024 }, { 7, 621, 1024 }, { 7, 622, 1024 }, { 8, 623, 1024 },
   { 5, 624, 1024 }, { 6, 625, 1024 }, { 6, 626, 1024 }, { 7, 627, 1024 }, { 6, 628, 1024 }, { 7, 629, 1024 }, { 7, 630, 1024 }, { 8, 631, 1024 },
   { 6, 632, 1024 }, { 7, 633, 1024 }, { 7, 634, 1024 }, { 8, 635, 1024 }, { 7, 636, 1024 }, { 8, 637, 1024 }, { 8, 638, 1024 }, { 9, 639, 1024 },
   { 3, 640, 1024 }, { 4, 641, 1024 }, { 4, 642, 1024 }, { 5, 643, 1024 }, { 4, 644, 1024 }, { 5, 645, 1024 }, { 5, 646, 1024 }, { 6, 647, 1024 },
   { 4, 648, 1024 }, { 5, 649, 1024 }, { 5, 650, 1024 }, { 6, 651, 1024 }, { 5, 652, 1024 }, { 6, 653, 1024 }, { 6, 654, 1024 }, { 7, 655, 1024 },
   { 4, 656, 1024 }, { 5, 657, 1024 }, { 5, 658, 1024 }, { 6, 659, 1024 }, { 5, 660, 1024 }, { 6, 661, 1024 }, { 6, 662, 1024 }, { 7, 663, 1024 },
   { 5, 664, 1024 }, { 6, 665, 1024 }, { 6, 666, 1024 }, { 7, 667, 1024 }, { 6, 668, 1024 }, { 7, 669, 1024 }, { 7, 670, 1024 }, { 8, 671, 1024 },
   { 4, 672, 1024 }, { 5, 673, 1024 }, { 5, 674, 1024 }, { 6, 675, 1024 }, { 5, 676, 1024 }, { 6, 677, 1024 }, { 6, 678, 1024 }, { 7, 679, 1024 },
   { 5, 680, 1024 }, { 6, 681, 1024 }, { 6, 682, 1024 }, { 7, 683, 1024 }, { 6, 684, 1024 }, { 7, 685, 1024 }, { 7, 686, 1024 }, { 8, 687, 1024 },
   { 5, 688, 1024 }, { 6, 689, 1024 }, { 6, 690, 1024 }, { 7, 691, 1024 }, { 6, 692, 1024 }, { 7, 693, 1024 }, { 7, 694, 1024 }, { 8, 695, 1024 },
   { 6, 696, 1024 }, { 7, 697, 1024 }, { 7, 698, 1024 }, { 8, 699, 1024 }, { 7, 700, 1024 }, { 8, 701, 1024 }, { 8, 702, 1024 }, { 9, 703, 1024 },
   { 4, 704, 1024 }, { 5, 705, 1024 }, { 5, 706, 1024 }, { 6, 707, 1024 }, { 5, 708, 1024 }, { 6, 709, 1024 }, { 6, 710, 1024 }, { 7, 711, 1024 },
   { 5, 712, 1024 }, { 6, 713, 1024 }, { 6, 714, 1024 }, { 7, 715, 1024 }, { 6, 716, 1024 }, { 7, 717, 1024 }, { 7, 718, 1024 }, { 8, 719, 1024 },
   { 5, 720, 1024 }, { 6, 721, 1024 }, { 6, 722, 1024 }, { 7, 723, 1024 }, { 6, 724, 1024 }, { 7, 725, 1024 }, { 7, 726, 1024 }, { 8, 727, 1024 },
   { 6, 728, 1024 }, { 7, 729, 1024 }, { 7, 730, 1024 }, { 8, 731, 1024 }, { 7, 732, 1024 }, { 8, 733, 1024 }, { 8, 734, 1024 }, { 9, 735, 1024 },
   { 5, 736, 1024 }, { 6, 737, 1024 }, { 6, 738, 1024 }, { 7, 739, 1024 }, { 6, 740, 1024 }, { 7, 741, 1024 }, { 7, 742, 1024 }, { 8, 743, 1024 },
   { 6, 744, 1024 }, { 7, 745, 1024 }, { 7, 746, 1024 }, { 8, 747, 1024 }, { 7, 748, 1024 }, { 8, 749, 1024 }, { 8, 750, 1024 }, { 9, 751, 1024 },
   { 6, 752, 1024 }, { 7, 753, 1024 }, { 7, 754, 1024 }, { 8, 755, 1024 }, { 7, 756, 1024 }, { 8, 757, 1024 }, { 8, 758, 1024 }, { 9, 759, 1024 },
   { 7, 760, 1024 }, { 8, 761, 1024 }, { 8, 762, 1024 }, { 9, 763, 1024 }, { 8, 764, 1024 }, { 9, 765, 1024 }, { 9, 766, 1024 }, { 10, 767, 1024 },
   { 3, 768, 1024 }, { 4, 769, 1024 }, { 4, 770, 1024 }, { 5, 771, 1024 }, { 4, 772, 1024 }, { 5, 773, 1024 }, { 5, 774, 1024 }, { 6, 775, 1024 },
   { 4, 776, 1024 }, { 5, 777, 1024 }, { 5, 778, 1024 }, { 6, 779, 1024 }, { 5, 780, 1024 }, { 6, 781, 1024 }, { 6, 782, 1024 }, { 7, 783, 1024 },
   { 4, 784, 1024 }, { 5, 785, 1024 }, { 5, 786, 1024 }, { 6, 787, 1024 }, { 5, 788, 1024 }, { 6, 789, 1024 }, { 6, 790, 1024 }, { 7, 791, 1024 },
   { 5, 792, 1024 }, { 6, 793, 1024 }, { 6, 794, 1024 }, { 7, 795, 1024 }, { 6, 796, 1024 }, { 7, 797, 1024 }, { 7, 798, 1024 }, { 8, 799, 1024 },
   { 4, 800, 1024 }, { 5, 801, 1024 }, { 5, 802, 1024 }, { 6, 803, 1024 }, { 5, 804, 1024 }, { 6, 805, 1024 }, { 6, 806, 1024 }, { 7, 807, 1024 },
   { 5, 808, 1024 }, { 6, 809, 1024 }, { 6, 810, 1024 }, { 7, 811, 1024 }, { 6, 812, 1024 }, { 7, 813, 1024 }, { 7, 814, 1024 }, { 8, 815, 1024 },
   { 5, 816, 1024 }, { 6, 817, 1024 }, { 6, 818, 1024 }, { 7, 819, 1024 }, { 6, 820, 1024 }, { 7, 821, 1024 }, { 7, 822, 1024 }, { 8, 823, 1024 },
   { 6, 824, 1024 }, { 7, 825, 1024 }, { 7, 826, 1024 }, { 8, 827, 1024 }, { 7, 828, 1024 }, { 8, 829, 1024 }, { 8, 830, 1024 }, { 9, 831, 1024 },
   { 4, 832, 1024 }, { 5, 833, 1024 }, { 5, 834, 1024 }, { 6, 835, 1024 }, { 5, 836, 1024 }, { 6, 837, 1024 }, { 6, 838, 1024 }, { 7, 839, 1024 },
   { 5, 840, 1024 }, { 6, 841, 1024 }, { 6, 842, 1024 }, { 7, 843, 1024 }, { 6, 844, 1024 }, { 7, 845, 1024 }, { 7, 846, 1024 }, { 8, 847, 1024 },
   { 5, 848, 1024 }, { 6, 849, 1024 }, { 6, 850, 1024 }, { 7, 851, 1024 }, { 6, 852, 1024 }, { 7, 853, 1024 }, { 7, 854, 1024 }, { 8, 855, 1024 },
   { 6, 856, 1024 }, { 7, 857, 1024 }, { 7, 858, 1024 }, { 8, 859, 1024 }, { 7, 860, 1024 }, { 8, 861, 1024 }, { 8, 862, 1024 }, { 9, 863, 1024 },
   { 5, 864, 1024 }, { 6, 865, 1024 }, { 6, 866, 1024 }, { 7, 867, 1024 }, { 6, 868, 1024 }, { 7, 869, 1024 }, { 7, 870, 1024 }, { 8, 871, 1024 },
   { 6, 872, 1024 }, { 7, 873, 1024 }, { 7, 874, 1024 }, { 8, 875, 1024 }, { 7, 876, 1024 }, { 8, 877, 1024 }, { 8, 878, 1024 }, { 9, 879, 1024 },
   { 6, 880, 1024 }, { 7, 881, 1024 }, { 7, 882, 1024 }, { 8, 883, 1024 }, { 7, 884, 1024 }, { 8, 885, 1024 }, { 8, 886, 1024 }, { 9, 887, 1024 },
   { 7, 888, 1024 }, { 8, 889, 1024 }, { 8, 890, 1024 }, { 9, 891, 1024 }, { 8, 892, 1024 }, { 9, 893, 1024 }, { 9, 894, 1024 }, { 10, 895, 1024 },
   { 4, 896, 1024 }, { 5, 897, 1024 }, { 5, 898, 1024 }, { 6, 899, 1024 }, { 5, 900, 1024 }, { 6, 901, 1024 }, { 6, 902, 1024 }, { 7, 903, 1024 },
   { 5, 904, 1024 }, { 6, 905, 1024 }, { 6, 906, 1024 }, { 7, 907, 1024 }, { 6, 908, 1024 }, { 7, 909, 1024 }, { 7, 910, 1024 }, { 8, 911, 1024 },
   { 5, 912, 1024 }, { 6, 913, 1024 }, { 6, 914, 1024 }, { 7, 915, 1024 }, { 6, 916, 1024 }, { 7, 917, 1024 }, { 7, 918, 1024 }, { 8, 919, 1024 },
   { 6, 920, 1024 }, { 7, 921, 1024 }, { 7, 922, 1024 }, { 8, 923, 1024 }, { 7, 924, 1024 }, { 8, 925, 1024 }, { 8, 926, 1024 }, { 9, 927, 1024 },
   { 5, 928, 1024 }, { 6, 929, 1024 }, { 6, 930, 1024 }, { 7, 931, 1024 }, { 6, 932, 1024 }, { 7, 933, 1024 }, { 7, 934, 1024 }, { 8, 935, 1024 },
   { 6, 936, 1024 }, { 7, 937, 1024 }, { 7, 938, 1024 }, { 8, 939, 1024 }, { 7, 940, 1024 }, { 8, 941, 1024 }, { 8, 942, 1024 }, { 9, 943, 1024 },
   { 6, 944, 1024 }, { 7, 945, 1024 }, { 7, 946, 1024 }, { 8, 947, 1024 }, { 7, 948, 1024 }, { 8, 949, 1024 }, { 8, 950, 1024 }, { 9, 951, 1024 },
   { 7, 952, 1024 }, { 8, 953, 1024 }, { 8, 954, 1024 }, { 9, 955, 1024 }, { 8, 956, 1024 }, { 9, 957, 1024 }, { 9, 958, 1024 }, { 10, 959, 1024 },
   { 5, 960, 1024 }, { 6, 961, 1024 }, { 6, 962, 1024 }, { 7, 963, 1024 }, { 6, 964, 1024 }, { 7, 965, 1024 }, { 7, 966, 1024 }, { 8, 967, 1024 },
   { 6, 968, 1024 }, { 7, 969, 1024 }, { 7, 970, 1024 }, { 8, 971, 1024 }, { 7, 972, 1024 }, { 8, 973, 1024 }, { 8, 974, 1024 }, { 9, 975, 1024 },
   { 6, 976, 1024 }, { 7, 977, 1024 }, { 7, 978, 1024 }, { 8, 979, 1024 }, { 7, 980, 1024 }, { 8, 981, 1024 }, { 8, 982, 1024 }, { 9, 983, 1024 },
   { 7, 984, 1024 }, { 8, 985, 1024 }, { 8, 986, 1024 }, { 9, 987, 1024 }, { 8, 988, 1024 }, { 9, 989, 1024 }, { 9, 990, 1024 }, { 10, 991, 1024 },
   { 6, 992, 1024 }, { 7, 993, 1024 }, { 7, 994, 1024 }, { 8, 995, 1024 }, { 7, 996, 1024 }, { 8, 997, 1024 }, { 8, 998, 1024 }, { 9, 999, 1024 },
   { 7, 1000, 1024 }, { 8, 1001, 1024 }, { 8, 1002, 1024 }, { 9, 1003, 1024 }, { 8, 1004, 1024 }, { 9, 1005, 1024 }, { 9, 1006, 1024 }, { 10, 1007, 1024 },
   { 7, 1008, 1024 }, { 8, 1009, 1024 }, { 8, 1010, 1024 }, { 9, 1011, 1024 }, { 8, 1012, 1024 }, { 9, 1013, 1024 }, { 9, 1014, 1024 }, { 10, 1015, 1024 },
   { 8, 1016, 1024 }, { 9, 1017, 1024 }, { 9, 1018, 1024 }, { 10, 1019, 1024 }, { 9, 1020, 1024 }, { 10, 1021, 1024 }, { 10, 1022, 1024 }, { 11, 1023, 1024 },
#if FP_LUT > 11
   { 1, 0, 0 }, { 2, 1, 2048 }, { 2, 2, 2048 }, { 3, 3, 2048 }, { 2, 4, 2048 }, { 3, 5, 2048 }, { 3, 6, 2048 }, { 4, 7, 2048 },
   { 2, 8, 2048 }, { 3, 9, 2048 }, { 3, 10, 2048 }, { 4, 11, 2048 }, { 3, 12, 2048 }, { 4, 13, 2048 }, { 4, 14, 2048 }, { 5, 15, 2048 },
   { 2, 16, 2048 }, { 3, 17, 2048 }, { 3, 18, 2048 }, { 4, 19, 2048 }, { 3, 20, 2048 }, { 4, 21, 2048 }, { 4, 22, 2048 }, { 5, 23, 2048 },
   { 3, 24, 2048 }, { 4, 25, 2048 }, { 4, 26, 2048 }, { 5, 27, 2048 }, { 4, 28, 2048 }, { 5, 29, 2048 }, { 5, 30, 2048 }, { 6, 31, 2048 },
   { 2, 32, 2048 }, { 3, 33, 2048 }, { 3, 34, 2048 }, { 4, 35, 2048 }, { 3, 36, 2048 }, { 4, 37, 2048 }, { 4, 38, 2048 }, { 5, 39, 2048 },
   { 3, 40, 2048 }, { 4, 41, 2048 }, { 4, 42, 2048 }, { 5, 43, 2048 }, { 4, 44, 2048 }, { 5, 45, 2048 }, { 5, 46, 2048 }, { 6, 47, 2048 },
   { 3, 48, 2048 }, { 4, 49, 2048 }, { 4, 50, 2048 }, { 5, 51, 2048 }, { 4, 52, 2048 }, { 5, 53, 2048 }, { 5, 54, 2048 }, { 6, 55, 2048 },
   { 4, 56, 2048 }, { 5, 57, 2048 }, { 5, 58, 2048 }, { 6, 59, 2048 }, { 5, 60, 2048 }, { 6, 61, 2048 }, { 6, 62, 2048 }, { 7, 63, 2048 },
   { 2, 64, 2048 }, { 3, 65, 2048 }, { 3, 66, 2048 }, { 4, 67, 2048 }, { 3, 68, 2048 }, { 4, 69, 2048 }, { 4, 70, 2048 }, { 5, 71, 2048 },
   { 3, 72, 2048 }, { 4, 73, 2048 }, { 4, 74, 2048 }, { 5, 75, 2048 }, { 4, 76, 2048 }, { 5, 77, 2048 }, { 5, 78, 2048 }, { 6, 79, 2048 },
   { 3, 80, 2048 }, { 4, 81, 2048 }, { 4, 82, 2048 }, { 5, 83, 2048 }, { 4, 84, 2048 }, { 5, 85, 2048 }, { 5, 86, 2048 }, { 6, 87, 2048 },
   { 4, 88, 2048 }, { 5, 89, 2048 }, { 5, 90, 2048 }, { 6, 91, 2048 }, { 5, 92, 2048 }, { 6, 93, 2048 }, { 6, 94, 2048 }, { 7, 95, 2048 },
   { 3, 96, 2048 }, { 4, 97, 2048 }, { 4, 98, 2048 }, { 5, 99, 2048 }, { 4, 100, 2048 }, { 5, 101, 2048 }, { 5, 102, 2048 }, { 6, 103, 2048 },
   { 4, 104, 2048 }, { 5, 105, 2048 }, { 5, 106, 2048 }, { 6, 107, 2048 }, { 5, 108, 2048 }, { 6, 109, 2048 }, { 6, 110, 2048 }, { 7, 111, 2048 },
   { 4, 112, 2048 }, { 5, 113, 2048 }, { 5, 114, 2048 }, { 6, 115, 2048 }, { 5, 116, 2048 }, { 6, 117, 2048 }, { 6, 118, 2048 }, { 7, 119, 2048 },
   { 5, 120, 2048 }, { 6, 121, 2048 }, { 6, 122, 2048 }, { 7, 123, 2048 }, { 6, 124, 2048 }, { 7, 125, 2048 }, { 7, 126, 2048 }, { 8, 127, 2048 },
   { 2, 128, 2048 }, { 3, 129, 2048 }, { 3, 130, 2048 }, { 4, 131, 2048 }, { 3, 132, 2048 }, { 4, 133, 2048 }, { 4, 134, 2048 }, { 5, 135, 2048 },
   { 3, 136, 2048 }, { 4, 137, 2048 }, { 4, 138, 2048 }, { 5, 139, 2048 }, { 4, 140, 2048 }, { 5, 141, 2048 }, { 5, 142, 2048 }, { 6, 143, 2048 },
   { 3, 144, 2048 }, { 4, 145, 2048 }, { 4, 146, 2048 }, { 5, 147, 2048 }, { 4, 148, 2048 }, { 5, 149, 2048 }, { 5, 150, 2048 }, { 6, 151, 2048 },
   { 4, 152, 2048 }, { 5, 153, 2048 }, { 5, 154, 2048 }, { 6, 155, 2048 }, { 5, 156, 2048 }, { 6, 157, 2048 }, { 6, 158, 2048 }, { 7, 159, 2048 },
   { 3, 160, 2048 }, { 4, 161, 2048 }, { 4, 162, 2048 }, { 5, 163, 2048 }, { 4, 164, 2048 }, { 5, 165, 2048 }, { 5, 166, 2048 }, { 6, 167, 2048 },
   { 4, 168, 2048 }, { 5, 169, 2048 }, { 5, 170, 2048 }, { 6, 171, 2048 }, { 5, 172, 2048 }, { 6, 173, 2048 }, { 6, 174, 2048 }, { 7, 175, 2048 },
   { 4, 176, 2048 }, { 5, 177, 2048 }, { 5, 178, 2048 }, { 6, 179, 2048 }, { 5, 180, 2048 }, { 6, 181, 2048 }, { 6, 182, 2048 }, { 7, 183, 2048 },
   { 5, 184, 2048 }, { 6, 185, 2048 }, { 6, 186, 2048 }, { 7, 187, 2048 }, { 6, 188, 2048 }, { 7, 189, 2048 }, { 7, 190, 2048 }, { 8, 191, 2048 },
   { 3, 192, 2048 }, { 4, 193, 2048 }, { 4, 194, 2048 }, { 5, 195, 2048 }, { 4, 196, 2048 }, { 5, 197, 2048 }, { 5, 198, 2048 }, { 6, 199, 2048 },
   { 4, 200, 2048 }, { 5, 201, 2048 }, { 5, 202, 2048 }, { 6, 203, 2048 }, { 5, 204, 2048 }, { 6, 205, 2048 }, { 6, 206, 2048 }, { 7, 207, 2048 },
   { 4, 208, 2048 }, { 5, 209, 2048 }, { 5, 210, 2048 }, { 6, 211, 2048 }, { 5, 212, 2048 }, { 6, 213, 2048 }, { 6, 214, 2048 }, { 7, 215, 2048 },
   { 5, 216, 2048 }, { 6, 217, 2048 }, { 6, 218, 2048 }, { 7, 219, 2048 }, { 6, 220, 2048 }, { 7, 221, 2048 }, { 7, 222, 2048 }, { 8, 223, 2048 },
