Xuyi Wang
/
wolfSSL
Important changes to repositories hosted on mbed.com
Mbed hosted mercurial repositories are deprecated and are due to be permanently deleted in July 2026.
To keep a copy of this software download the repository Zip archive or clone locally using Mercurial.
It is also possible to export all your personal repositories from the account settings page.
wolfcrypt/src/ecc.c
- Committer:
- wolfSSL
- Date:
- 2018-08-18
- Revision:
- 15:117db924cf7c
File content as of revision 15:117db924cf7c:
/* ecc.c
*
* Copyright (C) 2006-2017 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
#if defined(HAVE_FIPS_VERSION) && (HAVE_FIPS_VERSION >= 2)
/* set NO_WRAPPERS before headers, use direct internal f()s not wrappers */
#define FIPS_NO_WRAPPERS
#ifdef USE_WINDOWS_API
#pragma code_seg(".fipsA$f")
#pragma const_seg(".fipsB$f")
#endif
#endif
#include <wolfssl/wolfcrypt/ecc.h>
#include <wolfssl/wolfcrypt/asn.h>
#include <wolfssl/wolfcrypt/error-crypt.h>
#include <wolfssl/wolfcrypt/logging.h>
#include <wolfssl/wolfcrypt/types.h>
#ifdef WOLFSSL_HAVE_SP_ECC
#include <wolfssl/wolfcrypt/sp.h>
#endif
#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 WOLF_CRYPTO_DEV
#include <wolfssl/wolfcrypt/cryptodev.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 WOLFSSL_SP_MATH
#define GEN_MEM_ERR MP_MEM
#elif defined(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
#ifdef HAVE_OID_ENCODING
#define CODED_SECP112R1 {1,3,132,0,6}
#define CODED_SECP112R1_SZ 5
#else
#define CODED_SECP112R1 {0x2B,0x81,0x04,0x00,0x06}
#define CODED_SECP112R1_SZ 5
#endif
#ifndef USE_WINDOWS_API
static const ecc_oid_t ecc_oid_secp112r1[] = CODED_SECP112R1;
#else
#define ecc_oid_secp112r1 CODED_SECP112R1
#endif
#define ecc_oid_secp112r1_sz CODED_SECP112R1_SZ
#endif /* !NO_ECC_SECP */
#ifdef HAVE_ECC_SECPR2
#ifdef HAVE_OID_ENCODING
#define CODED_SECP112R2 {1,3,132,0,7}
#define CODED_SECP112R2_SZ 5
#else
#define CODED_SECP112R2 {0x2B,0x81,0x04,0x00,0x07}
#define CODED_SECP112R2_SZ 5
#endif
#ifndef USE_WINDOWS_API
static const ecc_oid_t ecc_oid_secp112r2[] = CODED_SECP112R2;
#else
#define ecc_oid_secp112r2 CODED_SECP112R2
#endif
#define ecc_oid_secp112r2_sz CODED_SECP112R2_SZ
#endif /* HAVE_ECC_SECPR2 */
#endif /* ECC112 */
#ifdef ECC128
#ifndef NO_ECC_SECP
#ifdef HAVE_OID_ENCODING
#define CODED_SECP128R1 {1,3,132,0,28}
#define CODED_SECP128R1_SZ 5
#else
#define CODED_SECP128R1 {0x2B,0x81,0x04,0x00,0x1C}
#define CODED_SECP128R1_SZ 5
#endif
#ifndef USE_WINDOWS_API
static const ecc_oid_t ecc_oid_secp128r1[] = CODED_SECP128R1;
#else
#define ecc_oid_secp128r1 CODED_SECP128R1
#endif
#define ecc_oid_secp128r1_sz CODED_SECP128R1_SZ
#endif /* !NO_ECC_SECP */
#ifdef HAVE_ECC_SECPR2
#ifdef HAVE_OID_ENCODING
#define CODED_SECP128R2 {1,3,132,0,29}
#define CODED_SECP128R2_SZ 5
#else
#define CODED_SECP128R2 {0x2B,0x81,0x04,0x00,0x1D}
#define CODED_SECP128R2_SZ 5
#endif
#ifndef USE_WINDOWS_API
static const ecc_oid_t ecc_oid_secp128r2[] = CODED_SECP128R2;
#else
#define ecc_oid_secp128r2 CODED_SECP128R2
#endif
#define ecc_oid_secp128r2_sz CODED_SECP128R2_SZ
#endif /* HAVE_ECC_SECPR2 */
#endif /* ECC128 */
#ifdef ECC160
#ifndef NO_ECC_SECP
#ifdef HAVE_OID_ENCODING
#define CODED_SECP160R1 {1,3,132,0,8}
#define CODED_SECP160R1_SZ 5
#else
#define CODED_SECP160R1 {0x2B,0x81,0x04,0x00,0x08}
#define CODED_SECP160R1_SZ 5
#endif
#ifndef USE_WINDOWS_API
static const ecc_oid_t ecc_oid_secp160r1[] = CODED_SECP160R1;
#else
#define ecc_oid_secp160r1 CODED_SECP160R1
#endif
#define ecc_oid_secp160r1_sz CODED_SECP160R1_SZ
#endif /* !NO_ECC_SECP */
#ifdef HAVE_ECC_SECPR2
#ifdef HAVE_OID_ENCODING
#define CODED_SECP160R2 {1,3,132,0,30}
#define CODED_SECP160R1_SZ 5
#else
#define CODED_SECP160R2 {0x2B,0x81,0x04,0x00,0x1E}
#define CODED_SECP160R2_SZ 5
#endif
#ifndef USE_WINDOWS_API
static const ecc_oid_t ecc_oid_secp160r2[] = CODED_SECP160R2;
#else
#define ecc_oid_secp160r2 CODED_SECP160R2
#endif
#define ecc_oid_secp160r2_sz CODED_SECP160R2_SZ
#endif /* HAVE_ECC_SECPR2 */
#ifdef HAVE_ECC_KOBLITZ
#ifdef HAVE_OID_ENCODING
#define CODED_SECP160K1 {1,3,132,0,9}
#define CODED_SECP160K1_SZ 5
#else
#define CODED_SECP160K1 {0x2B,0x81,0x04,0x00,0x09}
#define CODED_SECP160K1_SZ 5
#endif
#ifndef USE_WINDOWS_API
static const ecc_oid_t ecc_oid_secp160k1[] = CODED_SECP160K1;
#else
#define ecc_oid_secp160k1 CODED_SECP160K1
#endif
#define ecc_oid_secp160k1_sz CODED_SECP160K1_SZ
#endif /* HAVE_ECC_KOBLITZ */
#ifdef HAVE_ECC_BRAINPOOL
#ifdef HAVE_OID_ENCODING
#define CODED_BRAINPOOLP160R1 {1,3,36,3,3,2,8,1,1,1}
#define CODED_BRAINPOOLP160R1_SZ 10
#else
#define CODED_BRAINPOOLP160R1 {0x2B,0x24,0x03,0x03,0x02,0x08,0x01,0x01,0x01}
#define CODED_BRAINPOOLP160R1_SZ 9
#endif
#ifndef USE_WINDOWS_API
static const ecc_oid_t ecc_oid_brainpoolp160r1[] = CODED_BRAINPOOLP160R1;
#else
#define ecc_oid_brainpoolp160r1 CODED_BRAINPOOLP160R1
#endif
#define ecc_oid_brainpoolp160r1_sz CODED_BRAINPOOLP160R1_SZ
#endif /* HAVE_ECC_BRAINPOOL */
#endif /* ECC160 */
#ifdef ECC192
#ifndef NO_ECC_SECP
#ifdef HAVE_OID_ENCODING
#define CODED_SECP192R1 {1,2,840,10045,3,1,1}
#define CODED_SECP192R1_SZ 7
#else
#define CODED_SECP192R1 {0x2A,0x86,0x48,0xCE,0x3D,0x03,0x01,0x01}
#define CODED_SECP192R1_SZ 8
#endif
#ifndef USE_WINDOWS_API
static const ecc_oid_t ecc_oid_secp192r1[] = CODED_SECP192R1;
#else
#define ecc_oid_secp192r1 CODED_SECP192R1
#endif
#define ecc_oid_secp192r1_sz CODED_SECP192R1_SZ
#endif /* !NO_ECC_SECP */
#ifdef HAVE_ECC_SECPR2
#ifdef HAVE_OID_ENCODING
#define CODED_PRIME192V2 {1,2,840,10045,3,1,2}
#define CODED_PRIME192V2_SZ 7
#else
#define CODED_PRIME192V2 {0x2A,0x86,0x48,0xCE,0x3D,0x03,0x01,0x02}
#define CODED_PRIME192V2_SZ 8
#endif
#ifndef USE_WINDOWS_API
static const ecc_oid_t ecc_oid_prime192v2[] = CODED_PRIME192V2;
#else
#define ecc_oid_prime192v2 CODED_PRIME192V2
#endif
#define ecc_oid_prime192v2_sz CODED_PRIME192V2_SZ
#endif /* HAVE_ECC_SECPR2 */
#ifdef HAVE_ECC_SECPR3
#ifdef HAVE_OID_ENCODING
#define CODED_PRIME192V3 {1,2,840,10045,3,1,3}
#define CODED_PRIME192V3_SZ 7
#else
#define CODED_PRIME192V3 {0x2A,0x86,0x48,0xCE,0x3D,0x03,0x01,0x03}
#define CODED_PRIME192V3_SZ 8
#endif
#ifndef USE_WINDOWS_API
static const ecc_oid_t ecc_oid_prime192v3[] = CODED_PRIME192V3;
#else
#define ecc_oid_prime192v3 CODED_PRIME192V3
#endif
#define ecc_oid_prime192v3_sz CODED_PRIME192V3_SZ
#endif /* HAVE_ECC_SECPR3 */
#ifdef HAVE_ECC_KOBLITZ
#ifdef HAVE_OID_ENCODING
#define CODED_SECP192K1 {1,3,132,0,31}
#define CODED_SECP192K1_SZ 5
#else
#define CODED_SECP192K1 {0x2B,0x81,0x04,0x00,0x1F}
#define CODED_SECP192K1_SZ 5
#endif
#ifndef USE_WINDOWS_API