   { 4, 224, 2048 }, { 5, 225, 2048 }, { 5, 226, 2048 }, { 6, 227, 2048 }, { 5, 228, 2048 }, { 6, 229, 2048 }, { 6, 230, 2048 }, { 7, 231, 2048 },
   { 5, 232, 2048 }, { 6, 233, 2048 }, { 6, 234, 2048 }, { 7, 235, 2048 }, { 6, 236, 2048 }, { 7, 237, 2048 }, { 7, 238, 2048 }, { 8, 239, 2048 },
   { 5, 240, 2048 }, { 6, 241, 2048 }, { 6, 242, 2048 }, { 7, 243, 2048 }, { 6, 244, 2048 }, { 7, 245, 2048 }, { 7, 246, 2048 }, { 8, 247, 2048 },
   { 6, 248, 2048 }, { 7, 249, 2048 }, { 7, 250, 2048 }, { 8, 251, 2048 }, { 7, 252, 2048 }, { 8, 253, 2048 }, { 8, 254, 2048 }, { 9, 255, 2048 },
   { 2, 256, 2048 }, { 3, 257, 2048 }, { 3, 258, 2048 }, { 4, 259, 2048 }, { 3, 260, 2048 }, { 4, 261, 2048 }, { 4, 262, 2048 }, { 5, 263, 2048 },
   { 3, 264, 2048 }, { 4, 265, 2048 }, { 4, 266, 2048 }, { 5, 267, 2048 }, { 4, 268, 2048 }, { 5, 269, 2048 }, { 5, 270, 2048 }, { 6, 271, 2048 },
   { 3, 272, 2048 }, { 4, 273, 2048 }, { 4, 274, 2048 }, { 5, 275, 2048 }, { 4, 276, 2048 }, { 5, 277, 2048 }, { 5, 278, 2048 }, { 6, 279, 2048 },
   { 4, 280, 2048 }, { 5, 281, 2048 }, { 5, 282, 2048 }, { 6, 283, 2048 }, { 5, 284, 2048 }, { 6, 285, 2048 }, { 6, 286, 2048 }, { 7, 287, 2048 },
   { 3, 288, 2048 }, { 4, 289, 2048 }, { 4, 290, 2048 }, { 5, 291, 2048 }, { 4, 292, 2048 }, { 5, 293, 2048 }, { 5, 294, 2048 }, { 6, 295, 2048 },
   { 4, 296, 2048 }, { 5, 297, 2048 }, { 5, 298, 2048 }, { 6, 299, 2048 }, { 5, 300, 2048 }, { 6, 301, 2048 }, { 6, 302, 2048 }, { 7, 303, 2048 },
   { 4, 304, 2048 }, { 5, 305, 2048 }, { 5, 306, 2048 }, { 6, 307, 2048 }, { 5, 308, 2048 }, { 6, 309, 2048 }, { 6, 310, 2048 }, { 7, 311, 2048 },
   { 5, 312, 2048 }, { 6, 313, 2048 }, { 6, 314, 2048 }, { 7, 315, 2048 }, { 6, 316, 2048 }, { 7, 317, 2048 }, { 7, 318, 2048 }, { 8, 319, 2048 },
   { 3, 320, 2048 }, { 4, 321, 2048 }, { 4, 322, 2048 }, { 5, 323, 2048 }, { 4, 324, 2048 }, { 5, 325, 2048 }, { 5, 326, 2048 }, { 6, 327, 2048 },
   { 4, 328, 2048 }, { 5, 329, 2048 }, { 5, 330, 2048 }, { 6, 331, 2048 }, { 5, 332, 2048 }, { 6, 333, 2048 }, { 6, 334, 2048 }, { 7, 335, 2048 },
   { 4, 336, 2048 }, { 5, 337, 2048 }, { 5, 338, 2048 }, { 6, 339, 2048 }, { 5, 340, 2048 }, { 6, 341, 2048 }, { 6, 342, 2048 }, { 7, 343, 2048 },
   { 5, 344, 2048 }, { 6, 345, 2048 }, { 6, 346, 2048 }, { 7, 347, 2048 }, { 6, 348, 2048 }, { 7, 349, 2048 }, { 7, 350, 2048 }, { 8, 351, 2048 },
   { 4, 352, 2048 }, { 5, 353, 2048 }, { 5, 354, 2048 }, { 6, 355, 2048 }, { 5, 356, 2048 }, { 6, 357, 2048 }, { 6, 358, 2048 }, { 7, 359, 2048 },
   { 5, 360, 2048 }, { 6, 361, 2048 }, { 6, 362, 2048 }, { 7, 363, 2048 }, { 6, 364, 2048 }, { 7, 365, 2048 }, { 7, 366, 2048 }, { 8, 367, 2048 },
   { 5, 368, 2048 }, { 6, 369, 2048 }, { 6, 370, 2048 }, { 7, 371, 2048 }, { 6, 372, 2048 }, { 7, 373, 2048 }, { 7, 374, 2048 }, { 8, 375, 2048 },
   { 6, 376, 2048 }, { 7, 377, 2048 }, { 7, 378, 2048 }, { 8, 379, 2048 }, { 7, 380, 2048 }, { 8, 381, 2048 }, { 8, 382, 2048 }, { 9, 383, 2048 },
   { 3, 384, 2048 }, { 4, 385, 2048 }, { 4, 386, 2048 }, { 5, 387, 2048 }, { 4, 388, 2048 }, { 5, 389, 2048 }, { 5, 390, 2048 }, { 6, 391, 2048 },
   { 4, 392, 2048 }, { 5, 393, 2048 }, { 5, 394, 2048 }, { 6, 395, 2048 }, { 5, 396, 2048 }, { 6, 397, 2048 }, { 6, 398, 2048 }, { 7, 399, 2048 },
   { 4, 400, 2048 }, { 5, 401, 2048 }, { 5, 402, 2048 }, { 6, 403, 2048 }, { 5, 404, 2048 }, { 6, 405, 2048 }, { 6, 406, 2048 }, { 7, 407, 2048 },
   { 5, 408, 2048 }, { 6, 409, 2048 }, { 6, 410, 2048 }, { 7, 411, 2048 }, { 6, 412, 2048 }, { 7, 413, 2048 }, { 7, 414, 2048 }, { 8, 415, 2048 },
   { 4, 416, 2048 }, { 5, 417, 2048 }, { 5, 418, 2048 }, { 6, 419, 2048 }, { 5, 420, 2048 }, { 6, 421, 2048 }, { 6, 422, 2048 }, { 7, 423, 2048 },
   { 5, 424, 2048 }, { 6, 425, 2048 }, { 6, 426, 2048 }, { 7, 427, 2048 }, { 6, 428, 2048 }, { 7, 429, 2048 }, { 7, 430, 2048 }, { 8, 431, 2048 },
   { 5, 432, 2048 }, { 6, 433, 2048 }, { 6, 434, 2048 }, { 7, 435, 2048 }, { 6, 436, 2048 }, { 7, 437, 2048 }, { 7, 438, 2048 }, { 8, 439, 2048 },
   { 6, 440, 2048 }, { 7, 441, 2048 }, { 7, 442, 2048 }, { 8, 443, 2048 }, { 7, 444, 2048 }, { 8, 445, 2048 }, { 8, 446, 2048 }, { 9, 447, 2048 },
   { 4, 448, 2048 }, { 5, 449, 2048 }, { 5, 450, 2048 }, { 6, 451, 2048 }, { 5, 452, 2048 }, { 6, 453, 2048 }, { 6, 454, 2048 }, { 7, 455, 2048 },
   { 5, 456, 2048 }, { 6, 457, 2048 }, { 6, 458, 2048 }, { 7, 459, 2048 }, { 6, 460, 2048 }, { 7, 461, 2048 }, { 7, 462, 2048 }, { 8, 463, 2048 },
   { 5, 464, 2048 }, { 6, 465, 2048 }, { 6, 466, 2048 }, { 7, 467, 2048 }, { 6, 468, 2048 }, { 7, 469, 2048 }, { 7, 470, 2048 }, { 8, 471, 2048 },
   { 6, 472, 2048 }, { 7, 473, 2048 }, { 7, 474, 2048 }, { 8, 475, 2048 }, { 7, 476, 2048 }, { 8, 477, 2048 }, { 8, 478, 2048 }, { 9, 479, 2048 },
   { 5, 480, 2048 }, { 6, 481, 2048 }, { 6, 482, 2048 }, { 7, 483, 2048 }, { 6, 484, 2048 }, { 7, 485, 2048 }, { 7, 486, 2048 }, { 8, 487, 2048 },
   { 6, 488, 2048 }, { 7, 489, 2048 }, { 7, 490, 2048 }, { 8, 491, 2048 }, { 7, 492, 2048 }, { 8, 493, 2048 }, { 8, 494, 2048 }, { 9, 495, 2048 },
   { 6, 496, 2048 }, { 7, 497, 2048 }, { 7, 498, 2048 }, { 8, 499, 2048 }, { 7, 500, 2048 }, { 8, 501, 2048 }, { 8, 502, 2048 }, { 9, 503, 2048 },
   { 7, 504, 2048 }, { 8, 505, 2048 }, { 8, 506, 2048 }, { 9, 507, 2048 }, { 8, 508, 2048 }, { 9, 509, 2048 }, { 9, 510, 2048 }, { 10, 511, 2048 },
   { 2, 512, 2048 }, { 3, 513, 2048 }, { 3, 514, 2048 }, { 4, 515, 2048 }, { 3, 516, 2048 }, { 4, 517, 2048 }, { 4, 518, 2048 }, { 5, 519, 2048 },
   { 3, 520, 2048 }, { 4, 521, 2048 }, { 4, 522, 2048 }, { 5, 523, 2048 }, { 4, 524, 2048 }, { 5, 525, 2048 }, { 5, 526, 2048 }, { 6, 527, 2048 },
   { 3, 528, 2048 }, { 4, 529, 2048 }, { 4, 530, 2048 }, { 5, 531, 2048 }, { 4, 532, 2048 }, { 5, 533, 2048 }, { 5, 534, 2048 }, { 6, 535, 2048 },
   { 4, 536, 2048 }, { 5, 537, 2048 }, { 5, 538, 2048 }, { 6, 539, 2048 }, { 5, 540, 2048 }, { 6, 541, 2048 }, { 6, 542, 2048 }, { 7, 543, 2048 },
   { 3, 544, 2048 }, { 4, 545, 2048 }, { 4, 546, 2048 }, { 5, 547, 2048 }, { 4, 548, 2048 }, { 5, 549, 2048 }, { 5, 550, 2048 }, { 6, 551, 2048 },
   { 4, 552, 2048 }, { 5, 553, 2048 }, { 5, 554, 2048 }, { 6, 555, 2048 }, { 5, 556, 2048 }, { 6, 557, 2048 }, { 6, 558, 2048 }, { 7, 559, 2048 },
   { 4, 560, 2048 }, { 5, 561, 2048 }, { 5, 562, 2048 }, { 6, 563, 2048 }, { 5, 564, 2048 }, { 6, 565, 2048 }, { 6, 566, 2048 }, { 7, 567, 2048 },
   { 5, 568, 2048 }, { 6, 569, 2048 }, { 6, 570, 2048 }, { 7, 571, 2048 }, { 6, 572, 2048 }, { 7, 573, 2048 }, { 7, 574, 2048 }, { 8, 575, 2048 },
   { 3, 576, 2048 }, { 4, 577, 2048 }, { 4, 578, 2048 }, { 5, 579, 2048 }, { 4, 580, 2048 }, { 5, 581, 2048 }, { 5, 582, 2048 }, { 6, 583, 2048 },
   { 4, 584, 2048 }, { 5, 585, 2048 }, { 5, 586, 2048 }, { 6, 587, 2048 }, { 5, 588, 2048 }, { 6, 589, 2048 }, { 6, 590, 2048 }, { 7, 591, 2048 },
   { 4, 592, 2048 }, { 5, 593, 2048 }, { 5, 594, 2048 }, { 6, 595, 2048 }, { 5, 596, 2048 }, { 6, 597, 2048 }, { 6, 598, 2048 }, { 7, 599, 2048 },
   { 5, 600, 2048 }, { 6, 601, 2048 }, { 6, 602, 2048 }, { 7, 603, 2048 }, { 6, 604, 2048 }, { 7, 605, 2048 }, { 7, 606, 2048 }, { 8, 607, 2048 },
   { 4, 608, 2048 }, { 5, 609, 2048 }, { 5, 610, 2048 }, { 6, 611, 2048 }, { 5, 612, 2048 }, { 6, 613, 2048 }, { 6, 614, 2048 }, { 7, 615, 2048 },
   { 5, 616, 2048 }, { 6, 617, 2048 }, { 6, 618, 2048 }, { 7, 619, 2048 }, { 6, 620, 2048 }, { 7, 621, 2048 }, { 7, 622, 2048 }, { 8, 623, 2048 },
   { 5, 624, 2048 }, { 6, 625, 2048 }, { 6, 626, 2048 }, { 7, 627, 2048 }, { 6, 628, 2048 }, { 7, 629, 2048 }, { 7, 630, 2048 }, { 8, 631, 2048 },
   { 6, 632, 2048 }, { 7, 633, 2048 }, { 7, 634, 2048 }, { 8, 635, 2048 }, { 7, 636, 2048 }, { 8, 637, 2048 }, { 8, 638, 2048 }, { 9, 639, 2048 },
   { 3, 640, 2048 }, { 4, 641, 2048 }, { 4, 642, 2048 }, { 5, 643, 2048 }, { 4, 644, 2048 }, { 5, 645, 2048 }, { 5, 646, 2048 }, { 6, 647, 2048 },
   { 4, 648, 2048 }, { 5, 649, 2048 }, { 5, 650, 2048 }, { 6, 651, 2048 }, { 5, 652, 2048 }, { 6, 653, 2048 }, { 6, 654, 2048 }, { 7, 655, 2048 },
   { 4, 656, 2048 }, { 5, 657, 2048 }, { 5, 658, 2048 }, { 6, 659, 2048 }, { 5, 660, 2048 }, { 6, 661, 2048 }, { 6, 662, 2048 }, { 7, 663, 2048 },
   { 5, 664, 2048 }, { 6, 665, 2048 }, { 6, 666, 2048 }, { 7, 667, 2048 }, { 6, 668, 2048 }, { 7, 669, 2048 }, { 7, 670, 2048 }, { 8, 671, 2048 },
   { 4, 672, 2048 }, { 5, 673, 2048 }, { 5, 674, 2048 }, { 6, 675, 2048 }, { 5, 676, 2048 }, { 6, 677, 2048 }, { 6, 678, 2048 }, { 7, 679, 2048 },
   { 5, 680, 2048 }, { 6, 681, 2048 }, { 6, 682, 2048 }, { 7, 683, 2048 }, { 6, 684, 2048 }, { 7, 685, 2048 }, { 7, 686, 2048 }, { 8, 687, 2048 },
   { 5, 688, 2048 }, { 6, 689, 2048 }, { 6, 690, 2048 }, { 7, 691, 2048 }, { 6, 692, 2048 }, { 7, 693, 2048 }, { 7, 694, 2048 }, { 8, 695, 2048 },
   { 6, 696, 2048 }, { 7, 697, 2048 }, { 7, 698, 2048 }, { 8, 699, 2048 }, { 7, 700, 2048 }, { 8, 701, 2048 }, { 8, 702, 2048 }, { 9, 703, 2048 },
   { 4, 704, 2048 }, { 5, 705, 2048 }, { 5, 706, 2048 }, { 6, 707, 2048 }, { 5, 708, 2048 }, { 6, 709, 2048 }, { 6, 710, 2048 }, { 7, 711, 2048 },
   { 5, 712, 2048 }, { 6, 713, 2048 }, { 6, 714, 2048 }, { 7, 715, 2048 }, { 6, 716, 2048 }, { 7, 717, 2048 }, { 7, 718, 2048 }, { 8, 719, 2048 },
   { 5, 720, 2048 }, { 6, 721, 2048 }, { 6, 722, 2048 }, { 7, 723, 2048 }, { 6, 724, 2048 }, { 7, 725, 2048 }, { 7, 726, 2048 }, { 8, 727, 2048 },
   { 6, 728, 2048 }, { 7, 729, 2048 }, { 7, 730, 2048 }, { 8, 731, 2048 }, { 7, 732, 2048 }, { 8, 733, 2048 }, { 8, 734, 2048 }, { 9, 735, 2048 },
   { 5, 736, 2048 }, { 6, 737, 2048 }, { 6, 738, 2048 }, { 7, 739, 2048 }, { 6, 740, 2048 }, { 7, 741, 2048 }, { 7, 742, 2048 }, { 8, 743, 2048 },
   { 6, 744, 2048 }, { 7, 745, 2048 }, { 7, 746, 2048 }, { 8, 747, 2048 }, { 7, 748, 2048 }, { 8, 749, 2048 }, { 8, 750, 2048 }, { 9, 751, 2048 },
   { 6, 752, 2048 }, { 7, 753, 2048 }, { 7, 754, 2048 }, { 8, 755, 2048 }, { 7, 756, 2048 }, { 8, 757, 2048 }, { 8, 758, 2048 }, { 9, 759, 2048 },
   { 7, 760, 2048 }, { 8, 761, 2048 }, { 8, 762, 2048 }, { 9, 763, 2048 }, { 8, 764, 2048 }, { 9, 765, 2048 }, { 9, 766, 2048 }, { 10, 767, 2048 },
   { 3, 768, 2048 }, { 4, 769, 2048 }, { 4, 770, 2048 }, { 5, 771, 2048 }, { 4, 772, 2048 }, { 5, 773, 2048 }, { 5, 774, 2048 }, { 6, 775, 2048 },
   { 4, 776, 2048 }, { 5, 777, 2048 }, { 5, 778, 2048 }, { 6, 779, 2048 }, { 5, 780, 2048 }, { 6, 781, 2048 }, { 6, 782, 2048 }, { 7, 783, 2048 },
   { 4, 784, 2048 }, { 5, 785, 2048 }, { 5, 786, 2048 }, { 6, 787, 2048 }, { 5, 788, 2048 }, { 6, 789, 2048 }, { 6, 790, 2048 }, { 7, 791, 2048 },
   { 5, 792, 2048 }, { 6, 793, 2048 }, { 6, 794, 2048 }, { 7, 795, 2048 }, { 6, 796, 2048 }, { 7, 797, 2048 }, { 7, 798, 2048 }, { 8, 799, 2048 },
   { 4, 800, 2048 }, { 5, 801, 2048 }, { 5, 802, 2048 }, { 6, 803, 2048 }, { 5, 804, 2048 }, { 6, 805, 2048 }, { 6, 806, 2048 }, { 7, 807, 2048 },
   { 5, 808, 2048 }, { 6, 809, 2048 }, { 6, 810, 2048 }, { 7, 811, 2048 }, { 6, 812, 2048 }, { 7, 813, 2048 }, { 7, 814, 2048 }, { 8, 815, 2048 },
   { 5, 816, 2048 }, { 6, 817, 2048 }, { 6, 818, 2048 }, { 7, 819, 2048 }, { 6, 820, 2048 }, { 7, 821, 2048 }, { 7, 822, 2048 }, { 8, 823, 2048 },
   { 6, 824, 2048 }, { 7, 825, 2048 }, { 7, 826, 2048 }, { 8, 827, 2048 }, { 7, 828, 2048 }, { 8, 829, 2048 }, { 8, 830, 2048 }, { 9, 831, 2048 },
   { 4, 832, 2048 }, { 5, 833, 2048 }, { 5, 834, 2048 }, { 6, 835, 2048 }, { 5, 836, 2048 }, { 6, 837, 2048 }, { 6, 838, 2048 }, { 7, 839, 2048 },
   { 5, 840, 2048 }, { 6, 841, 2048 }, { 6, 842, 2048 }, { 7, 843, 2048 }, { 6, 844, 2048 }, { 7, 845, 2048 }, { 7, 846, 2048 }, { 8, 847, 2048 },
   { 5, 848, 2048 }, { 6, 849, 2048 }, { 6, 850, 2048 }, { 7, 851, 2048 }, { 6, 852, 2048 }, { 7, 853, 2048 }, { 7, 854, 2048 }, { 8, 855, 2048 },