static const ecc_oid_t ecc_oid_secp192k1[] = CODED_SECP192K1;
#else
#define ecc_oid_secp192k1 CODED_SECP192K1
#endif
#define ecc_oid_secp192k1_sz CODED_SECP192K1_SZ
#endif /* HAVE_ECC_KOBLITZ */
#ifdef HAVE_ECC_BRAINPOOL
#ifdef HAVE_OID_ENCODING
#define CODED_BRAINPOOLP192R1 {1,3,36,3,3,2,8,1,1,3}
#define CODED_BRAINPOOLP192R1_SZ 10
#else
#define CODED_BRAINPOOLP192R1 {0x2B,0x24,0x03,0x03,0x02,0x08,0x01,0x01,0x03}
#define CODED_BRAINPOOLP192R1_SZ 9
#endif
#ifndef USE_WINDOWS_API
static const ecc_oid_t ecc_oid_brainpoolp192r1[] = CODED_BRAINPOOLP192R1;
#else
#define ecc_oid_brainpoolp192r1 CODED_BRAINPOOLP192R1
#endif
#define ecc_oid_brainpoolp192r1_sz CODED_BRAINPOOLP192R1_SZ
#endif /* HAVE_ECC_BRAINPOOL */
#endif /* ECC192 */
#ifdef ECC224
#ifndef NO_ECC_SECP
#ifdef HAVE_OID_ENCODING
#define CODED_SECP224R1 {1,3,132,0,33}
#define CODED_SECP224R1_SZ 5
#else
#define CODED_SECP224R1 {0x2B,0x81,0x04,0x00,0x21}
#define CODED_SECP224R1_SZ 5
#endif
#ifndef USE_WINDOWS_API
static const ecc_oid_t ecc_oid_secp224r1[] = CODED_SECP224R1;
#else
#define ecc_oid_secp224r1 CODED_SECP224R1
#endif
#define ecc_oid_secp224r1_sz CODED_SECP224R1_SZ
#endif /* !NO_ECC_SECP */
#ifdef HAVE_ECC_KOBLITZ
#ifdef HAVE_OID_ENCODING
#define CODED_SECP224K1 {1,3,132,0,32}
#define CODED_SECP224K1_SZ 5
#else
#define CODED_SECP224K1 {0x2B,0x81,0x04,0x00,0x20}
#define CODED_SECP224K1_SZ 5
#endif
#ifndef USE_WINDOWS_API
static const ecc_oid_t ecc_oid_secp224k1[] = CODED_SECP224K1;
#else
#define ecc_oid_secp224k1 CODED_SECP224K1
#endif
#define ecc_oid_secp224k1_sz CODED_SECP224K1_SZ
#endif /* HAVE_ECC_KOBLITZ */
#ifdef HAVE_ECC_BRAINPOOL
#ifdef HAVE_OID_ENCODING
#define CODED_BRAINPOOLP224R1 {1,3,36,3,3,2,8,1,1,5}
#define CODED_BRAINPOOLP224R1_SZ 10
#else
#define CODED_BRAINPOOLP224R1 {0x2B,0x24,0x03,0x03,0x02,0x08,0x01,0x01,0x05}
#define CODED_BRAINPOOLP224R1_SZ 9
#endif
#ifndef USE_WINDOWS_API
static const ecc_oid_t ecc_oid_brainpoolp224r1[] = CODED_BRAINPOOLP224R1;
#else
#define ecc_oid_brainpoolp224r1 CODED_BRAINPOOLP224R1
#endif
#define ecc_oid_brainpoolp224r1_sz CODED_BRAINPOOLP224R1_SZ
#endif /* HAVE_ECC_BRAINPOOL */
#endif /* ECC224 */
#ifdef ECC239
#ifndef NO_ECC_SECP
#ifdef HAVE_OID_ENCODING
#define CODED_PRIME239V1 {1,2,840,10045,3,1,4}
#define CODED_PRIME239V1_SZ 7
#else
#define CODED_PRIME239V1 {0x2A,0x86,0x48,0xCE,0x3D,0x03,0x01,0x04}
#define CODED_PRIME239V1_SZ 8
#endif
#ifndef USE_WINDOWS_API
static const ecc_oid_t ecc_oid_prime239v1[] = CODED_PRIME239V1;
#else
#define ecc_oid_prime239v1 CODED_PRIME239V1
#endif
#define ecc_oid_prime239v1_sz CODED_PRIME239V1_SZ
#endif /* !NO_ECC_SECP */
#ifdef HAVE_ECC_SECPR2
#ifdef HAVE_OID_ENCODING
#define CODED_PRIME239V2 {1,2,840,10045,3,1,5}
#define CODED_PRIME239V2_SZ 7
#else
#define CODED_PRIME239V2 {0x2A,0x86,0x48,0xCE,0x3D,0x03,0x01,0x05}
#define CODED_PRIME239V2_SZ 8
#endif
#ifndef USE_WINDOWS_API
static const ecc_oid_t ecc_oid_prime239v2[] = CODED_PRIME239V2;
#else
#define ecc_oid_prime239v2 CODED_PRIME239V2
#endif
#define ecc_oid_prime239v2_sz CODED_PRIME239V2_SZ
#endif /* HAVE_ECC_SECPR2 */
#ifdef HAVE_ECC_SECPR3
#ifdef HAVE_OID_ENCODING
#define CODED_PRIME239V3 {1,2,840,10045,3,1,6}
#define CODED_PRIME239V3_SZ 7
#else
#define CODED_PRIME239V3 {0x2A,0x86,0x48,0xCE,0x3D,0x03,0x01,0x06}
#define CODED_PRIME239V3_SZ 8
#endif
#ifndef USE_WINDOWS_API
static const ecc_oid_t ecc_oid_prime239v3[] = CODED_PRIME239V3;
#else
#define ecc_oid_prime239v3 CODED_PRIME239V3
#endif
#define ecc_oid_prime239v3_sz CODED_PRIME239V3_SZ
#endif /* HAVE_ECC_SECPR3 */
#endif /* ECC239 */
#ifdef ECC256
#ifndef NO_ECC_SECP
#ifdef HAVE_OID_ENCODING
#define CODED_SECP256R1 {1,2,840,10045,3,1,7}
#define CODED_SECP256R1_SZ 7
#else
#define CODED_SECP256R1 {0x2A,0x86,0x48,0xCE,0x3D,0x03,0x01,0x07}
#define CODED_SECP256R1_SZ 8
#endif
#ifndef USE_WINDOWS_API
static const ecc_oid_t ecc_oid_secp256r1[] = CODED_SECP256R1;
#else
#define ecc_oid_secp256r1 CODED_SECP256R1
#endif
#define ecc_oid_secp256r1_sz CODED_SECP256R1_SZ
#endif /* !NO_ECC_SECP */
#ifdef HAVE_ECC_KOBLITZ
#ifdef HAVE_OID_ENCODING
#define CODED_SECP256K1 {1,3,132,0,10}
#define CODED_SECP256K1_SZ 5
#else
#define CODED_SECP256K1 {0x2B,0x81,0x04,0x00,0x0A}
#define CODED_SECP256K1_SZ 5
#endif
#ifndef USE_WINDOWS_API
static const ecc_oid_t ecc_oid_secp256k1[] = CODED_SECP256K1;
#else
#define ecc_oid_secp256k1 CODED_SECP256K1
#endif
#define ecc_oid_secp256k1_sz CODED_SECP256K1_SZ
#endif /* HAVE_ECC_KOBLITZ */
#ifdef HAVE_ECC_BRAINPOOL
#ifdef HAVE_OID_ENCODING
#define CODED_BRAINPOOLP256R1 {1,3,36,3,3,2,8,1,1,7}
#define CODED_BRAINPOOLP256R1_SZ 10
#else
#define CODED_BRAINPOOLP256R1 {0x2B,0x24,0x03,0x03,0x02,0x08,0x01,0x01,0x07}
#define CODED_BRAINPOOLP256R1_SZ 9
#endif
#ifndef USE_WINDOWS_API
static const ecc_oid_t ecc_oid_brainpoolp256r1[] = CODED_BRAINPOOLP256R1;
#else
#define ecc_oid_brainpoolp256r1 CODED_BRAINPOOLP256R1
#endif
#define ecc_oid_brainpoolp256r1_sz CODED_BRAINPOOLP256R1_SZ
#endif /* HAVE_ECC_BRAINPOOL */
#endif /* ECC256 */
#ifdef ECC320
#ifdef HAVE_ECC_BRAINPOOL
#ifdef HAVE_OID_ENCODING
#define CODED_BRAINPOOLP320R1 {1,3,36,3,3,2,8,1,1,9}
#define CODED_BRAINPOOLP320R1_SZ 10
#else
#define CODED_BRAINPOOLP320R1 {0x2B,0x24,0x03,0x03,0x02,0x08,0x01,0x01,0x09}
#define CODED_BRAINPOOLP320R1_SZ 9
#endif
#ifndef USE_WINDOWS_API
static const ecc_oid_t ecc_oid_brainpoolp320r1[] = CODED_BRAINPOOLP320R1;
#else
#define ecc_oid_brainpoolp320r1 CODED_BRAINPOOLP320R1
#endif
#define ecc_oid_brainpoolp320r1_sz CODED_BRAINPOOLP320R1_SZ
#endif /* HAVE_ECC_BRAINPOOL */
#endif /* ECC320 */
#ifdef ECC384
#ifndef NO_ECC_SECP
#ifdef HAVE_OID_ENCODING
#define CODED_SECP384R1 {1,3,132,0,34}
#define CODED_SECP384R1_SZ 5
#else
#define CODED_SECP384R1 {0x2B,0x81,0x04,0x00,0x22}
#define CODED_SECP384R1_SZ 5
#endif
#ifndef USE_WINDOWS_API
static const ecc_oid_t ecc_oid_secp384r1[] = CODED_SECP384R1;
#define CODED_SECP384R1_OID ecc_oid_secp384r1
#else
#define ecc_oid_secp384r1 CODED_SECP384R1
#endif
#define ecc_oid_secp384r1_sz CODED_SECP384R1_SZ
#endif /* !NO_ECC_SECP */
#ifdef HAVE_ECC_BRAINPOOL
#ifdef HAVE_OID_ENCODING
#define CODED_BRAINPOOLP384R1 {1,3,36,3,3,2,8,1,1,11}
#define CODED_BRAINPOOLP384R1_SZ 10
#else
#define CODED_BRAINPOOLP384R1 {0x2B,0x24,0x03,0x03,0x02,0x08,0x01,0x01,0x0B}
#define CODED_BRAINPOOLP384R1_SZ 9
#endif
#ifndef USE_WINDOWS_API
static const ecc_oid_t ecc_oid_brainpoolp384r1[] = CODED_BRAINPOOLP384R1;
#else
#define ecc_oid_brainpoolp384r1 CODED_BRAINPOOLP384R1
#endif
#define ecc_oid_brainpoolp384r1_sz CODED_BRAINPOOLP384R1_SZ
#endif /* HAVE_ECC_BRAINPOOL */
#endif /* ECC384 */
#ifdef ECC512
#ifdef HAVE_ECC_BRAINPOOL