   { 6, 856, 2048 }, { 7, 857, 2048 }, { 7, 858, 2048 }, { 8, 859, 2048 }, { 7, 860, 2048 }, { 8, 861, 2048 }, { 8, 862, 2048 }, { 9, 863, 2048 },
   { 5, 864, 2048 }, { 6, 865, 2048 }, { 6, 866, 2048 }, { 7, 867, 2048 }, { 6, 868, 2048 }, { 7, 869, 2048 }, { 7, 870, 2048 }, { 8, 871, 2048 },
   { 6, 872, 2048 }, { 7, 873, 2048 }, { 7, 874, 2048 }, { 8, 875, 2048 }, { 7, 876, 2048 }, { 8, 877, 2048 }, { 8, 878, 2048 }, { 9, 879, 2048 },
   { 6, 880, 2048 }, { 7, 881, 2048 }, { 7, 882, 2048 }, { 8, 883, 2048 }, { 7, 884, 2048 }, { 8, 885, 2048 }, { 8, 886, 2048 }, { 9, 887, 2048 },
   { 7, 888, 2048 }, { 8, 889, 2048 }, { 8, 890, 2048 }, { 9, 891, 2048 }, { 8, 892, 2048 }, { 9, 893, 2048 }, { 9, 894, 2048 }, { 10, 895, 2048 },
   { 4, 896, 2048 }, { 5, 897, 2048 }, { 5, 898, 2048 }, { 6, 899, 2048 }, { 5, 900, 2048 }, { 6, 901, 2048 }, { 6, 902, 2048 }, { 7, 903, 2048 },
   { 5, 904, 2048 }, { 6, 905, 2048 }, { 6, 906, 2048 }, { 7, 907, 2048 }, { 6, 908, 2048 }, { 7, 909, 2048 }, { 7, 910, 2048 }, { 8, 911, 2048 },
   { 5, 912, 2048 }, { 6, 913, 2048 }, { 6, 914, 2048 }, { 7, 915, 2048 }, { 6, 916, 2048 }, { 7, 917, 2048 }, { 7, 918, 2048 }, { 8, 919, 2048 },
   { 6, 920, 2048 }, { 7, 921, 2048 }, { 7, 922, 2048 }, { 8, 923, 2048 }, { 7, 924, 2048 }, { 8, 925, 2048 }, { 8, 926, 2048 }, { 9, 927, 2048 },
   { 5, 928, 2048 }, { 6, 929, 2048 }, { 6, 930, 2048 }, { 7, 931, 2048 }, { 6, 932, 2048 }, { 7, 933, 2048 }, { 7, 934, 2048 }, { 8, 935, 2048 },
   { 6, 936, 2048 }, { 7, 937, 2048 }, { 7, 938, 2048 }, { 8, 939, 2048 }, { 7, 940, 2048 }, { 8, 941, 2048 }, { 8, 942, 2048 }, { 9, 943, 2048 },
   { 6, 944, 2048 }, { 7, 945, 2048 }, { 7, 946, 2048 }, { 8, 947, 2048 }, { 7, 948, 2048 }, { 8, 949, 2048 }, { 8, 950, 2048 }, { 9, 951, 2048 },
   { 7, 952, 2048 }, { 8, 953, 2048 }, { 8, 954, 2048 }, { 9, 955, 2048 }, { 8, 956, 2048 }, { 9, 957, 2048 }, { 9, 958, 2048 }, { 10, 959, 2048 },
   { 5, 960, 2048 }, { 6, 961, 2048 }, { 6, 962, 2048 }, { 7, 963, 2048 }, { 6, 964, 2048 }, { 7, 965, 2048 }, { 7, 966, 2048 }, { 8, 967, 2048 },
   { 6, 968, 2048 }, { 7, 969, 2048 }, { 7, 970, 2048 }, { 8, 971, 2048 }, { 7, 972, 2048 }, { 8, 973, 2048 }, { 8, 974, 2048 }, { 9, 975, 2048 },
   { 6, 976, 2048 }, { 7, 977, 2048 }, { 7, 978, 2048 }, { 8, 979, 2048 }, { 7, 980, 2048 }, { 8, 981, 2048 }, { 8, 982, 2048 }, { 9, 983, 2048 },
   { 7, 984, 2048 }, { 8, 985, 2048 }, { 8, 986, 2048 }, { 9, 987, 2048 }, { 8, 988, 2048 }, { 9, 989, 2048 }, { 9, 990, 2048 }, { 10, 991, 2048 },
   { 6, 992, 2048 }, { 7, 993, 2048 }, { 7, 994, 2048 }, { 8, 995, 2048 }, { 7, 996, 2048 }, { 8, 997, 2048 }, { 8, 998, 2048 }, { 9, 999, 2048 },
   { 7, 1000, 2048 }, { 8, 1001, 2048 }, { 8, 1002, 2048 }, { 9, 1003, 2048 }, { 8, 1004, 2048 }, { 9, 1005, 2048 }, { 9, 1006, 2048 }, { 10, 1007, 2048 },
   { 7, 1008, 2048 }, { 8, 1009, 2048 }, { 8, 1010, 2048 }, { 9, 1011, 2048 }, { 8, 1012, 2048 }, { 9, 1013, 2048 }, { 9, 1014, 2048 }, { 10, 1015, 2048 },
   { 8, 1016, 2048 }, { 9, 1017, 2048 }, { 9, 1018, 2048 }, { 10, 1019, 2048 }, { 9, 1020, 2048 }, { 10, 1021, 2048 }, { 10, 1022, 2048 }, { 11, 1023, 2048 },
   { 2, 1024, 2048 }, { 3, 1025, 2048 }, { 3, 1026, 2048 }, { 4, 1027, 2048 }, { 3, 1028, 2048 }, { 4, 1029, 2048 }, { 4, 1030, 2048 }, { 5, 1031, 2048 },
   { 3, 1032, 2048 }, { 4, 1033, 2048 }, { 4, 1034, 2048 }, { 5, 1035, 2048 }, { 4, 1036, 2048 }, { 5, 1037, 2048 }, { 5, 1038, 2048 }, { 6, 1039, 2048 },
   { 3, 1040, 2048 }, { 4, 1041, 2048 }, { 4, 1042, 2048 }, { 5, 1043, 2048 }, { 4, 1044, 2048 }, { 5, 1045, 2048 }, { 5, 1046, 2048 }, { 6, 1047, 2048 },
   { 4, 1048, 2048 }, { 5, 1049, 2048 }, { 5, 1050, 2048 }, { 6, 1051, 2048 }, { 5, 1052, 2048 }, { 6, 1053, 2048 }, { 6, 1054, 2048 }, { 7, 1055, 2048 },
   { 3, 1056, 2048 }, { 4, 1057, 2048 }, { 4, 1058, 2048 }, { 5, 1059, 2048 }, { 4, 1060, 2048 }, { 5, 1061, 2048 }, { 5, 1062, 2048 }, { 6, 1063, 2048 },
   { 4, 1064, 2048 }, { 5, 1065, 2048 }, { 5, 1066, 2048 }, { 6, 1067, 2048 }, { 5, 1068, 2048 }, { 6, 1069, 2048 }, { 6, 1070, 2048 }, { 7, 1071, 2048 },
   { 4, 1072, 2048 }, { 5, 1073, 2048 }, { 5, 1074, 2048 }, { 6, 1075, 2048 }, { 5, 1076, 2048 }, { 6, 1077, 2048 }, { 6, 1078, 2048 }, { 7, 1079, 2048 },
   { 5, 1080, 2048 }, { 6, 1081, 2048 }, { 6, 1082, 2048 }, { 7, 1083, 2048 }, { 6, 1084, 2048 }, { 7, 1085, 2048 }, { 7, 1086, 2048 }, { 8, 1087, 2048 },
   { 3, 1088, 2048 }, { 4, 1089, 2048 }, { 4, 1090, 2048 }, { 5, 1091, 2048 }, { 4, 1092, 2048 }, { 5, 1093, 2048 }, { 5, 1094, 2048 }, { 6, 1095, 2048 },
   { 4, 1096, 2048 }, { 5, 1097, 2048 }, { 5, 1098, 2048 }, { 6, 1099, 2048 }, { 5, 1100, 2048 }, { 6, 1101, 2048 }, { 6, 1102, 2048 }, { 7, 1103, 2048 },
   { 4, 1104, 2048 }, { 5, 1105, 2048 }, { 5, 1106, 2048 }, { 6, 1107, 2048 }, { 5, 1108, 2048 }, { 6, 1109, 2048 }, { 6, 1110, 2048 }, { 7, 1111, 2048 },
   { 5, 1112, 2048 }, { 6, 1113, 2048 }, { 6, 1114, 2048 }, { 7, 1115, 2048 }, { 6, 1116, 2048 }, { 7, 1117, 2048 }, { 7, 1118, 2048 }, { 8, 1119, 2048 },
   { 4, 1120, 2048 }, { 5, 1121, 2048 }, { 5, 1122, 2048 }, { 6, 1123, 2048 }, { 5, 1124, 2048 }, { 6, 1125, 2048 }, { 6, 1126, 2048 }, { 7, 1127, 2048 },
   { 5, 1128, 2048 }, { 6, 1129, 2048 }, { 6, 1130, 2048 }, { 7, 1131, 2048 }, { 6, 1132, 2048 }, { 7, 1133, 2048 }, { 7, 1134, 2048 }, { 8, 1135, 2048 },
   { 5, 1136, 2048 }, { 6, 1137, 2048 }, { 6, 1138, 2048 }, { 7, 1139, 2048 }, { 6, 1140, 2048 }, { 7, 1141, 2048 }, { 7, 1142, 2048 }, { 8, 1143, 2048 },
   { 6, 1144, 2048 }, { 7, 1145, 2048 }, { 7, 1146, 2048 }, { 8, 1147, 2048 }, { 7, 1148, 2048 }, { 8, 1149, 2048 }, { 8, 1150, 2048 }, { 9, 1151, 2048 },
   { 3, 1152, 2048 }, { 4, 1153, 2048 }, { 4, 1154, 2048 }, { 5, 1155, 2048 }, { 4, 1156, 2048 }, { 5, 1157, 2048 }, { 5, 1158, 2048 }, { 6, 1159, 2048 },
   { 4, 1160, 2048 }, { 5, 1161, 2048 }, { 5, 1162, 2048 }, { 6, 1163, 2048 }, { 5, 1164, 2048 }, { 6, 1165, 2048 }, { 6, 1166, 2048 }, { 7, 1167, 2048 },
   { 4, 1168, 2048 }, { 5, 1169, 2048 }, { 5, 1170, 2048 }, { 6, 1171, 2048 }, { 5, 1172, 2048 }, { 6, 1173, 2048 }, { 6, 1174, 2048 }, { 7, 1175, 2048 },
   { 5, 1176, 2048 }, { 6, 1177, 2048 }, { 6, 1178, 2048 }, { 7, 1179, 2048 }, { 6, 1180, 2048 }, { 7, 1181, 2048 }, { 7, 1182, 2048 }, { 8, 1183, 2048 },
   { 4, 1184, 2048 }, { 5, 1185, 2048 }, { 5, 1186, 2048 }, { 6, 1187, 2048 }, { 5, 1188, 2048 }, { 6, 1189, 2048 }, { 6, 1190, 2048 }, { 7, 1191, 2048 },
   { 5, 1192, 2048 }, { 6, 1193, 2048 }, { 6, 1194, 2048 }, { 7, 1195, 2048 }, { 6, 1196, 2048 }, { 7, 1197, 2048 }, { 7, 1198, 2048 }, { 8, 1199, 2048 },
   { 5, 1200, 2048 }, { 6, 1201, 2048 }, { 6, 1202, 2048 }, { 7, 1203, 2048 }, { 6, 1204, 2048 }, { 7, 1205, 2048 }, { 7, 1206, 2048 }, { 8, 1207, 2048 },
   { 6, 1208, 2048 }, { 7, 1209, 2048 }, { 7, 1210, 2048 }, { 8, 1211, 2048 }, { 7, 1212, 2048 }, { 8, 1213, 2048 }, { 8, 1214, 2048 }, { 9, 1215, 2048 },
   { 4, 1216, 2048 }, { 5, 1217, 2048 }, { 5, 1218, 2048 }, { 6, 1219, 2048 }, { 5, 1220, 2048 }, { 6, 1221, 2048 }, { 6, 1222, 2048 }, { 7, 1223, 2048 },
   { 5, 1224, 2048 }, { 6, 1225, 2048 }, { 6, 1226, 2048 }, { 7, 1227, 2048 }, { 6, 1228, 2048 }, { 7, 1229, 2048 }, { 7, 1230, 2048 }, { 8, 1231, 2048 },
   { 5, 1232, 2048 }, { 6, 1233, 2048 }, { 6, 1234, 2048 }, { 7, 1235, 2048 }, { 6, 1236, 2048 }, { 7, 1237, 2048 }, { 7, 1238, 2048 }, { 8, 1239, 2048 },
   { 6, 1240, 2048 }, { 7, 1241, 2048 }, { 7, 1242, 2048 }, { 8, 1243, 2048 }, { 7, 1244, 2048 }, { 8, 1245, 2048 }, { 8, 1246, 2048 }, { 9, 1247, 2048 },
   { 5, 1248, 2048 }, { 6, 1249, 2048 }, { 6, 1250, 2048 }, { 7, 1251, 2048 }, { 6, 1252, 2048 }, { 7, 1253, 2048 }, { 7, 1254, 2048 }, { 8, 1255, 2048 },
   { 6, 1256, 2048 }, { 7, 1257, 2048 }, { 7, 1258, 2048 }, { 8, 1259, 2048 }, { 7, 1260, 2048 }, { 8, 1261, 2048 }, { 8, 1262, 2048 }, { 9, 1263, 2048 },
   { 6, 1264, 2048 }, { 7, 1265, 2048 }, { 7, 1266, 2048 }, { 8, 1267, 2048 }, { 7, 1268, 2048 }, { 8, 1269, 2048 }, { 8, 1270, 2048 }, { 9, 1271, 2048 },
   { 7, 1272, 2048 }, { 8, 1273, 2048 }, { 8, 1274, 2048 }, { 9, 1275, 2048 }, { 8, 1276, 2048 }, { 9, 1277, 2048 }, { 9, 1278, 2048 }, { 10, 1279, 2048 },
   { 3, 1280, 2048 }, { 4, 1281, 2048 }, { 4, 1282, 2048 }, { 5, 1283, 2048 }, { 4, 1284, 2048 }, { 5, 1285, 2048 }, { 5, 1286, 2048 }, { 6, 1287, 2048 },
   { 4, 1288, 2048 }, { 5, 1289, 2048 }, { 5, 1290, 2048 }, { 6, 1291, 2048 }, { 5, 1292, 2048 }, { 6, 1293, 2048 }, { 6, 1294, 2048 }, { 7, 1295, 2048 },
   { 4, 1296, 2048 }, { 5, 1297, 2048 }, { 5, 1298, 2048 }, { 6, 1299, 2048 }, { 5, 1300, 2048 }, { 6, 1301, 2048 }, { 6, 1302, 2048 }, { 7, 1303, 2048 },
   { 5, 1304, 2048 }, { 6, 1305, 2048 }, { 6, 1306, 2048 }, { 7, 1307, 2048 }, { 6, 1308, 2048 }, { 7, 1309, 2048 }, { 7, 1310, 2048 }, { 8, 1311, 2048 },
   { 4, 1312, 2048 }, { 5, 1313, 2048 }, { 5, 1314, 2048 }, { 6, 1315, 2048 }, { 5, 1316, 2048 }, { 6, 1317, 2048 }, { 6, 1318, 2048 }, { 7, 1319, 2048 },
   { 5, 1320, 2048 }, { 6, 1321, 2048 }, { 6, 1322, 2048 }, { 7, 1323, 2048 }, { 6, 1324, 2048 }, { 7, 1325, 2048 }, { 7, 1326, 2048 }, { 8, 1327, 2048 },
   { 5, 1328, 2048 }, { 6, 1329, 2048 }, { 6, 1330, 2048 }, { 7, 1331, 2048 }, { 6, 1332, 2048 }, { 7, 1333, 2048 }, { 7, 1334, 2048 }, { 8, 1335, 2048 },
   { 6, 1336, 2048 }, { 7, 1337, 2048 }, { 7, 1338, 2048 }, { 8, 1339, 2048 }, { 7, 1340, 2048 }, { 8, 1341, 2048 }, { 8, 1342, 2048 }, { 9, 1343, 2048 },
   { 4, 1344, 2048 }, { 5, 1345, 2048 }, { 5, 1346, 2048 }, { 6, 1347, 2048 }, { 5, 1348, 2048 }, { 6, 1349, 2048 }, { 6, 1350, 2048 }, { 7, 1351, 2048 },
   { 5, 1352, 2048 }, { 6, 1353, 2048 }, { 6, 1354, 2048 }, { 7, 1355, 2048 }, { 6, 1356, 2048 }, { 7, 1357, 2048 }, { 7, 1358, 2048 }, { 8, 1359, 2048 },
   { 5, 1360, 2048 }, { 6, 1361, 2048 }, { 6, 1362, 2048 }, { 7, 1363, 2048 }, { 6, 1364, 2048 }, { 7, 1365, 2048 }, { 7, 1366, 2048 }, { 8, 1367, 2048 },
   { 6, 1368, 2048 }, { 7, 1369, 2048 }, { 7, 1370, 2048 }, { 8, 1371, 2048 }, { 7, 1372, 2048 }, { 8, 1373, 2048 }, { 8, 1374, 2048 }, { 9, 1375, 2048 },
   { 5, 1376, 2048 }, { 6, 1377, 2048 }, { 6, 1378, 2048 }, { 7, 1379, 2048 }, { 6, 1380, 2048 }, { 7, 1381, 2048 }, { 7, 1382, 2048 }, { 8, 1383, 2048 },
   { 6, 1384, 2048 }, { 7, 1385, 2048 }, { 7, 1386, 2048 }, { 8, 1387, 2048 }, { 7, 1388, 2048 }, { 8, 1389, 2048 }, { 8, 1390, 2048 }, { 9, 1391, 2048 },
   { 6, 1392, 2048 }, { 7, 1393, 2048 }, { 7, 1394, 2048 }, { 8, 1395, 2048 }, { 7, 1396, 2048 }, { 8, 1397, 2048 }, { 8, 1398, 2048 }, { 9, 1399, 2048 },
   { 7, 1400, 2048 }, { 8, 1401, 2048 }, { 8, 1402, 2048 }, { 9, 1403, 2048 }, { 8, 1404, 2048 }, { 9, 1405, 2048 }, { 9, 1406, 2048 }, { 10, 1407, 2048 },
   { 4, 1408, 2048 }, { 5, 1409, 2048 }, { 5, 1410, 2048 }, { 6, 1411, 2048 }, { 5, 1412, 2048 }, { 6, 1413, 2048 }, { 6, 1414, 2048 }, { 7, 1415, 2048 },
   { 5, 1416, 2048 }, { 6, 1417, 2048 }, { 6, 1418, 2048 }, { 7, 1419, 2048 }, { 6, 1420, 2048 }, { 7, 1421, 2048 }, { 7, 1422, 2048 }, { 8, 1423, 2048 },
   { 5, 1424, 2048 }, { 6, 1425, 2048 }, { 6, 1426, 2048 }, { 7, 1427, 2048 }, { 6, 1428, 2048 }, { 7, 1429, 2048 }, { 7, 1430, 2048 }, { 8, 1431, 2048 },
   { 6, 1432, 2048 }, { 7, 1433, 2048 }, { 7, 1434, 2048 }, { 8, 1435, 2048 }, { 7, 1436, 2048 }, { 8, 1437, 2048 }, { 8, 1438, 2048 }, { 9, 1439, 2048 },
   { 5, 1440, 2048 }, { 6, 1441, 2048 }, { 6, 1442, 2048 }, { 7, 1443, 2048 }, { 6, 1444, 2048 }, { 7, 1445, 2048 }, { 7, 1446, 2048 }, { 8, 1447, 2048 },
   { 6, 1448, 2048 }, { 7, 1449, 2048 }, { 7, 1450, 2048 }, { 8, 1451, 2048 }, { 7, 1452, 2048 }, { 8, 1453, 2048 }, { 8, 1454, 2048 }, { 9, 1455, 2048 },
   { 6, 1456, 2048 }, { 7, 1457, 2048 }, { 7, 1458, 2048 }, { 8, 1459, 2048 }, { 7, 1460, 2048 }, { 8, 1461, 2048 }, { 8, 1462, 2048 }, { 9, 1463, 2048 },
   { 7, 1464, 2048 }, { 8, 1465, 2048 }, { 8, 1466, 2048 }, { 9, 1467, 2048 }, { 8, 1468, 2048 }, { 9, 1469, 2048 }, { 9, 1470, 2048 }, { 10, 1471, 2048 },
   { 5, 1472, 2048 }, { 6, 1473, 2048 }, { 6, 1474, 2048 }, { 7, 1475, 2048 }, { 6, 1476, 2048 }, { 7, 1477, 2048 }, { 7, 1478, 2048 }, { 8, 1479, 2048 },
   { 6, 1480, 2048 }, { 7, 1481, 2048 }, { 7, 1482, 2048 }, { 8, 1483, 2048 }, { 7, 1484, 2048 }, { 8, 1485, 2048 }, { 8, 1486, 2048 }, { 9, 1487, 2048 },
   { 6, 1488, 2048 }, { 7, 1489, 2048 }, { 7, 1490, 2048 }, { 8, 1491, 2048 }, { 7, 1492, 2048 }, { 8, 1493, 2048 }, { 8, 1494, 2048 }, { 9, 1495, 2048 },
   { 7, 1496, 2048 }, { 8, 1497, 2048 }, { 8, 1498, 2048 }, { 9, 1499, 2048 }, { 8, 1500, 2048 }, { 9, 1501, 2048 }, { 9, 1502, 2048 }, { 10, 1503, 2048 },
   { 6, 1504, 2048 }, { 7, 1505, 2048 }, { 7, 1506, 2048 }, { 8, 1507, 2048 }, { 7, 1508, 2048 }, { 8, 1509, 2048 }, { 8, 1510, 2048 }, { 9, 1511, 2048 },
   { 7, 1512, 2048 }, { 8, 1513, 2048 }, { 8, 1514, 2048 }, { 9, 1515, 2048 }, { 8, 1516, 2048 }, { 9, 1517, 2048 }, { 9, 1518, 2048 }, { 10, 1519, 2048 },
   { 7, 1520, 2048 }, { 8, 1521, 2048 }, { 8, 1522, 2048 }, { 9, 1523, 2048 }, { 8, 1524, 2048 }, { 9, 1525, 2048 }, { 9, 1526, 2048 }, { 10, 1527, 2048 },
   { 8, 1528, 2048 }, { 9, 1529, 2048 }, { 9, 1530, 2048 }, { 10, 1531, 2048 }, { 9, 1532, 2048 }, { 10, 1533, 2048 }, { 10, 1534, 2048 }, { 11, 1535, 2048 },
   { 3, 1536, 2048 }, { 4, 1537, 2048 }, { 4, 1538, 2048 }, { 5, 1539, 2048 }, { 4, 1540, 2048 }, { 5, 1541, 2048 }, { 5, 1542, 2048 }, { 6, 1543, 2048 },
   { 4, 1544, 2048 }, { 5, 1545, 2048 }, { 5, 1546, 2048 }, { 6, 1547, 2048 }, { 5, 1548, 2048 }, { 6, 1549, 2048 }, { 6, 1550, 2048 }, { 7, 1551, 2048 },
   { 4, 1552, 2048 }, { 5, 1553, 2048 }, { 5, 1554, 2048 }, { 6, 1555, 2048 }, { 5, 1556, 2048 }, { 6, 1557, 2048 }, { 6, 1558, 2048 }, { 7, 1559, 2048 },
   { 5, 1560, 2048 }, { 6, 1561, 2048 }, { 6, 1562, 2048 }, { 7, 1563, 2048 }, { 6, 1564, 2048 }, { 7, 1565, 2048 }, { 7, 1566, 2048 }, { 8, 1567, 2048 },
   { 4, 1568, 2048 }, { 5, 1569, 2048 }, { 5, 1570, 2048 }, { 6, 1571, 2048 }, { 5, 1572, 2048 }, { 6, 1573, 2048 }, { 6, 1574, 2048 }, { 7, 1575, 2048 },
   { 5, 1576, 2048 }, { 6, 1577, 2048 }, { 6, 1578, 2048 }, { 7, 1579, 2048 }, { 6, 1580, 2048 }, { 7, 1581, 2048 }, { 7, 1582, 2048 }, { 8, 1583, 2048 },
   { 5, 1584, 2048 }, { 6, 1585, 2048 }, { 6, 1586, 2048 }, { 7, 1587, 2048 }, { 6, 1588, 2048 }, { 7, 1589, 2048 }, { 7, 1590, 2048 }, { 8, 1591, 2048 },
   { 6, 1592, 2048 }, { 7, 1593, 2048 }, { 7, 1594, 2048 }, { 8, 1595, 2048 }, { 7, 1596, 2048 }, { 8, 1597, 2048 }, { 8, 1598, 2048 }, { 9, 1599, 2048 },
   { 4, 1600, 2048 }, { 5, 1601, 2048 }, { 5, 1602, 2048 }, { 6, 1603, 2048 }, { 5, 1604, 2048 }, { 6, 1605, 2048 }, { 6, 1606, 2048 }, { 7, 1607, 2048 },
   { 5, 1608, 2048 }, { 6, 1609, 2048 }, { 6, 1610, 2048 }, { 7, 1611, 2048 }, { 6, 1612, 2048 }, { 7, 1613, 2048 }, { 7, 1614, 2048 }, { 8, 1615, 2048 },
   { 5, 1616, 2048 }, { 6, 1617, 2048 }, { 6, 1618, 2048 }, { 7, 1619, 2048 }, { 6, 1620, 2048 }, { 7, 1621, 2048 }, { 7, 1622, 2048 }, { 8, 1623, 2048 },
   { 6, 1624, 2048 }, { 7, 1625, 2048 }, { 7, 1626, 2048 }, { 8, 1627, 2048 }, { 7, 1628, 2048 }, { 8, 1629, 2048 }, { 8, 1630, 2048 }, { 9, 1631, 2048 },
   { 5, 1632, 2048 }, { 6, 1633, 2048 }, { 6, 1634, 2048 }, { 7, 1635, 2048 }, { 6, 1636, 2048 }, { 7, 1637, 2048 }, { 7, 1638, 2048 }, { 8, 1639, 2048 },
   { 6, 1640, 2048 }, { 7, 1641, 2048 }, { 7, 1642, 2048 }, { 8, 1643, 2048 }, { 7, 1644, 2048 }, { 8, 1645, 2048 }, { 8, 1646, 2048 }, { 9, 1647, 2048 },
   { 6, 1648, 2048 }, { 7, 1649, 2048 }, { 7, 1650, 2048 }, { 8, 1651, 2048 }, { 7, 1652, 2048 }, { 8, 1653, 2048 }, { 8, 1654, 2048 }, { 9, 1655, 2048 },
   { 7, 1656, 2048 }, { 8, 1657, 2048 }, { 8, 1658, 2048 }, { 9, 1659, 2048 }, { 8, 1660, 2048 }, { 9, 1661, 2048 }, { 9, 1662, 2048 }, { 10, 1663, 2048 },
   { 4, 1664, 2048 }, { 5, 1665, 2048 }, { 5, 1666, 2048 }, { 6, 1667, 2048 }, { 5, 1668, 2048 }, { 6, 1669, 2048 }, { 6, 1670, 2048 }, { 7, 1671, 2048 },
   { 5, 1672, 2048 }, { 6, 1673, 2048 }, { 6, 1674, 2048 }, { 7, 1675, 2048 }, { 6, 1676, 2048 }, { 7, 1677, 2048 }, { 7, 1678, 2048 }, { 8, 1679, 2048 },
   { 5, 1680, 2048 }, { 6, 1681, 2048 }, { 6, 1682, 2048 }, { 7, 1683, 2048 }, { 6, 1684, 2048 }, { 7, 1685, 2048 }, { 7, 1686, 2048 }, { 8, 1687, 2048 },
   { 6, 1688, 2048 }, { 7, 1689, 2048 }, { 7, 1690, 2048 }, { 8, 1691, 2048 }, { 7, 1692, 2048 }, { 8, 1693, 2048 }, { 8, 1694, 2048 }, { 9, 1695, 2048 },
   { 5, 1696, 2048 }, { 6, 1697, 2048 }, { 6, 1698, 2048 }, { 7, 1699, 2048 }, { 6, 1700, 2048 }, { 7, 1701, 2048 }, { 7, 1702, 2048 }, { 8, 1703, 2048 },
   { 6, 1704, 2048 }, { 7, 1705, 2048 }, { 7, 1706, 2048 }, { 8, 1707, 2048 }, { 7, 1708, 2048 }, { 8, 1709, 2048 }, { 8, 1710, 2048 }, { 9, 1711, 2048 },
   { 6, 1712, 2048 }, { 7, 1713, 2048 }, { 7, 1714, 2048 }, { 8, 1715, 2048 }, { 7, 1716, 2048 }, { 8, 1717, 2048 }, { 8, 1718, 2048 }, { 9, 1719, 2048 },
   { 7, 1720, 2048 }, { 8, 1721, 2048 }, { 8, 1722, 2048 }, { 9, 1723, 2048 }, { 8, 1724, 2048 }, { 9, 1725, 2048 }, { 9, 1726, 2048 }, { 10, 1727, 2048 },
   { 5, 1728, 2048 }, { 6, 1729, 2048 }, { 6, 1730, 2048 }, { 7, 1731, 2048 }, { 6, 1732, 2048 }, { 7, 1733, 2048 }, { 7, 1734, 2048 }, { 8, 1735, 2048 },
   { 6, 1736, 2048 }, { 7, 1737, 2048 }, { 7, 1738, 2048 }, { 8, 1739, 2048 }, { 7, 1740, 2048 }, { 8, 1741, 2048 }, { 8, 1742, 2048 }, { 9, 1743, 2048 },
   { 6, 1744, 2048 }, { 7, 1745, 2048 }, { 7, 1746, 2048 }, { 8, 1747, 2048 }, { 7, 1748, 2048 }, { 8, 1749, 2048 }, { 8, 1750, 2048 }, { 9, 1751, 2048 },
   { 7, 1752, 2048 }, { 8, 1753, 2048 }, { 8, 1754, 2048 }, { 9, 1755, 2048 }, { 8, 1756, 2048 }, { 9, 1757, 2048 }, { 9, 1758, 2048 }, { 10, 1759, 2048 },
   { 6, 1760, 2048 }, { 7, 1761, 2048 }, { 7, 1762, 2048 }, { 8, 1763, 2048 }, { 7, 1764, 2048 }, { 8, 1765, 2048 }, { 8, 1766, 2048 }, { 9, 1767, 2048 },
   { 7, 1768, 2048 }, { 8, 1769, 2048 }, { 8, 1770, 2048 }, { 9, 1771, 2048 }, { 8, 1772, 2048 }, { 9, 1773, 2048 }, { 9, 1774, 2048 }, { 10, 1775, 2048 },
   { 7, 1776, 2048 }, { 8, 1777, 2048 }, { 8, 1778, 2048 }, { 9, 1779, 2048 }, { 8, 1780, 2048 }, { 9, 1781, 2048 }, { 9, 1782, 2048 }, { 10, 1783, 2048 },
   { 8, 1784, 2048 }, { 9, 1785, 2048 }, { 9, 1786, 2048 }, { 10, 1787, 2048 }, { 9, 1788, 2048 }, { 10, 1789, 2048 }, { 10, 1790, 2048 }, { 11, 1791, 2048 },
   { 4, 1792, 2048 }, { 5, 1793, 2048 }, { 5, 1794, 2048 }, { 6, 1795, 2048 }, { 5, 1796, 2048 }, { 6, 1797, 2048 }, { 6, 1798, 2048 }, { 7, 1799, 2048 },
   { 5, 1800, 2048 }, { 6, 1801, 2048 }, { 6, 1802, 2048 }, { 7, 1803, 2048 }, { 6, 1804, 2048 }, { 7, 1805, 2048 }, { 7, 1806, 2048 }, { 8, 1807, 2048 },
   { 5, 1808, 2048 }, { 6, 1809, 2048 }, { 6, 1810, 2048 }, { 7, 1811, 2048 }, { 6, 1812, 2048 }, { 7, 1813, 2048 }, { 7, 1814, 2048 }, { 8, 1815, 2048 },
   { 6, 1816, 2048 }, { 7, 1817, 2048 }, { 7, 1818, 2048 }, { 8, 1819, 2048 }, { 7, 1820, 2048 }, { 8, 1821, 2048 }, { 8, 1822, 2048 }, { 9, 1823, 2048 },
   { 5, 1824, 2048 }, { 6, 1825, 2048 }, { 6, 1826, 2048 }, { 7, 1827, 2048 }, { 6, 1828, 2048 }, { 7, 1829, 2048 }, { 7, 1830, 2048 }, { 8, 1831, 2048 },
   { 6, 1832, 2048 }, { 7, 1833, 2048 }, { 7, 1834, 2048 }, { 8, 1835, 2048 }, { 7, 1836, 2048 }, { 8, 1837, 2048 }, { 8, 1838, 2048 }, { 9, 1839, 2048 },
   { 6, 1840, 2048 }, { 7, 1841, 2048 }, { 7, 1842, 2048 }, { 8, 1843, 2048 }, { 7, 1844, 2048 }, { 8, 1845, 2048 }, { 8, 1846, 2048 }, { 9, 1847, 2048 },
   { 7, 1848, 2048 }, { 8, 1849, 2048 }, { 8, 1850, 2048 }, { 9, 1851, 2048 }, { 8, 1852, 2048 }, { 9, 1853, 2048 }, { 9, 1854, 2048 }, { 10, 1855, 2048 },
   { 5, 1856, 2048 }, { 6, 1857, 2048 }, { 6, 1858, 2048 }, { 7, 1859, 2048 }, { 6, 1860, 2048 }, { 7, 1861, 2048 }, { 7, 1862, 2048 }, { 8, 1863, 2048 },
   { 6, 1864, 2048 }, { 7, 1865, 2048 }, { 7, 1866, 2048 }, { 8, 1867, 2048 }, { 7, 1868, 2048 }, { 8, 1869, 2048 }, { 8, 1870, 2048 }, { 9, 1871, 2048 },
   { 6, 1872, 2048 }, { 7, 1873, 2048 }, { 7, 1874, 2048 }, { 8, 1875, 2048 }, { 7, 1876, 2048 }, { 8, 1877, 2048 }, { 8, 1878, 2048 }, { 9, 1879, 2048 },
   { 7, 1880, 2048 }, { 8, 1881, 2048 }, { 8, 1882, 2048 }, { 9, 1883, 2048 }, { 8, 1884, 2048 }, { 9, 1885, 2048 }, { 9, 1886, 2048 }, { 10, 1887, 2048 },
   { 6, 1888, 2048 }, { 7, 1889, 2048 }, { 7, 1890, 2048 }, { 8, 1891, 2048 }, { 7, 1892, 2048 }, { 8, 1893, 2048 }, { 8, 1894, 2048 }, { 9, 1895, 2048 },
   { 7, 1896, 2048 }, { 8, 1897, 2048 }, { 8, 1898, 2048 }, { 9, 1899, 2048 }, { 8, 1900, 2048 }, { 9, 1901, 2048 }, { 9, 1902, 2048 }, { 10, 1903, 2048 },
   { 7, 1904, 2048 }, { 8, 1905, 2048 }, { 8, 1906, 2048 }, { 9, 1907, 2048 }, { 8, 1908, 2048 }, { 9, 1909, 2048 }, { 9, 1910, 2048 }, { 10, 1911, 2048 },
   { 8, 1912, 2048 }, { 9, 1913, 2048 }, { 9, 1914, 2048 }, { 10, 1915, 2048 }, { 9, 1916, 2048 }, { 10, 1917, 2048 }, { 10, 1918, 2048 }, { 11, 1919, 2048 },
   { 5, 1920, 2048 }, { 6, 1921, 2048 }, { 6, 1922, 2048 }, { 7, 1923, 2048 }, { 6, 1924, 2048 }, { 7, 1925, 2048 }, { 7, 1926, 2048 }, { 8, 1927, 2048 },
   { 6, 1928, 2048 }, { 7, 1929, 2048 }, { 7, 1930, 2048 }, { 8, 1931, 2048 }, { 7, 1932, 2048 }, { 8, 1933, 2048 }, { 8, 1934, 2048 }, { 9, 1935, 2048 },
   { 6, 1936, 2048 }, { 7, 1937, 2048 }, { 7, 1938, 2048 }, { 8, 1939, 2048 }, { 7, 1940, 2048 }, { 8, 1941, 2048 }, { 8, 1942, 2048 }, { 9, 1943, 2048 },
   { 7, 1944, 2048 }, { 8, 1945, 2048 }, { 8, 1946, 2048 }, { 9, 1947, 2048 }, { 8, 1948, 2048 }, { 9, 1949, 2048 }, { 9, 1950, 2048 }, { 10, 1951, 2048 },
   { 6, 1952, 2048 }, { 7, 1953, 2048 }, { 7, 1954, 2048 }, { 8, 1955, 2048 }, { 7, 1956, 2048 }, { 8, 1957, 2048 }, { 8, 1958, 2048 }, { 9, 1959, 2048 },
   { 7, 1960, 2048 }, { 8, 1961, 2048 }, { 8, 1962, 2048 }, { 9, 1963, 2048 }, { 8, 1964, 2048 }, { 9, 1965, 2048 }, { 9, 1966, 2048 }, { 10, 1967, 2048 },
   { 7, 1968, 2048 }, { 8, 1969, 2048 }, { 8, 1970, 2048 }, { 9, 1971, 2048 }, { 8, 1972, 2048 }, { 9, 1973, 2048 }, { 9, 1974, 2048 }, { 10, 1975, 2048 },
   { 8, 1976, 2048 }, { 9, 1977, 2048 }, { 9, 1978, 2048 }, { 10, 1979, 2048 }, { 9, 1980, 2048 }, { 10, 1981, 2048 }, { 10, 1982, 2048 }, { 11, 1983, 2048 },
   { 6, 1984, 2048 }, { 7, 1985, 2048 }, { 7, 1986, 2048 }, { 8, 1987, 2048 }, { 7, 1988, 2048 }, { 8, 1989, 2048 }, { 8, 1990, 2048 }, { 9, 1991, 2048 },
   { 7, 1992, 2048 }, { 8, 1993, 2048 }, { 8, 1994, 2048 }, { 9, 1995, 2048 }, { 8, 1996, 2048 }, { 9, 1997, 2048 }, { 9, 1998, 2048 }, { 10, 1999, 2048 },
   { 7, 2000, 2048 }, { 8, 2001, 2048 }, { 8, 2002, 2048 }, { 9, 2003, 2048 }, { 8, 2004, 2048 }, { 9, 2005, 2048 }, { 9, 2006, 2048 }, { 10, 2007, 2048 },
   { 8, 2008, 2048 }, { 9, 2009, 2048 }, { 9, 2010, 2048 }, { 10, 2011, 2048 }, { 9, 2012, 2048 }, { 10, 2013, 2048 }, { 10, 2014, 2048 }, { 11, 2015, 2048 },
   { 7, 2016, 2048 }, { 8, 2017, 2048 }, { 8, 2018, 2048 }, { 9, 2019, 2048 }, { 8, 2020, 2048 }, { 9, 2021, 2048 }, { 9, 2022, 2048 }, { 10, 2023, 2048 },
   { 8, 2024, 2048 }, { 9, 2025, 2048 }, { 9, 2026, 2048 }, { 10, 2027, 2048 }, { 9, 2028, 2048 }, { 10, 2029, 2048 }, { 10, 2030, 2048 }, { 11, 2031, 2048 },
   { 8, 2032, 2048 }, { 9, 2033, 2048 }, { 9, 2034, 2048 }, { 10, 2035, 2048 }, { 9, 2036, 2048 }, { 10, 2037, 2048 }, { 10, 2038, 2048 }, { 11, 2039, 2048 },
   { 9, 2040, 2048 }, { 10, 2041, 2048 }, { 10, 2042, 2048 }, { 11, 2043, 2048 }, { 10, 2044, 2048 }, { 11, 2045, 2048 }, { 11, 2046, 2048 }, { 12, 2047, 2048 },
#endif
#endif
#endif
#endif
#endif
#endif
};