#ifdef HAVE_OID_ENCODING
#define CODED_BRAINPOOLP512R1 {1,3,36,3,3,2,8,1,1,13}
#define CODED_BRAINPOOLP512R1_SZ 10
#else
#define CODED_BRAINPOOLP512R1 {0x2B,0x24,0x03,0x03,0x02,0x08,0x01,0x01,0x0D}
#define CODED_BRAINPOOLP512R1_SZ 9
#endif
#ifndef USE_WINDOWS_API
static const ecc_oid_t ecc_oid_brainpoolp512r1[] = CODED_BRAINPOOLP512R1;
#else
#define ecc_oid_brainpoolp512r1 CODED_BRAINPOOLP512R1
#endif
#define ecc_oid_brainpoolp512r1_sz CODED_BRAINPOOLP512R1_SZ
#endif /* HAVE_ECC_BRAINPOOL */
#endif /* ECC512 */
#ifdef ECC521
#ifndef NO_ECC_SECP
#ifdef HAVE_OID_ENCODING
#define CODED_SECP521R1 {1,3,132,0,35}
#define CODED_SECP521R1_SZ 5
#else
#define CODED_SECP521R1 {0x2B,0x81,0x04,0x00,0x23}
#define CODED_SECP521R1_SZ 5
#endif
#ifndef USE_WINDOWS_API
static const ecc_oid_t ecc_oid_secp521r1[] = CODED_SECP521R1;
#else
#define ecc_oid_secp521r1 CODED_SECP521R1
#endif
#define ecc_oid_secp521r1_sz CODED_SECP521R1_SZ
#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 */
ecc_oid_secp112r1_sz,
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 */
ecc_oid_secp112r2_sz,
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 */
ecc_oid_secp128r1_sz,
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 */
ecc_oid_secp128r2_sz,
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 */
ecc_oid_secp160r1_sz,
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 */
ecc_oid_secp160r2_sz,
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 */
ecc_oid_secp160k1_sz,
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 */
ecc_oid_brainpoolp160r1_sz,
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 */
ecc_oid_secp192r1_sz,
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 */
ecc_oid_prime192v2_sz,
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 */
ecc_oid_prime192v3_sz,
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 */
ecc_oid_secp192k1_sz,
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 */
ecc_oid_brainpoolp192r1_sz,
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 */
ecc_oid_secp224r1_sz,
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 */
ecc_oid_secp224k1_sz,
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 */
ecc_oid_brainpoolp224r1_sz,
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 */
ecc_oid_prime239v1_sz,
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 */
ecc_oid_prime239v2_sz,
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 */
ecc_oid_prime239v3_sz,
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 */
ecc_oid_secp256r1_sz,
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 */
ecc_oid_secp256k1_sz,
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 */
ecc_oid_brainpoolp256r1_sz,
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, ecc_oid_brainpoolp320r1_sz, /* 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, ecc_oid_secp384r1_sz, /* 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, ecc_oid_brainpoolp384r1_sz, /* 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, ecc_oid_brainpoolp512r1_sz, /* 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, ecc_oid_secp521r1_sz, /* oid/oidSz */
ECC_SECP521R1_OID, /* oid sum */
1, /* cofactor */
},
#endif /* !NO_ECC_SECP */
#endif /* ECC521 */
#if defined(WOLFSSL_CUSTOM_CURVES) && defined(ECC_CACHE_CURVE)
/* place holder for custom curve index for cache */
{
1, /* non-zero */
ECC_CURVE_CUSTOM,
#ifndef USE_WINDOWS_API
NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL,
#else
0, 0, 0, 0, 0, 0, 0, 0,
#endif
0, 0, 0
},
#endif
{
0, -1,
#ifndef USE_WINDOWS_API
NULL, NULL, NULL, NULL, NULL, NULL, NULL, NULL,
#else
0, 0, 0, 0, 0, 0, 0, 0,
#endif
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
#ifdef WOLFSSL_ATECC508A
typedef void* ecc_curve_spec;
#else
#if defined(WOLFSSL_VALIDATE_ECC_KEYGEN) || !defined(WOLFSSL_SP_MATH)
static int ecc_check_pubkey_order(ecc_key* key, ecc_point* pubkey, mp_int* a,
mp_int* prime, mp_int* order);
#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(curve, intcount) ecc_curve_spec* curve = NULL
#define ALLOC_CURVE_SPECS(intcount)
#define FREE_CURVE_SPECS()
#elif defined(WOLFSSL_SMALL_STACK)
#define DECLARE_CURVE_SPECS(curve, intcount) \
mp_int* spec_ints = NULL; \
ecc_curve_spec curve_lcl; \
ecc_curve_spec* curve = &curve_lcl; \
XMEMSET(curve, 0, sizeof(ecc_curve_spec)); \
curve->spec_count = intcount
#define ALLOC_CURVE_SPECS(intcount) \
spec_ints = (mp_int*)XMALLOC(sizeof(mp_int) * (intcount), NULL, \
DYNAMIC_TYPE_ECC); \
if (spec_ints == NULL) \
return MEMORY_E; \
curve->spec_ints = spec_ints
#define FREE_CURVE_SPECS() \
XFREE(spec_ints, NULL, DYNAMIC_TYPE_ECC)
#else
#define DECLARE_CURVE_SPECS(curve, 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
#define ALLOC_CURVE_SPECS(intcount)
#define FREE_CURVE_SPECS()
#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, MP_RADIX_HEX);
#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;
#if !defined(SINGLE_THREADED)
ret = wc_LockMutex(&ecc_curve_cache_mutex);
if (ret != 0) {
return ret;
}
#endif
/* 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) {
#if defined(ECC_CACHE_CURVE) && !defined(SINGLE_THREADED)
wc_UnLockMutex(&ecc_curve_cache_mutex);
#endif
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 */
/* determine items to load */
load_items = (((byte)~(word32)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;
/* default values */
key->idx = 0;
key->dp = NULL;
/* 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;
}
#ifdef ALT_ECC_SIZE
static void alt_fp_init(fp_int* a)
{
a->size = FP_SIZE_ECC;
fp_zero(a);
}
#endif /* ALT_ECC_SIZE */
#ifndef WOLFSSL_ATECC508A
#if !defined(WOLFSSL_SP_MATH) || defined(WOLFSSL_PUBLIC_ECC_ADD_DBL)
/**
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)
{
#ifndef WOLFSSL_SP_MATH
#ifdef WOLFSSL_SMALL_STACK
mp_int* t1 = NULL;
mp_int* t2 = NULL;
#ifdef ALT_ECC_SIZE
mp_int* rx = NULL;
mp_int* ry = NULL;
mp_int* rz = NULL;
#endif
#else
mp_int t1[1], t2[1];
#ifdef ALT_ECC_SIZE
mp_int rx[1], ry[1], rz[1];
#endif
#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;
}
#ifdef WOLFSSL_SMALL_STACK
#ifdef WOLFSSL_SMALL_STACK_CACHE
if (R->key != NULL) {
t1 = R->key->t1;
t2 = R->key->t2;
#ifdef ALT_ECC_SIZE
rx = R->key->x;
ry = R->key->y;
rz = R->key->z;
#endif
}
else
#endif /* WOLFSSL_SMALL_STACK_CACHE */
{
t1 = (mp_int*)XMALLOC(sizeof(mp_int), NULL, DYNAMIC_TYPE_ECC);
t2 = (mp_int*)XMALLOC(sizeof(mp_int), NULL, DYNAMIC_TYPE_ECC);
if (t1 == NULL || t2 == NULL) {
XFREE(t1, NULL, DYNAMIC_TYPE_ECC);
XFREE(t2, NULL, DYNAMIC_TYPE_ECC);
return MEMORY_E;
}
#ifdef ALT_ECC_SIZE