/* find a hole and free as required, return -1 if no hole found */
static int find_hole(void)
{
   unsigned x;
   int      y, z;
   for (z = -1, y = INT_MAX, x = 0; x < FP_ENTRIES; x++) {
       if (fp_cache[x].lru_count < y && fp_cache[x].lock == 0) {
          z = x;
          y = fp_cache[x].lru_count;
       }
   }

   /* decrease all */
   for (x = 0; x < FP_ENTRIES; x++) {
      if (fp_cache[x].lru_count > 3) {
         --(fp_cache[x].lru_count);
      }
   }

   /* free entry z */
   if (z >= 0 && fp_cache[z].g) {
      mp_clear(&fp_cache[z].mu);
      wc_ecc_del_point(fp_cache[z].g);
      fp_cache[z].g  = NULL;
      for (x = 0; x < (1U<<FP_LUT); x++) {
         wc_ecc_del_point(fp_cache[z].LUT[x]);
         fp_cache[z].LUT[x] = NULL;
      }
      fp_cache[z].lru_count = 0;
   }
   return z;
}

/* determine if a base is already in the cache and if so, where */
static int find_base(ecc_point* g)
{
   int x;
   for (x = 0; x < FP_ENTRIES; x++) {
      if (fp_cache[x].g != NULL &&
          mp_cmp(fp_cache[x].g->x, g->x) == MP_EQ &&
          mp_cmp(fp_cache[x].g->y, g->y) == MP_EQ &&
          mp_cmp(fp_cache[x].g->z, g->z) == MP_EQ) {
         break;
      }
   }
   if (x == FP_ENTRIES) {
      x = -1;
   }
   return x;
}

/* add a new base to the cache */
static int add_entry(int idx, ecc_point *g)
{
   unsigned x, y;

   /* allocate base and LUT */
   fp_cache[idx].g = wc_ecc_new_point();
   if (fp_cache[idx].g == NULL) {
      return GEN_MEM_ERR;
   }

   /* copy x and y */
   if ((mp_copy(g->x, fp_cache[idx].g->x) != MP_OKAY) ||
       (mp_copy(g->y, fp_cache[idx].g->y) != MP_OKAY) ||
       (mp_copy(g->z, fp_cache[idx].g->z) != MP_OKAY)) {
      wc_ecc_del_point(fp_cache[idx].g);
      fp_cache[idx].g = NULL;
      return GEN_MEM_ERR;
   }

   for (x = 0; x < (1U<<FP_LUT); x++) {
      fp_cache[idx].LUT[x] = wc_ecc_new_point();
      if (fp_cache[idx].LUT[x] == NULL) {
         for (y = 0; y < x; y++) {
            wc_ecc_del_point(fp_cache[idx].LUT[y]);
            fp_cache[idx].LUT[y] = NULL;
         }
         wc_ecc_del_point(fp_cache[idx].g);
         fp_cache[idx].g         = NULL;
         fp_cache[idx].lru_count = 0;
         return GEN_MEM_ERR;
      }
   }

   fp_cache[idx].lru_count = 0;

   return MP_OKAY;
}

/* build the LUT by spacing the bits of the input by #modulus/FP_LUT bits apart
 *
 * The algorithm builds patterns in increasing bit order by first making all
 * single bit input patterns, then all two bit input patterns and so on
 */
static int build_lut(int idx, mp_int* a, mp_int* modulus, mp_digit mp,
    mp_int* mu)
{
   int err;
   unsigned x, y, bitlen, lut_gap;
   mp_int tmp;

   if (mp_init(&tmp) != MP_OKAY)
       return GEN_MEM_ERR;

   /* sanity check to make sure lut_order table is of correct size,
      should compile out to a NOP if true */
   if ((sizeof(lut_orders) / sizeof(lut_orders[0])) < (1U<<FP_LUT)) {
       err = BAD_FUNC_ARG;
   }
   else {
    /* get bitlen and round up to next multiple of FP_LUT */
    bitlen  = mp_unsigned_bin_size(modulus) << 3;
    x       = bitlen % FP_LUT;
    if (x) {
      bitlen += FP_LUT - x;
    }
    lut_gap = bitlen / FP_LUT;

    /* init the mu */
    err = mp_init_copy(&fp_cache[idx].mu, mu);
   }

   /* copy base */
   if (err == MP_OKAY) {
     if ((mp_mulmod(fp_cache[idx].g->x, mu, modulus,
                  fp_cache[idx].LUT[1]->x) != MP_OKAY) ||
         (mp_mulmod(fp_cache[idx].g->y, mu, modulus,
                  fp_cache[idx].LUT[1]->y) != MP_OKAY) ||
         (mp_mulmod(fp_cache[idx].g->z, mu, modulus,
                  fp_cache[idx].LUT[1]->z) != MP_OKAY)) {
       err = MP_MULMOD_E;
     }
   }

   /* make all single bit entries */
   for (x = 1; x < FP_LUT; x++) {
      if (err != MP_OKAY)
          break;
      if ((mp_copy(fp_cache[idx].LUT[1<<(x-1)]->x,
                   fp_cache[idx].LUT[1<<x]->x) != MP_OKAY) ||
          (mp_copy(fp_cache[idx].LUT[1<<(x-1)]->y,
                   fp_cache[idx].LUT[1<<x]->y) != MP_OKAY) ||
          (mp_copy(fp_cache[idx].LUT[1<<(x-1)]->z,
                   fp_cache[idx].LUT[1<<x]->z) != MP_OKAY)){
          err = MP_INIT_E;
          break;
      } else {

         /* now double it bitlen/FP_LUT times */
         for (y = 0; y < lut_gap; y++) {
             if ((err = ecc_projective_dbl_point(fp_cache[idx].LUT[1<<x],
                            fp_cache[idx].LUT[1<<x], a, modulus, mp)) != MP_OKAY) {
                 break;
             }
         }
     }
  }

   /* now make all entries in increase order of hamming weight */
   for (x = 2; x <= FP_LUT; x++) {
       if (err != MP_OKAY)
           break;
       for (y = 0; y < (1UL<<FP_LUT); y++) {
           if (lut_orders[y].ham != (int)x) continue;

           /* perform the add */
           if ((err = ecc_projective_add_point(
                           fp_cache[idx].LUT[lut_orders[y].terma],
                           fp_cache[idx].LUT[lut_orders[y].termb],
                           fp_cache[idx].LUT[y], a, modulus, mp)) != MP_OKAY) {
              break;
           }
       }
   }

   /* now map all entries back to affine space to make point addition faster */
   for (x = 1; x < (1UL<<FP_LUT); x++) {
       if (err != MP_OKAY)
           break;

       /* convert z to normal from montgomery */
       err = mp_montgomery_reduce(fp_cache[idx].LUT[x]->z, modulus, mp);

       /* invert it */
       if (err == MP_OKAY)
         err = mp_invmod(fp_cache[idx].LUT[x]->z, modulus,
                         fp_cache[idx].LUT[x]->z);

       if (err == MP_OKAY)
         /* now square it */
         err = mp_sqrmod(fp_cache[idx].LUT[x]->z, modulus, &tmp);

       if (err == MP_OKAY)
         /* fix x */
         err = mp_mulmod(fp_cache[idx].LUT[x]->x, &tmp, modulus,
                         fp_cache[idx].LUT[x]->x);

       if (err == MP_OKAY)
         /* get 1/z^3 */
         err = mp_mulmod(&tmp, fp_cache[idx].LUT[x]->z, modulus, &tmp);

       if (err == MP_OKAY)
         /* fix y */
         err = mp_mulmod(fp_cache[idx].LUT[x]->y, &tmp, modulus,
                         fp_cache[idx].LUT[x]->y);

       if (err == MP_OKAY)
         /* free z */
         mp_clear(fp_cache[idx].LUT[x]->z);
   }

   mp_clear(&tmp);

   if (err == MP_OKAY)
     return MP_OKAY;

   /* err cleanup */
   for (y = 0; y < (1U<<FP_LUT); y++) {
      wc_ecc_del_point(fp_cache[idx].LUT[y]);
      fp_cache[idx].LUT[y] = NULL;
   }
   wc_ecc_del_point(fp_cache[idx].g);
   fp_cache[idx].g         = NULL;
   fp_cache[idx].lru_count = 0;
   mp_clear(&fp_cache[idx].mu);

   return err;
}

/* perform a fixed point ECC mulmod */
static int accel_fp_mul(int idx, mp_int* k, ecc_point *R, mp_int* a,
                        mp_int* modulus, mp_digit mp, int map)
{
#define KB_SIZE 128

#ifdef WOLFSSL_SMALL_STACK
   unsigned char* kb = NULL;
#else
   unsigned char kb[KB_SIZE];
#endif
   int      x, err;
   unsigned y, z = 0, bitlen, bitpos, lut_gap, first;
   mp_int   tk, order;

   if (mp_init_multi(&tk, &order, NULL, NULL, NULL, NULL) != MP_OKAY)
       return MP_INIT_E;

   /* if it's smaller than modulus we fine */
   if (mp_unsigned_bin_size(k) > mp_unsigned_bin_size(modulus)) {
      /* find order */
      y = mp_unsigned_bin_size(modulus);
      for (x = 0; ecc_sets[x].size; x++) {
         if (y <= (unsigned)ecc_sets[x].size) break;
      }

      /* back off if we are on the 521 bit curve */
      if (y == 66) --x;

      if ((err = mp_read_radix(&order, ecc_sets[x].order, 16)) != MP_OKAY) {
         goto done;
      }

      /* k must be less than modulus */
      if (mp_cmp(k, &order) != MP_LT) {
         if ((err = mp_mod(k, &order, &tk)) != MP_OKAY) {
            goto done;
         }
      } else {
         if ((err = mp_copy(k, &tk)) != MP_OKAY) {
            goto done;
         }
      }
   } else {
      if ((err = mp_copy(k, &tk)) != MP_OKAY) {
         goto done;
      }
   }

   /* get bitlen and round up to next multiple of FP_LUT */
   bitlen  = mp_unsigned_bin_size(modulus) << 3;
   x       = bitlen % FP_LUT;
   if (x) {
      bitlen += FP_LUT - x;
   }
   lut_gap = bitlen / FP_LUT;

   /* get the k value */
   if (mp_unsigned_bin_size(&tk) > (int)(KB_SIZE - 2)) {
      err = BUFFER_E; goto done;
   }

   /* store k */
#ifdef WOLFSSL_SMALL_STACK
   kb = (unsigned char*)XMALLOC(KB_SIZE, NULL, DYNAMIC_TYPE_TMP_BUFFER);
   if (kb == NULL) {
      err = MEMORY_E; goto done;
   }
#endif

   XMEMSET(kb, 0, KB_SIZE);
   if ((err = mp_to_unsigned_bin(&tk, kb)) == MP_OKAY) {
      /* let's reverse kb so it's little endian */
      x = 0;
      y = mp_unsigned_bin_size(&tk);
      if (y > 0) {
          y -= 1;
      }

      while ((unsigned)x < y) {
         z = kb[x]; kb[x] = kb[y]; kb[y] = z;
         ++x; --y;
      }

      /* at this point we can start, yipee */
      first = 1;
      for (x = lut_gap-1; x >= 0; x--) {
          /* extract FP_LUT bits from kb spread out by lut_gap bits and offset
             by x bits from the start */
          bitpos = x;
          for (y = z = 0; y < FP_LUT; y++) {
             z |= ((kb[bitpos>>3] >> (bitpos&7)) & 1) << y;
             bitpos += lut_gap;  /* it's y*lut_gap + x, but here we can avoid
                                    the mult in each loop */
          }

          /* double if not first */
          if (!first) {
             if ((err = ecc_projective_dbl_point(R, R, a, modulus,
                                                             mp)) != MP_OKAY) {
                break;
             }
          }

          /* add if not first, otherwise copy */
          if (!first && z) {
             if ((err = ecc_projective_add_point(R, fp_cache[idx].LUT[z], R,
                                                 a, modulus, mp)) != MP_OKAY) {
                break;
             }
          } else if (z) {
             if ((mp_copy(fp_cache[idx].LUT[z]->x, R->x) != MP_OKAY) ||
                 (mp_copy(fp_cache[idx].LUT[z]->y, R->y) != MP_OKAY) ||
                 (mp_copy(&fp_cache[idx].mu,       R->z) != MP_OKAY)) {
                 err = GEN_MEM_ERR;
                 break;
             }
                 first = 0;
          }
      }
   }

   if (err == MP_OKAY) {
      (void) z; /* Acknowledge the unused assignment */
      ForceZero(kb, KB_SIZE);

      /* map R back from projective space */
      if (map) {
         err = ecc_map(R, modulus, mp);
      } else {
         err = MP_OKAY;
      }
   }

done:
   /* cleanup */
   mp_clear(&order);
   mp_clear(&tk);

#ifdef WOLFSSL_SMALL_STACK
   XFREE(kb, NULL, DYNAMIC_TYPE_TMP_BUFFER);
#endif

#undef KB_SIZE

   return err;
}

#ifdef ECC_SHAMIR
/* perform a fixed point ECC mulmod */
static int accel_fp_mul2add(int idx1, int idx2,
                            mp_int* kA, mp_int* kB,
                            ecc_point *R, mp_int* a,
                            mp_int* modulus, mp_digit mp)
{
#define KB_SIZE 128

#ifdef WOLFSSL_SMALL_STACK
   unsigned char* kb[2] = {NULL, NULL};
#else
   unsigned char kb[2][KB_SIZE];
#endif
   int      x, err;
   unsigned y, z, bitlen, bitpos, lut_gap, first, zA, zB;
   mp_int tka, tkb, order;

   if (mp_init_multi(&tka, &tkb, &order, NULL, NULL, NULL) != MP_OKAY)
       return MP_INIT_E;

   /* if it's smaller than modulus we fine */
   if (mp_unsigned_bin_size(kA) > mp_unsigned_bin_size(modulus)) {
      /* find order */
      y = mp_unsigned_bin_size(modulus);
      for (x = 0; ecc_sets[x].size; x++) {
         if (y <= (unsigned)ecc_sets[x].size) break;
      }

      /* back off if we are on the 521 bit curve */
      if (y == 66) --x;

      if ((err = mp_read_radix(&order, ecc_sets[x].order, 16)) != MP_OKAY) {
         goto done;
      }

      /* kA must be less than modulus */
      if (mp_cmp(kA, &order) != MP_LT) {
         if ((err = mp_mod(kA, &order, &tka)) != MP_OKAY) {
            goto done;
         }
      } else {
         if ((err = mp_copy(kA, &tka)) != MP_OKAY) {
            goto done;
         }
      }
   } else {
      if ((err = mp_copy(kA, &tka)) != MP_OKAY) {
         goto done;
      }
   }

   /* if it's smaller than modulus we fine */
   if (mp_unsigned_bin_size(kB) > mp_unsigned_bin_size(modulus)) {
      /* find order */
      y = mp_unsigned_bin_size(modulus);
      for (x = 0; ecc_sets[x].size; x++) {
         if (y <= (unsigned)ecc_sets[x].size) break;
      }

      /* back off if we are on the 521 bit curve */
      if (y == 66) --x;

      if ((err = mp_read_radix(&order, ecc_sets[x].order, 16)) != MP_OKAY) {
         goto done;
      }

      /* kB must be less than modulus */
      if (mp_cmp(kB, &order) != MP_LT) {
         if ((err = mp_mod(kB, &order, &tkb)) != MP_OKAY) {
            goto done;
         }
      } else {
         if ((err = mp_copy(kB, &tkb)) != MP_OKAY) {
            goto done;
         }
      }
   } else {
      if ((err = mp_copy(kB, &tkb)) != MP_OKAY) {
         goto done;
      }
   }

   /* get bitlen and round up to next multiple of FP_LUT */
   bitlen  = mp_unsigned_bin_size(modulus) << 3;
   x       = bitlen % FP_LUT;
   if (x) {
      bitlen += FP_LUT - x;
   }
   lut_gap = bitlen / FP_LUT;

   /* get the k value */
   if ((mp_unsigned_bin_size(&tka) > (int)(KB_SIZE - 2)) ||
       (mp_unsigned_bin_size(&tkb) > (int)(KB_SIZE - 2))  ) {
      err = BUFFER_E; goto done;
   }

   /* store k */
#ifdef WOLFSSL_SMALL_STACK
   kb[0] = (unsigned char*)XMALLOC(KB_SIZE, NULL, DYNAMIC_TYPE_TMP_BUFFER);
   if (kb[0] == NULL) {
      err = MEMORY_E; goto done;
   }
#endif

   XMEMSET(kb[0], 0, KB_SIZE);
   if ((err = mp_to_unsigned_bin(&tka, kb[0])) != MP_OKAY) {
      goto done;
   }

   /* let's reverse kb so it's little endian */
   x = 0;
   y = mp_unsigned_bin_size(&tka);
   if (y > 0) {
       y -= 1;
   }
   mp_clear(&tka);
   while ((unsigned)x < y) {
      z = kb[0][x]; kb[0][x] = kb[0][y]; kb[0][y] = z;
      ++x; --y;
   }

   /* store b */
#ifdef WOLFSSL_SMALL_STACK
   kb[1] = (unsigned char*)XMALLOC(KB_SIZE, NULL, DYNAMIC_TYPE_TMP_BUFFER);
   if (kb[1] == NULL) {
      err = MEMORY_E; goto done;
   }
#endif

   XMEMSET(kb[1], 0, KB_SIZE);
   if ((err = mp_to_unsigned_bin(&tkb, kb[1])) == MP_OKAY) {
      x = 0;
      y = mp_unsigned_bin_size(&tkb);
      if (y > 0) {
          y -= 1;
      }

      while ((unsigned)x < y) {
         z = kb[1][x]; kb[1][x] = kb[1][y]; kb[1][y] = z;
         ++x; --y;
      }

      /* at this point we can start, yipee */
      first = 1;
      for (x = lut_gap-1; x >= 0; x--) {
          /* extract FP_LUT bits from kb spread out by lut_gap bits and
             offset by x bits from the start */
          bitpos = x;
          for (y = zA = zB = 0; y < FP_LUT; y++) {
             zA |= ((kb[0][bitpos>>3] >> (bitpos&7)) & 1) << y;
             zB |= ((kb[1][bitpos>>3] >> (bitpos&7)) & 1) << y;
             bitpos += lut_gap;    /* it's y*lut_gap + x, but here we can avoid
                                      the mult in each loop */
          }

          /* double if not first */
          if (!first) {
             if ((err = ecc_projective_dbl_point(R, R, a, modulus,
                                                              mp)) != MP_OKAY) {
                break;
             }
          }

          /* add if not first, otherwise copy */
          if (!first) {
             if (zA) {
                if ((err = ecc_projective_add_point(R, fp_cache[idx1].LUT[zA],
                                                  R, a, modulus, mp)) != MP_OKAY) {
                   break;
                }
             }
             if (zB) {
                if ((err = ecc_projective_add_point(R, fp_cache[idx2].LUT[zB],
                                                  R, a, modulus, mp)) != MP_OKAY) {
                   break;
                }
             }
          } else {
             if (zA) {
                 if ((mp_copy(fp_cache[idx1].LUT[zA]->x, R->x) != MP_OKAY) ||
                    (mp_copy(fp_cache[idx1].LUT[zA]->y,  R->y) != MP_OKAY) ||
                    (mp_copy(&fp_cache[idx1].mu,         R->z) != MP_OKAY)) {
                     err = GEN_MEM_ERR;
                     break;
                 }
                    first = 0;
             }
             if (zB && first == 0) {
                if (zB) {
                   if ((err = ecc_projective_add_point(R,
                           fp_cache[idx2].LUT[zB], R, a, modulus, mp)) != MP_OKAY){
                      break;
                   }
                }
             } else if (zB && first == 1) {
                 if ((mp_copy(fp_cache[idx2].LUT[zB]->x, R->x) != MP_OKAY) ||
                    (mp_copy(fp_cache[idx2].LUT[zB]->y, R->y) != MP_OKAY) ||
                    (mp_copy(&fp_cache[idx2].mu,        R->z) != MP_OKAY)) {
                     err = GEN_MEM_ERR;
                     break;
                 }
                    first = 0;
             }
          }
      }
   }

done:
   /* cleanup */
   mp_clear(&tkb);
   mp_clear(&tka);
   mp_clear(&order);

#ifdef WOLFSSL_SMALL_STACK
   if (kb[0])
#endif
      ForceZero(kb[0], KB_SIZE);
#ifdef WOLFSSL_SMALL_STACK
   if (kb[1])
#endif
      ForceZero(kb[1], KB_SIZE);

#ifdef WOLFSSL_SMALL_STACK
   XFREE(kb[0], NULL, DYNAMIC_TYPE_TMP_BUFFER);
   XFREE(kb[1], NULL, DYNAMIC_TYPE_TMP_BUFFER);
#endif

#undef KB_SIZE

    if (err != MP_OKAY)
        return err;

   return ecc_map(R, modulus, mp);
}


/** ECC Fixed Point mulmod global with heap hint used
  Computes kA*A + kB*B = C using Shamir's Trick
  A        First point to multiply
  kA       What to multiple A by
  B        Second point to multiply
  kB       What to multiple B by
  C        [out] Destination point (can overlap with A or B)
  a        ECC curve parameter a
  modulus  Modulus for curve
  return MP_OKAY on success
*/
int ecc_mul2add(ecc_point* A, mp_int* kA,
                ecc_point* B, mp_int* kB,
                ecc_point* C, mp_int* a, mp_int* modulus, void* heap)
{
   int  idx1 = -1, idx2 = -1, err = MP_OKAY, mpInit = 0;
   mp_digit mp;
   mp_int   mu;

   err = mp_init(&mu);
   if (err != MP_OKAY)
       return err;

#ifndef HAVE_THREAD_LS
   if (initMutex == 0) {
        wc_InitMutex(&ecc_fp_lock);
        initMutex = 1;
   }
   if (wc_LockMutex(&ecc_fp_lock) != 0)
      return BAD_MUTEX_E;
#endif /* HAVE_THREAD_LS */

      /* find point */
      idx1 = find_base(A);

      /* no entry? */
      if (idx1 == -1) {
         /* find hole and add it */
         if ((idx1 = find_hole()) >= 0) {
            err = add_entry(idx1, A);
         }
      }
      if (err == MP_OKAY && idx1 != -1) {
         /* increment LRU */
         ++(fp_cache[idx1].lru_count);
      }

      if (err == MP_OKAY)
        /* find point */
        idx2 = find_base(B);

      if (err == MP_OKAY) {
        /* no entry? */
        if (idx2 == -1) {
           /* find hole and add it */
           if ((idx2 = find_hole()) >= 0)
              err = add_entry(idx2, B);
         }
      }

      if (err == MP_OKAY && idx2 != -1) {
         /* increment LRU */
         ++(fp_cache[idx2].lru_count);
      }

      if (err == MP_OKAY) {
        /* if it's 2 build the LUT, if it's higher just use the LUT */
        if (idx1 >= 0 && fp_cache[idx1].lru_count == 2) {
           /* compute mp */
           err = mp_montgomery_setup(modulus, &mp);

           if (err == MP_OKAY) {
             mpInit = 1;
             err = mp_montgomery_calc_normalization(&mu, modulus);
           }

           if (err == MP_OKAY)
             /* build the LUT */
               err = build_lut(idx1, a, modulus, mp, &mu);
        }
      }

      if (err == MP_OKAY) {
        /* if it's 2 build the LUT, if it's higher just use the LUT */
        if (idx2 >= 0 && fp_cache[idx2].lru_count == 2) {
           if (mpInit == 0) {
                /* compute mp */
                err = mp_montgomery_setup(modulus, &mp);
                if (err == MP_OKAY) {
                    mpInit = 1;
                    err = mp_montgomery_calc_normalization(&mu, modulus);
                }
            }

            if (err == MP_OKAY)
            /* build the LUT */
              err = build_lut(idx2, a, modulus, mp, &mu);
        }
      }


      if (err == MP_OKAY) {
        if (idx1 >=0 && idx2 >= 0 && fp_cache[idx1].lru_count >= 2 &&
                                     fp_cache[idx2].lru_count >= 2) {
           if (mpInit == 0) {
              /* compute mp */
              err = mp_montgomery_setup(modulus, &mp);
           }
           if (err == MP_OKAY)
             err = accel_fp_mul2add(idx1, idx2, kA, kB, C, a, modulus, mp);
        } else {
           err = normal_ecc_mul2add(A, kA, B, kB, C, a, modulus, heap);
        }
    }

#ifndef HAVE_THREAD_LS
    wc_UnLockMutex(&ecc_fp_lock);
#endif /* HAVE_THREAD_LS */
    mp_clear(&mu);

    return err;
}
#endif /* ECC_SHAMIR */

/** ECC Fixed Point mulmod global
    k        The multiplicand
    G        Base point to multiply
    R        [out] Destination of product
    a        ECC curve parameter a
    modulus  The modulus for the curve
    map      [boolean] If non-zero maps the point back to affine co-ordinates,
             otherwise it's left in jacobian-montgomery form
    return MP_OKAY if successful
*/
int wc_ecc_mulmod_ex(mp_int* k, ecc_point *G, ecc_point *R, mp_int* a,
    mp_int* modulus, int map, void* heap)
{
   int   idx, err = MP_OKAY;
   mp_digit mp;
   mp_int   mu;
   int      mpSetup = 0;

   if (mp_init(&mu) != MP_OKAY)
       return MP_INIT_E;

#ifndef HAVE_THREAD_LS
   if (initMutex == 0) {
        wc_InitMutex(&ecc_fp_lock);
        initMutex = 1;
   }

   if (wc_LockMutex(&ecc_fp_lock) != 0)
      return BAD_MUTEX_E;
#endif /* HAVE_THREAD_LS */

      /* find point */
      idx = find_base(G);

      /* no entry? */
      if (idx == -1) {
         /* find hole and add it */
         idx = find_hole();

         if (idx >= 0)
            err = add_entry(idx, G);
      }
      if (err == MP_OKAY && idx >= 0) {
         /* increment LRU */
         ++(fp_cache[idx].lru_count);
      }


      if (err == MP_OKAY) {
        /* if it's 2 build the LUT, if it's higher just use the LUT */
        if (idx >= 0 && fp_cache[idx].lru_count == 2) {
           /* compute mp */
           err = mp_montgomery_setup(modulus, &mp);

           if (err == MP_OKAY) {
             /* compute mu */
             mpSetup = 1;
             err = mp_montgomery_calc_normalization(&mu, modulus);
           }

           if (err == MP_OKAY)
             /* build the LUT */
             err = build_lut(idx, a, modulus, mp, &mu);
        }
      }

      if (err == MP_OKAY) {
        if (idx >= 0 && fp_cache[idx].lru_count >= 2) {
           if (mpSetup == 0) {
              /* compute mp */
              err = mp_montgomery_setup(modulus, &mp);
           }
           if (err == MP_OKAY)
             err = accel_fp_mul(idx, k, R, a, modulus, mp, map);
        } else {
           err = normal_ecc_mulmod(k, G, R, a, modulus, map, heap);
        }
     }