rx = (mp_int*)XMALLOC(sizeof(mp_int), NULL, DYNAMIC_TYPE_ECC);
ry = (mp_int*)XMALLOC(sizeof(mp_int), NULL, DYNAMIC_TYPE_ECC);
rz = (mp_int*)XMALLOC(sizeof(mp_int), NULL, DYNAMIC_TYPE_ECC);
if (rx == NULL || ry == NULL || rz == NULL) {
XFREE(rz, NULL, DYNAMIC_TYPE_ECC);
XFREE(ry, NULL, DYNAMIC_TYPE_ECC);
XFREE(rx, NULL, DYNAMIC_TYPE_ECC);
XFREE(t2, NULL, DYNAMIC_TYPE_ECC);
XFREE(t1, NULL, DYNAMIC_TYPE_ECC);
return MEMORY_E;
}
#endif
}
#endif /* WOLFSSL_SMALL_STACK */
if ((err = mp_init_multi(t1, t2, NULL, NULL, NULL, NULL)) != MP_OKAY) {
#ifdef WOLFSSL_SMALL_STACK
#ifdef WOLFSSL_SMALL_STACK_CACHE
if (R->key == NULL)
#endif
{
#ifdef ALT_ECC_SIZE
XFREE(rz, NULL, DYNAMIC_TYPE_ECC);
XFREE(ry, NULL, DYNAMIC_TYPE_ECC);
XFREE(rx, NULL, DYNAMIC_TYPE_ECC);
#endif
XFREE(t2, NULL, DYNAMIC_TYPE_ECC);
XFREE(t1, NULL, DYNAMIC_TYPE_ECC);
}
#endif
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);
#ifdef WOLFSSL_SMALL_STACK
#ifdef WOLFSSL_SMALL_STACK_CACHE
if (R->key == NULL)
#endif
{
#ifdef ALT_ECC_SIZE
XFREE(rz, NULL, DYNAMIC_TYPE_ECC);
XFREE(ry, NULL, DYNAMIC_TYPE_ECC);
XFREE(rx, NULL, DYNAMIC_TYPE_ECC);
#endif
XFREE(t2, NULL, DYNAMIC_TYPE_ECC);
XFREE(t1, NULL, DYNAMIC_TYPE_ECC);
}
#endif
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);
#ifdef WOLFSSL_SMALL_STACK
#ifdef WOLFSSL_SMALL_STACK_CACHE
if (R->key == NULL)
#endif
{
#ifdef ALT_ECC_SIZE
XFREE(rz, NULL, DYNAMIC_TYPE_ECC);
XFREE(ry, NULL, DYNAMIC_TYPE_ECC);
XFREE(rx, NULL, DYNAMIC_TYPE_ECC);
#endif
XFREE(t2, NULL, DYNAMIC_TYPE_ECC);
XFREE(t1, NULL, DYNAMIC_TYPE_ECC);
}
#endif
return err;
#else
if (P == NULL || Q == NULL || R == NULL || modulus == NULL) {
return ECC_BAD_ARG_E;
}
(void)a;
(void)mp;
return sp_ecc_proj_add_point_256(P->x, P->y, P->z, Q->x, Q->y, Q->z,
R->x, R->y, R->z);
#endif
}
/* ### 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)
{
#ifndef WOLFSSL_SP_MATH
#ifdef WOLFSSL_SMALL_STACK
mp_int* t1 = NULL;
mp_int* t2 = NULL;
#ifdef ALT_ECC_SIZE
mp_int* rx = NULL;
mp_int* ry = NULL;
mp_int* rz = NULL;
#endif
#else
mp_int t1[1], t2[1];
#ifdef ALT_ECC_SIZE
mp_int rx[1], ry[1], rz[1];
#endif
#endif
mp_int *x, *y, *z;
int err;
if (P == NULL || R == NULL || modulus == NULL)
return ECC_BAD_ARG_E;
#ifdef WOLFSSL_SMALL_STACK
#ifdef WOLFSSL_SMALL_STACK_CACHE
if (R->key != NULL) {
t1 = R->key->t1;
t2 = R->key->t2;
#ifdef ALT_ECC_SIZE
rx = R->key->x;
ry = R->key->y;
rz = R->key->z;
#endif
}
else
#endif /* WOLFSSL_SMALL_STACK_CACHE */
{
t1 = (mp_int*)XMALLOC(sizeof(mp_int), NULL, DYNAMIC_TYPE_ECC);
t2 = (mp_int*)XMALLOC(sizeof(mp_int), NULL, DYNAMIC_TYPE_ECC);
if (t1 == NULL || t2 == NULL) {
XFREE(t2, NULL, DYNAMIC_TYPE_ECC);
XFREE(t1, NULL, DYNAMIC_TYPE_ECC);
return MEMORY_E;
}
#ifdef ALT_ECC_SIZE
rx = (mp_int*)XMALLOC(sizeof(mp_int), NULL, DYNAMIC_TYPE_ECC);
ry = (mp_int*)XMALLOC(sizeof(mp_int), NULL, DYNAMIC_TYPE_ECC);
rz = (mp_int*)XMALLOC(sizeof(mp_int), NULL, DYNAMIC_TYPE_ECC);
if (rx == NULL || ry == NULL || rz == NULL) {
XFREE(rz, NULL, DYNAMIC_TYPE_ECC);
XFREE(ry, NULL, DYNAMIC_TYPE_ECC);
XFREE(rx, NULL, DYNAMIC_TYPE_ECC);
XFREE(t2, NULL, DYNAMIC_TYPE_ECC);
XFREE(t1, NULL, DYNAMIC_TYPE_ECC);
return MEMORY_E;
}
#endif
}
#endif
if ((err = mp_init_multi(t1, t2, NULL, NULL, NULL, NULL)) != MP_OKAY) {
#ifdef WOLFSSL_SMALL_STACK
#ifdef WOLFSSL_SMALL_STACK_CACHE
if (R->key == NULL)