#ifndef HAVE_THREAD_LS
    wc_UnLockMutex(&ecc_fp_lock);
#endif /* HAVE_THREAD_LS */
    mp_clear(&mu);

    return err;
}

/* helper function for freeing the cache ...
   must be called with the cache mutex locked */
static void wc_ecc_fp_free_cache(void)
{
   unsigned x, y;
   for (x = 0; x < FP_ENTRIES; x++) {
      if (fp_cache[x].g != NULL) {
         for (y = 0; y < (1U<<FP_LUT); y++) {
            wc_ecc_del_point(fp_cache[x].LUT[y]);
            fp_cache[x].LUT[y] = NULL;
         }
         wc_ecc_del_point(fp_cache[x].g);
         fp_cache[x].g         = NULL;
         mp_clear(&fp_cache[x].mu);
         fp_cache[x].lru_count = 0;
         fp_cache[x].lock = 0;
      }
   }
}

/** Free the Fixed Point cache */
void wc_ecc_fp_free(void)
{
#ifndef HAVE_THREAD_LS
   if (initMutex == 0) {
        wc_InitMutex(&ecc_fp_lock);
        initMutex = 1;
   }

   if (wc_LockMutex(&ecc_fp_lock) == 0) {
#endif /* HAVE_THREAD_LS */

       wc_ecc_fp_free_cache();

#ifndef HAVE_THREAD_LS
       wc_UnLockMutex(&ecc_fp_lock);
       wc_FreeMutex(&ecc_fp_lock);
       initMutex = 0;
   }
#endif /* HAVE_THREAD_LS */
}


#endif /* FP_ECC */

#ifdef HAVE_ECC_ENCRYPT


enum ecCliState {
    ecCLI_INIT      = 1,
    ecCLI_SALT_GET  = 2,
    ecCLI_SALT_SET  = 3,
    ecCLI_SENT_REQ  = 4,
    ecCLI_RECV_RESP = 5,
    ecCLI_BAD_STATE = 99
};

enum ecSrvState {
    ecSRV_INIT      = 1,
    ecSRV_SALT_GET  = 2,
    ecSRV_SALT_SET  = 3,
    ecSRV_RECV_REQ  = 4,
    ecSRV_SENT_RESP = 5,
    ecSRV_BAD_STATE = 99
};


struct ecEncCtx {
    const byte* kdfSalt;   /* optional salt for kdf */
    const byte* kdfInfo;   /* optional info for kdf */
    const byte* macSalt;   /* optional salt for mac */
    word32    kdfSaltSz;   /* size of kdfSalt */
    word32    kdfInfoSz;   /* size of kdfInfo */
    word32    macSaltSz;   /* size of macSalt */
    void*     heap;        /* heap hint for memory used */
    byte      clientSalt[EXCHANGE_SALT_SZ];  /* for msg exchange */
    byte      serverSalt[EXCHANGE_SALT_SZ];  /* for msg exchange */
    byte      encAlgo;     /* which encryption type */
    byte      kdfAlgo;     /* which key derivation function type */
    byte      macAlgo;     /* which mac function type */
    byte      protocol;    /* are we REQ_RESP client or server ? */
    byte      cliSt;       /* protocol state, for sanity checks */
    byte      srvSt;       /* protocol state, for sanity checks */
};


const byte* wc_ecc_ctx_get_own_salt(ecEncCtx* ctx)
{
    if (ctx == NULL || ctx->protocol == 0)
        return NULL;

    if (ctx->protocol == REQ_RESP_CLIENT) {
        if (ctx->cliSt == ecCLI_INIT) {
            ctx->cliSt =  ecCLI_SALT_GET;
            return ctx->clientSalt;
        }
        else {
            ctx->cliSt = ecCLI_BAD_STATE;
            return NULL;
        }
    }
    else if (ctx->protocol == REQ_RESP_SERVER) {
        if (ctx->srvSt == ecSRV_INIT) {
            ctx->srvSt =  ecSRV_SALT_GET;
            return ctx->serverSalt;
        }
        else {
            ctx->srvSt = ecSRV_BAD_STATE;
            return NULL;
        }
    }

    return NULL;
}


/* optional set info, can be called before or after set_peer_salt */
int wc_ecc_ctx_set_info(ecEncCtx* ctx, const byte* info, int sz)
{
    if (ctx == NULL || info == 0 || sz < 0)
        return BAD_FUNC_ARG;

    ctx->kdfInfo   = info;
    ctx->kdfInfoSz = sz;

    return 0;
}


static const char* exchange_info = "Secure Message Exchange";

int wc_ecc_ctx_set_peer_salt(ecEncCtx* ctx, const byte* salt)
{
    byte tmp[EXCHANGE_SALT_SZ/2];
    int  halfSz = EXCHANGE_SALT_SZ/2;

    if (ctx == NULL || ctx->protocol == 0 || salt == NULL)
        return BAD_FUNC_ARG;

    if (ctx->protocol == REQ_RESP_CLIENT) {
        XMEMCPY(ctx->serverSalt, salt, EXCHANGE_SALT_SZ);
        if (ctx->cliSt == ecCLI_SALT_GET)
            ctx->cliSt =  ecCLI_SALT_SET;
        else {
            ctx->cliSt =  ecCLI_BAD_STATE;
            return BAD_STATE_E;
        }
    }
    else {
        XMEMCPY(ctx->clientSalt, salt, EXCHANGE_SALT_SZ);
        if (ctx->srvSt == ecSRV_SALT_GET)
            ctx->srvSt =  ecSRV_SALT_SET;
        else {
            ctx->srvSt =  ecSRV_BAD_STATE;
            return BAD_STATE_E;
        }
    }

    /* mix half and half */
    /* tmp stores 2nd half of client before overwrite */
    XMEMCPY(tmp, ctx->clientSalt + halfSz, halfSz);
    XMEMCPY(ctx->clientSalt + halfSz, ctx->serverSalt, halfSz);
    XMEMCPY(ctx->serverSalt, tmp, halfSz);

    ctx->kdfSalt   = ctx->clientSalt;
    ctx->kdfSaltSz = EXCHANGE_SALT_SZ;

    ctx->macSalt   = ctx->serverSalt;
    ctx->macSaltSz = EXCHANGE_SALT_SZ;

    if (ctx->kdfInfo == NULL) {
        /* default info */
        ctx->kdfInfo   = (const byte*)exchange_info;
        ctx->kdfInfoSz = EXCHANGE_INFO_SZ;
    }

    return 0;
}


static int ecc_ctx_set_salt(ecEncCtx* ctx, int flags, WC_RNG* rng)
{
    byte* saltBuffer = NULL;

    if (ctx == NULL || rng == NULL || flags == 0)
        return BAD_FUNC_ARG;

    saltBuffer = (flags == REQ_RESP_CLIENT) ? ctx->clientSalt : ctx->serverSalt;

    return wc_RNG_GenerateBlock(rng, saltBuffer, EXCHANGE_SALT_SZ);
}


static void ecc_ctx_init(ecEncCtx* ctx, int flags)
{
    if (ctx) {
        XMEMSET(ctx, 0, sizeof(ecEncCtx));

        ctx->encAlgo  = ecAES_128_CBC;
        ctx->kdfAlgo  = ecHKDF_SHA256;
        ctx->macAlgo  = ecHMAC_SHA256;
        ctx->protocol = (byte)flags;

        if (flags == REQ_RESP_CLIENT)
            ctx->cliSt = ecCLI_INIT;
        if (flags == REQ_RESP_SERVER)
            ctx->srvSt = ecSRV_INIT;
    }
}


/* allow ecc context reset so user doesn't have to init/free for reuse */
int wc_ecc_ctx_reset(ecEncCtx* ctx, WC_RNG* rng)
{
    if (ctx == NULL || rng == NULL)
        return BAD_FUNC_ARG;

    ecc_ctx_init(ctx, ctx->protocol);
    return ecc_ctx_set_salt(ctx, ctx->protocol, rng);
}


ecEncCtx* wc_ecc_ctx_new_ex(int flags, WC_RNG* rng, void* heap)
{
    int       ret = 0;
    ecEncCtx* ctx = (ecEncCtx*)XMALLOC(sizeof(ecEncCtx), heap,
                                                              DYNAMIC_TYPE_ECC);

    if (ctx) {
        ctx->protocol = (byte)flags;
        ctx->heap     = heap;
    }

    ret = wc_ecc_ctx_reset(ctx, rng);
    if (ret != 0) {
        wc_ecc_ctx_free(ctx);
        ctx = NULL;
    }

    return ctx;
}


/* alloc/init and set defaults, return new Context  */
ecEncCtx* wc_ecc_ctx_new(int flags, WC_RNG* rng)
{
    return wc_ecc_ctx_new_ex(flags, rng, NULL);
}


/* free any resources, clear any keys */
void wc_ecc_ctx_free(ecEncCtx* ctx)
{
    if (ctx) {
        ForceZero(ctx, sizeof(ecEncCtx));
        XFREE(ctx, ctx->heap, DYNAMIC_TYPE_ECC);
    }
}


static int ecc_get_key_sizes(ecEncCtx* ctx, int* encKeySz, int* ivSz,
                             int* keysLen, word32* digestSz, word32* blockSz)
{
    if (ctx) {
        switch (ctx->encAlgo) {
            case ecAES_128_CBC:
                *encKeySz = KEY_SIZE_128;
                *ivSz     = IV_SIZE_128;
                *blockSz  = AES_BLOCK_SIZE;
                break;
            default:
                return BAD_FUNC_ARG;
        }

        switch (ctx->macAlgo) {
            case ecHMAC_SHA256:
                *digestSz = SHA256_DIGEST_SIZE;
                break;
            default:
                return BAD_FUNC_ARG;
        }
    } else
        return BAD_FUNC_ARG;

    *keysLen  = *encKeySz + *ivSz + *digestSz;

    return 0;
}


/* ecc encrypt with shared secret run through kdf
   ctx holds non default algos and inputs
   msgSz should be the right size for encAlgo, i.e., already padded
   return 0 on success */
int wc_ecc_encrypt(ecc_key* privKey, ecc_key* pubKey, const byte* msg,
                word32 msgSz, byte* out, word32* outSz, ecEncCtx* ctx)
{
    int          ret;
    word32       blockSz;
    word32       digestSz;
    ecEncCtx     localCtx;
#ifdef WOLFSSL_SMALL_STACK
    byte*        sharedSecret;
    byte*        keys;
#else
    byte         sharedSecret[ECC_MAXSIZE];  /* 521 max size */
    byte         keys[ECC_BUFSIZE];         /* max size */
#endif
    word32       sharedSz = ECC_MAXSIZE;
    int          keysLen;
    int          encKeySz;
    int          ivSz;
    int          offset = 0;         /* keys offset if doing msg exchange */
    byte*        encKey;
    byte*        encIv;
    byte*        macKey;

    if (privKey == NULL || pubKey == NULL || msg == NULL || out == NULL ||
                           outSz  == NULL)
        return BAD_FUNC_ARG;

    if (ctx == NULL) {  /* use defaults */
        ecc_ctx_init(&localCtx, 0);
        ctx = &localCtx;
    }

    ret = ecc_get_key_sizes(ctx, &encKeySz, &ivSz, &keysLen, &digestSz,
                            &blockSz);
    if (ret != 0)
        return ret;

    if (ctx->protocol == REQ_RESP_SERVER) {
        offset = keysLen;
        keysLen *= 2;

        if (ctx->srvSt != ecSRV_RECV_REQ)
            return BAD_STATE_E;

        ctx->srvSt = ecSRV_BAD_STATE; /* we're done no more ops allowed */
    }
    else if (ctx->protocol == REQ_RESP_CLIENT) {
        if (ctx->cliSt != ecCLI_SALT_SET)
            return BAD_STATE_E;

        ctx->cliSt = ecCLI_SENT_REQ; /* only do this once */
    }

    if (keysLen > ECC_BUFSIZE) /* keys size */
        return BUFFER_E;

    if ( (msgSz%blockSz) != 0)
        return BAD_PADDING_E;

    if (*outSz < (msgSz + digestSz))
        return BUFFER_E;

#ifdef WOLFSSL_SMALL_STACK
    sharedSecret = (byte*)XMALLOC(ECC_MAXSIZE, NULL, DYNAMIC_TYPE_TMP_BUFFER);
    if (sharedSecret == NULL)
        return MEMORY_E;

    keys = (byte*)XMALLOC(ECC_BUFSIZE, NULL, DYNAMIC_TYPE_TMP_BUFFER);
    if (keys == NULL) {
        XFREE(sharedSecret, NULL, DYNAMIC_TYPE_TMP_BUFFER);
        return MEMORY_E;
    }
#endif

    ret = wc_ecc_shared_secret(privKey, pubKey, sharedSecret, &sharedSz);

    if (ret == 0) {
       switch (ctx->kdfAlgo) {
           case ecHKDF_SHA256 :
               ret = wc_HKDF(SHA256, sharedSecret, sharedSz, ctx->kdfSalt,
                          ctx->kdfSaltSz, ctx->kdfInfo, ctx->kdfInfoSz,
                          keys, keysLen);
               break;

           default:
               ret = BAD_FUNC_ARG;
               break;
       }
    }

    if (ret == 0) {
       encKey = keys + offset;
       encIv  = encKey + encKeySz;
       macKey = encKey + encKeySz + ivSz;

       switch (ctx->encAlgo) {
           case ecAES_128_CBC:
               {
                   Aes aes;
                   ret = wc_AesSetKey(&aes, encKey, KEY_SIZE_128, encIv,
                                                                AES_ENCRYPTION);
                   if (ret != 0)
                       break;
                   ret = wc_AesCbcEncrypt(&aes, out, msg, msgSz);
               }
               break;

           default:
               ret = BAD_FUNC_ARG;
               break;
       }
    }

    if (ret == 0) {
       switch (ctx->macAlgo) {
           case ecHMAC_SHA256:
               {
                   Hmac hmac;
                   ret = wc_HmacInit(&hmac, NULL, INVALID_DEVID);
                   if (ret == 0) {
                       ret = wc_HmacSetKey(&hmac, SHA256, macKey, SHA256_DIGEST_SIZE);
                       if (ret == 0)
                           ret = wc_HmacUpdate(&hmac, out, msgSz);
                       if (ret == 0)
                           ret = wc_HmacUpdate(&hmac, ctx->macSalt, ctx->macSaltSz);
                       if (ret == 0)
                           ret = wc_HmacFinal(&hmac, out+msgSz);
                       wc_HmacFree(&hmac);
                   }
               }
               break;

           default:
               ret = BAD_FUNC_ARG;
               break;
       }
    }

    if (ret == 0)
       *outSz = msgSz + digestSz;

#ifdef WOLFSSL_SMALL_STACK
    XFREE(sharedSecret, NULL, DYNAMIC_TYPE_TMP_BUFFER);
    XFREE(keys, NULL, DYNAMIC_TYPE_TMP_BUFFER);
#endif

    return ret;
}


/* ecc decrypt with shared secret run through kdf
   ctx holds non default algos and inputs
   return 0 on success */
int wc_ecc_decrypt(ecc_key* privKey, ecc_key* pubKey, const byte* msg,
                word32 msgSz, byte* out, word32* outSz, ecEncCtx* ctx)
{
    int          ret;
    word32       blockSz;
    word32       digestSz;
    ecEncCtx     localCtx;
#ifdef WOLFSSL_SMALL_STACK
    byte*        sharedSecret;
    byte*        keys;
#else
    byte         sharedSecret[ECC_MAXSIZE];  /* 521 max size */
    byte         keys[ECC_BUFSIZE];         /* max size */
#endif
    word32       sharedSz = ECC_MAXSIZE;
    int          keysLen;
    int          encKeySz;
    int          ivSz;
    int          offset = 0;       /* in case using msg exchange */
    byte*        encKey;
    byte*        encIv;
    byte*        macKey;

    if (privKey == NULL || pubKey == NULL || msg == NULL || out == NULL ||
                           outSz  == NULL)
        return BAD_FUNC_ARG;

    if (ctx == NULL) {  /* use defaults */
        ecc_ctx_init(&localCtx, 0);
        ctx = &localCtx;
    }

    ret = ecc_get_key_sizes(ctx, &encKeySz, &ivSz, &keysLen, &digestSz,
                            &blockSz);
    if (ret != 0)
        return ret;

    if (ctx->protocol == REQ_RESP_CLIENT) {
        offset = keysLen;
        keysLen *= 2;

        if (ctx->cliSt != ecCLI_SENT_REQ)
            return BAD_STATE_E;

        ctx->cliSt = ecSRV_BAD_STATE; /* we're done no more ops allowed */
    }
    else if (ctx->protocol == REQ_RESP_SERVER) {
        if (ctx->srvSt != ecSRV_SALT_SET)
            return BAD_STATE_E;

        ctx->srvSt = ecSRV_RECV_REQ; /* only do this once */
    }

    if (keysLen > ECC_BUFSIZE) /* keys size */
        return BUFFER_E;

    if ( ((msgSz-digestSz) % blockSz) != 0)
        return BAD_PADDING_E;

    if (*outSz < (msgSz - digestSz))
        return BUFFER_E;

#ifdef WOLFSSL_SMALL_STACK
    sharedSecret = (byte*)XMALLOC(ECC_MAXSIZE, NULL, DYNAMIC_TYPE_TMP_BUFFER);
    if (sharedSecret == NULL)
        return MEMORY_E;

    keys = (byte*)XMALLOC(ECC_BUFSIZE, NULL, DYNAMIC_TYPE_TMP_BUFFER);
    if (keys == NULL) {
        XFREE(sharedSecret, NULL, DYNAMIC_TYPE_TMP_BUFFER);
        return MEMORY_E;
    }
#endif

    ret = wc_ecc_shared_secret(privKey, pubKey, sharedSecret, &sharedSz);

    if (ret == 0) {
       switch (ctx->kdfAlgo) {
           case ecHKDF_SHA256 :
               ret = wc_HKDF(SHA256, sharedSecret, sharedSz, ctx->kdfSalt,
                          ctx->kdfSaltSz, ctx->kdfInfo, ctx->kdfInfoSz,
                          keys, keysLen);
               break;

           default:
               ret = BAD_FUNC_ARG;
               break;
       }
    }

    if (ret == 0) {
       encKey = keys + offset;
       encIv  = encKey + encKeySz;
       macKey = encKey + encKeySz + ivSz;

       switch (ctx->macAlgo) {
           case ecHMAC_SHA256:
           {
               byte verify[SHA256_DIGEST_SIZE];
               Hmac hmac;

               ret = wc_HmacInit(&hmac, NULL, INVALID_DEVID);
               if (ret == 0) {
                   ret = wc_HmacSetKey(&hmac, SHA256, macKey, SHA256_DIGEST_SIZE);
                   if (ret == 0)
                       ret = wc_HmacUpdate(&hmac, msg, msgSz-digestSz);
                   if (ret == 0)
                       ret = wc_HmacUpdate(&hmac, ctx->macSalt, ctx->macSaltSz);
                   if (ret == 0)
                       ret = wc_HmacFinal(&hmac, verify);
                   if (ret == 0) {
                      if (XMEMCMP(verify, msg + msgSz - digestSz, digestSz) != 0)
                          ret = -1;
                   }

                   wc_HmacFree(&hmac);
               }
               break;
           }

           default:
               ret = BAD_FUNC_ARG;
               break;
       }
    }

    if (ret == 0) {
       switch (ctx->encAlgo) {
    #ifdef HAVE_AES_CBC
           case ecAES_128_CBC:
               {
                   Aes aes;
                   ret = wc_AesSetKey(&aes, encKey, KEY_SIZE_128, encIv,
                                                                AES_DECRYPTION);
                   if (ret != 0)
                       break;
                   ret = wc_AesCbcDecrypt(&aes, out, msg, msgSz-digestSz);
               }
               break;
    #endif
           default:
               ret = BAD_FUNC_ARG;
               break;
       }
    }

    if (ret == 0)
       *outSz = msgSz - digestSz;

#ifdef WOLFSSL_SMALL_STACK
    XFREE(sharedSecret, NULL, DYNAMIC_TYPE_TMP_BUFFER);
    XFREE(keys, NULL, DYNAMIC_TYPE_TMP_BUFFER);
#endif

    return ret;
}


#endif /* HAVE_ECC_ENCRYPT */


#ifdef HAVE_COMP_KEY
#ifndef WOLFSSL_ATECC508A

int do_mp_jacobi(mp_int* a, mp_int* n, int* c);

int do_mp_jacobi(mp_int* a, mp_int* n, int* c)
{
  int      k, s, res;
  int      r = 0; /* initialize to help static analysis out */
  mp_digit residue;

  /* if a < 0 return MP_VAL */
  if (mp_isneg(a) == MP_YES) {
     return MP_VAL;
  }

  /* if n <= 0 return MP_VAL */
  if (mp_cmp_d(n, 0) != MP_GT) {
     return MP_VAL;
  }

  /* step 1. handle case of a == 0 */
  if (mp_iszero (a) == MP_YES) {
     /* special case of a == 0 and n == 1 */
     if (mp_cmp_d (n, 1) == MP_EQ) {
       *c = 1;
     } else {
       *c = 0;
     }
     return MP_OKAY;
  }

  /* step 2.  if a == 1, return 1 */
  if (mp_cmp_d (a, 1) == MP_EQ) {
    *c = 1;
    return MP_OKAY;
  }

  /* default */
  s = 0;

  /* divide out larger power of two */
  k = mp_cnt_lsb(a);
  res = mp_div_2d(a, k, a, NULL);

  if (res == MP_OKAY) {
    /* step 4.  if e is even set s=1 */
    if ((k & 1) == 0) {
      s = 1;
    } else {
      /* else set s=1 if p = 1/7 (mod 8) or s=-1 if p = 3/5 (mod 8) */
      residue = n->dp[0] & 7;

      if (residue == 1 || residue == 7) {
        s = 1;
      } else if (residue == 3 || residue == 5) {
        s = -1;
      }
    }

    /* step 5.  if p == 3 (mod 4) *and* a == 3 (mod 4) then s = -s */
    if ( ((n->dp[0] & 3) == 3) && ((a->dp[0] & 3) == 3)) {
      s = -s;
    }
  }

  if (res == MP_OKAY) {
    /* if a == 1 we're done */
    if (mp_cmp_d(a, 1) == MP_EQ) {
      *c = s;
    } else {
      /* n1 = n mod a */
      res = mp_mod (n, a, n);
      if (res == MP_OKAY)
        res = do_mp_jacobi(n, a, &r);

      if (res == MP_OKAY)
        *c = s * r;
    }
  }

  return res;
}


/* computes the jacobi c = (a | n) (or Legendre if n is prime)
 * HAC pp. 73 Algorithm 2.149
 * HAC is wrong here, as the special case of (0 | 1) is not
 * handled correctly.
 */
int mp_jacobi(mp_int* a, mp_int* n, int* c)
{
    mp_int   a1, n1;
    int      res;

    /* step 3.  write a = a1 * 2**k  */
    if ((res = mp_init_multi(&a1, &n1, NULL, NULL, NULL, NULL)) != MP_OKAY) {
        return res;
    }

    if ((res = mp_copy(a, &a1)) != MP_OKAY) {
        goto done;
    }

    if ((res = mp_copy(n, &n1)) != MP_OKAY) {
        goto done;
    }

    res = do_mp_jacobi(&a1, &n1, c);

done:
  /* cleanup */
  mp_clear(&n1);
  mp_clear(&a1);

  return res;
}


/* Solves the modular equation x^2 = n (mod p)
 * where prime number is greater than 2 (odd prime).
 * The result is returned in the third argument x
 * the function returns MP_OKAY on success, MP_VAL or another error on failure
 */
int mp_sqrtmod_prime(mp_int* n, mp_int* prime, mp_int* ret)
{
  int res, legendre, done = 0;
  mp_int t1, C, Q, S, Z, M, T, R, two;
  mp_digit i;

  /* first handle the simple cases n = 0 or n = 1 */
  if (mp_cmp_d(n, 0) == MP_EQ) {
    mp_zero(ret);
    return MP_OKAY;
  }
  if (mp_cmp_d(n, 1) == MP_EQ) {
    return mp_set(ret, 1);
  }

  /* prime must be odd */
  if (mp_cmp_d(prime, 2) == MP_EQ) {
    return MP_VAL;
  }

  /* is quadratic non-residue mod prime */
  if ((res = mp_jacobi(n, prime, &legendre)) != MP_OKAY) {
    return res;
  }
  if (legendre == -1) {
    return MP_VAL;
  }

  if ((res = mp_init_multi(&t1, &C, &Q, &S, &Z, &M)) != MP_OKAY)
    return res;

  if ((res = mp_init_multi(&T, &R, &two, NULL, NULL, NULL))
                          != MP_OKAY) {
    mp_clear(&t1); mp_clear(&C); mp_clear(&Q); mp_clear(&S); mp_clear(&Z);
    mp_clear(&M);
    return res;
  }

  /* SPECIAL CASE: if prime mod 4 == 3
   * compute directly: res = n^(prime+1)/4 mod prime
   * Handbook of Applied Cryptography algorithm 3.36
   */
  res = mp_mod_d(prime, 4, &i);
  if (res == MP_OKAY && i == 3) {
    res = mp_add_d(prime, 1, &t1);

    if (res == MP_OKAY)
      res = mp_div_2(&t1, &t1);
    if (res == MP_OKAY)
      res = mp_div_2(&t1, &t1);
    if (res == MP_OKAY)
      res = mp_exptmod(n, &t1, prime, ret);

    done = 1;
  }

  /* NOW: TonelliShanks algorithm */
  if (res == MP_OKAY && done == 0) {

    /* factor out powers of 2 from prime-1, defining Q and S
    *                                      as: prime-1 = Q*2^S */
    /* Q = prime - 1 */
    res = mp_copy(prime, &Q);
    if (res == MP_OKAY)
      res = mp_sub_d(&Q, 1, &Q);

    /* S = 0 */
    if (res == MP_OKAY)
      mp_zero(&S);

    while (res == MP_OKAY && mp_iseven(&Q) == MP_YES) {
      /* Q = Q / 2 */
      res = mp_div_2(&Q, &Q);

      /* S = S + 1 */
      if (res == MP_OKAY)
        res = mp_add_d(&S, 1, &S);
    }

    /* find a Z such that the Legendre symbol (Z|prime) == -1 */
    /* Z = 2 */
    if (res == MP_OKAY)
      res = mp_set_int(&Z, 2);

    while (res == MP_OKAY) {
      res = mp_jacobi(&Z, prime, &legendre);
      if (res == MP_OKAY && legendre == -1)
        break;

      /* Z = Z + 1 */
      if (res == MP_OKAY)
        res = mp_add_d(&Z, 1, &Z);
    }

    /* C = Z ^ Q mod prime */
    if (res == MP_OKAY)
      res = mp_exptmod(&Z, &Q, prime, &C);

    /* t1 = (Q + 1) / 2 */
    if (res == MP_OKAY)
      res = mp_add_d(&Q, 1, &t1);
    if (res == MP_OKAY)
      res = mp_div_2(&t1, &t1);

    /* R = n ^ ((Q + 1) / 2) mod prime */
    if (res == MP_OKAY)
      res = mp_exptmod(n, &t1, prime, &R);

    /* T = n ^ Q mod prime */
    if (res == MP_OKAY)
      res = mp_exptmod(n, &Q, prime, &T);

    /* M = S */
    if (res == MP_OKAY)
      res = mp_copy(&S, &M);

    if (res == MP_OKAY)
      res = mp_set_int(&two, 2);

    while (res == MP_OKAY && done == 0) {
      res = mp_copy(&T, &t1);

      /* reduce to 1 and count */
      i = 0;
      while (res == MP_OKAY) {
        if (mp_cmp_d(&t1, 1) == MP_EQ)
            break;
        res = mp_exptmod(&t1, &two, prime, &t1);
        if (res == MP_OKAY)
          i++;
      }
      if (res == MP_OKAY && i == 0) {
        res = mp_copy(&R, ret);
        done = 1;
      }

      if (done == 0) {
        /* t1 = 2 ^ (M - i - 1) */
        if (res == MP_OKAY)
          res = mp_sub_d(&M, i, &t1);
        if (res == MP_OKAY)
          res = mp_sub_d(&t1, 1, &t1);
        if (res == MP_OKAY)
          res = mp_exptmod(&two, &t1, prime, &t1);

        /* t1 = C ^ (2 ^ (M - i - 1)) mod prime */
        if (res == MP_OKAY)
          res = mp_exptmod(&C, &t1, prime, &t1);

        /* C = (t1 * t1) mod prime */
        if (res == MP_OKAY)
          res = mp_sqrmod(&t1, prime, &C);

        /* R = (R * t1) mod prime */
        if (res == MP_OKAY)
          res = mp_mulmod(&R, &t1, prime, &R);

        /* T = (T * C) mod prime */
        if (res == MP_OKAY)
          res = mp_mulmod(&T, &C, prime, &T);

        /* M = i */
        if (res == MP_OKAY)
          res = mp_set(&M, i);
      }
    }
  }

  /* done */
  mp_clear(&t1);
  mp_clear(&C);
  mp_clear(&Q);
  mp_clear(&S);
  mp_clear(&Z);
  mp_clear(&M);
  mp_clear(&T);
  mp_clear(&R);
  mp_clear(&two);

  return res;
}
#endif /* !WOLFSSL_ATECC508A */


/* export public ECC key in ANSI X9.63 format compressed */
static int wc_ecc_export_x963_compressed(ecc_key* key, byte* out, word32* outLen)
{
   word32 numlen;
   int    ret = MP_OKAY;

   if (key == NULL || out == NULL || outLen == NULL)
       return BAD_FUNC_ARG;

   if (wc_ecc_is_valid_idx(key->idx) == 0) {
      return ECC_BAD_ARG_E;
   }
   numlen = key->dp->size;

   if (*outLen < (1 + numlen)) {
      *outLen = 1 + numlen;
      return BUFFER_E;
   }

#ifdef WOLFSSL_ATECC508A
   /* TODO: Implement equiv call to ATECC508A */
   ret = BAD_COND_E;

#else

   /* store first byte */
   out[0] = mp_isodd(key->pubkey.y) == MP_YES ? 0x03 : 0x02;

   /* pad and store x */
   XMEMSET(out+1, 0, numlen);
   ret = mp_to_unsigned_bin(key->pubkey.x,
                       out+1 + (numlen - mp_unsigned_bin_size(key->pubkey.x)));
   *outLen = 1 + numlen;

#endif /* WOLFSSL_ATECC508A */

   return ret;
}

#endif /* HAVE_COMP_KEY */


int wc_ecc_get_oid(word32 oidSum, const byte** oid, word32* oidSz)
{
    int x;

    if (oidSum == 0) {
        return BAD_FUNC_ARG;
    }

    /* find matching OID sum (based on encoded value) */
    for (x = 0; ecc_sets[x].size != 0; x++) {
        if (ecc_sets[x].oidSum == oidSum) {
            int ret = 0;
        #ifdef HAVE_OID_ENCODING
            /* check cache */
            oid_cache_t* o = &ecc_oid_cache[x];
            if (o->oidSz == 0) {
                o->oidSz = sizeof(o->oid);
                ret = EncodeObjectId(ecc_sets[x].oid, ecc_sets[x].oidSz,
                                                            o->oid, &o->oidSz);
            }
            if (oidSz) {
                *oidSz = o->oidSz;
            }
            if (oid) {
                *oid = o->oid;
            }
        #else
            if (oidSz) {
                *oidSz = ecc_sets[x].oidSz;
            }
            if (oid) {
                *oid = ecc_sets[x].oid;
            }
        #endif
            /* on success return curve id */
            if (ret == 0) {
                ret = ecc_sets[x].id;
            }
            return ret;
        }
    }

    return NOT_COMPILED_IN;
}

#ifdef WOLFSSL_CUSTOM_CURVES
int wc_ecc_set_custom_curve(ecc_key* key, const ecc_set_type* dp)
{
    if (key == NULL || dp == NULL) {
        return BAD_FUNC_ARG;
    }

    key->idx = ECC_CUSTOM_IDX;
    key->dp = dp;

    return 0;
}
#endif /* WOLFSSL_CUSTOM_CURVES */

#ifdef HAVE_X963_KDF

static INLINE void IncrementX963KdfCounter(byte* inOutCtr)
{
    int i;

    /* in network byte order so start at end and work back */
    for (i = 3; i >= 0; i--) {
        if (++inOutCtr[i])  /* we're done unless we overflow */
            return;
    }
}

/* ASN X9.63 Key Derivation Function (SEC1) */
int wc_X963_KDF(enum wc_HashType type, const byte* secret, word32 secretSz,
                const byte* sinfo, word32 sinfoSz, byte* out, word32 outSz)
{
    int ret, i;
    int digestSz, copySz;
    int remaining = outSz;
    byte* outIdx;
    byte  counter[4];
    byte  tmp[WC_MAX_DIGEST_SIZE];

#ifdef WOLFSSL_SMALL_STACK
    wc_HashAlg* hash;
#else
    wc_HashAlg hash[1];
#endif

    if (secret == NULL || secretSz == 0 || out == NULL)
        return BAD_FUNC_ARG;

    /* X9.63 allowed algos only */
    if (type != WC_HASH_TYPE_SHA    && type != WC_HASH_TYPE_SHA224 &&
        type != WC_HASH_TYPE_SHA256 && type != WC_HASH_TYPE_SHA384 &&
        type != WC_HASH_TYPE_SHA512)
        return BAD_FUNC_ARG;

    digestSz = wc_HashGetDigestSize(type);
    if (digestSz < 0)
        return digestSz;

#ifdef WOLFSSL_SMALL_STACK
    hash = (wc_HashAlg*)XMALLOC(sizeof(wc_HashAlg), NULL,
                                DYNAMIC_TYPE_TMP_BUFFER);
    if (hash == NULL)
        return MEMORY_E;
#endif

    ret = wc_HashInit(hash, type);
    if (ret != 0) {
#ifdef WOLFSSL_SMALL_STACK
        XFREE(hash, NULL, DYNAMIC_TYPE_TMP_BUFFER);
#endif
        return ret;
    }

    outIdx = out;
    XMEMSET(counter, 0, sizeof(counter));

    for (i = 1; remaining > 0; i++) {

        IncrementX963KdfCounter(counter);

        ret = wc_HashUpdate(hash, type, secret, secretSz);
        if (ret != 0) {
#ifdef WOLFSSL_SMALL_STACK
            XFREE(hash, NULL, DYNAMIC_TYPE_TMP_BUFFER);
#endif
            return ret;
        }

        ret = wc_HashUpdate(hash, type, counter, sizeof(counter));
        if (ret != 0) {
#ifdef WOLFSSL_SMALL_STACK
            XFREE(hash, NULL, DYNAMIC_TYPE_TMP_BUFFER);
#endif
            return ret;
        }

        if (sinfo) {
            ret = wc_HashUpdate(hash, type, sinfo, sinfoSz);
            if (ret != 0) {
#ifdef WOLFSSL_SMALL_STACK
                XFREE(hash, NULL, DYNAMIC_TYPE_TMP_BUFFER);
#endif
                return ret;
            }
        }

        ret = wc_HashFinal(hash, type, tmp);
        if (ret != 0) {
#ifdef WOLFSSL_SMALL_STACK
            XFREE(hash, NULL, DYNAMIC_TYPE_TMP_BUFFER);
#endif
            return ret;
        }

        copySz = min(remaining, digestSz);
        XMEMCPY(outIdx, tmp, copySz);

        remaining -= copySz;
        outIdx += copySz;
    }

#ifdef WOLFSSL_SMALL_STACK
     XFREE(hash, NULL, DYNAMIC_TYPE_TMP_BUFFER);
#endif

    return 0;
}
#endif /* HAVE_X963_KDF */

#endif /* HAVE_ECC */