#endif
{
#ifdef ALT_ECC_SIZE
XFREE(rz, NULL, DYNAMIC_TYPE_ECC);
XFREE(ry, NULL, DYNAMIC_TYPE_ECC);
XFREE(rx, NULL, DYNAMIC_TYPE_ECC);
#endif
XFREE(t2, NULL, DYNAMIC_TYPE_ECC);
XFREE(t1, NULL, DYNAMIC_TYPE_ECC);
}
#endif
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);
#ifdef WOLFSSL_SMALL_STACK
#ifdef WOLFSSL_SMALL_STACK_CACHE
if (R->key == NULL)
#endif
{
#ifdef ALT_ECC_SIZE
XFREE(rz, NULL, DYNAMIC_TYPE_ECC);
XFREE(ry, NULL, DYNAMIC_TYPE_ECC);
XFREE(rx, NULL, DYNAMIC_TYPE_ECC);
#endif
XFREE(t2, NULL, DYNAMIC_TYPE_ECC);
XFREE(t1, NULL, DYNAMIC_TYPE_ECC);
}
#endif
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);
#ifdef WOLFSSL_SMALL_STACK
#ifdef WOLFSSL_SMALL_STACK_CACHE
if (R->key == NULL)
#endif
{
#ifdef ALT_ECC_SIZE
XFREE(rz, NULL, DYNAMIC_TYPE_ECC);
XFREE(ry, NULL, DYNAMIC_TYPE_ECC);
XFREE(rx, NULL, DYNAMIC_TYPE_ECC);
#endif
XFREE(t2, NULL, DYNAMIC_TYPE_ECC);
XFREE(t1, NULL, DYNAMIC_TYPE_ECC);
}
#endif
return err;
#else
if (P == NULL || R == NULL || modulus == NULL)
return ECC_BAD_ARG_E;
(void)a;
(void)mp;
return sp_ecc_proj_dbl_point_256(P->x, P->y, P->z, R->x, R->y, R->z);
#endif
}
/**
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)
{
#ifndef WOLFSSL_SP_MATH
#ifdef WOLFSSL_SMALL_STACK
mp_int* t1 = NULL;
mp_int* t2 = NULL;
#ifdef ALT_ECC_SIZE
mp_int* rx = NULL;
mp_int* ry = NULL;
mp_int* rz = NULL;
#endif
#else
mp_int t1[1], t2[1];
#ifdef ALT_ECC_SIZE
mp_int rx[1], ry[1], rz[1];
#endif
#endif /* WOLFSSL_SMALL_STACK */
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;
}
#ifdef WOLFSSL_SMALL_STACK
#ifdef WOLFSSL_SMALL_STACK_CACHE
if (P->key != NULL) {
t1 = P->key->t1;
t2 = P->key->t2;
#ifdef ALT_ECC_SIZE
rx = P->key->x;
ry = P->key->y;
rz = P->key->z;
#endif
}
else
#endif /* WOLFSSL_SMALL_STACK_CACHE */
{
t1 = (mp_int*)XMALLOC(sizeof(mp_int), NULL, DYNAMIC_TYPE_ECC);
t2 = (mp_int*)XMALLOC(sizeof(mp_int), NULL, DYNAMIC_TYPE_ECC);
if (t1 == NULL || t2 == NULL) {
XFREE(t2, NULL, DYNAMIC_TYPE_ECC);
XFREE(t1, NULL, DYNAMIC_TYPE_ECC);
return MEMORY_E;
}
#ifdef ALT_ECC_SIZE
rx = (mp_int*)XMALLOC(sizeof(mp_int), NULL, DYNAMIC_TYPE_ECC);
ry = (mp_int*)XMALLOC(sizeof(mp_int), NULL, DYNAMIC_TYPE_ECC);
rz = (mp_int*)XMALLOC(sizeof(mp_int), NULL, DYNAMIC_TYPE_ECC);
if (rx == NULL || ry == NULL || rz == NULL) {
XFREE(rz, NULL, DYNAMIC_TYPE_ECC);
XFREE(ry, NULL, DYNAMIC_TYPE_ECC);
XFREE(rx, NULL, DYNAMIC_TYPE_ECC);
XFREE(t2, NULL, DYNAMIC_TYPE_ECC);
XFREE(t1, NULL, DYNAMIC_TYPE_ECC);
return MEMORY_E;
}
#endif
}
#endif /* WOLFSSL_SMALL_STACK */
if ((err = mp_init_multi(t1, t2, NULL, NULL, NULL, NULL)) != MP_OKAY) {
#ifdef WOLFSSL_SMALL_STACK
#ifdef WOLFSSL_SMALL_STACK_CACHE
if (P->key == NULL)
#endif
{
#ifdef ALT_ECC_SIZE
XFREE(rz, NULL, DYNAMIC_TYPE_ECC);
XFREE(ry, NULL, DYNAMIC_TYPE_ECC);
XFREE(rx, NULL, DYNAMIC_TYPE_ECC);
#endif
XFREE(t2, NULL, DYNAMIC_TYPE_ECC);
XFREE(t1, NULL, DYNAMIC_TYPE_ECC);
}
#endif
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);
#ifdef WOLFSSL_SMALL_STACK
#ifdef WOLFSSL_SMALL_STACK_CACHE
if (P->key == NULL)
#endif
{
#ifdef ALT_ECC_SIZE
XFREE(rz, NULL, DYNAMIC_TYPE_ECC);
XFREE(ry, NULL, DYNAMIC_TYPE_ECC);
XFREE(rx, NULL, DYNAMIC_TYPE_ECC);
#endif
XFREE(t2, NULL, DYNAMIC_TYPE_ECC);
XFREE(t1, NULL, DYNAMIC_TYPE_ECC);
}
#endif
return err;
#else
if (P == NULL || modulus == NULL)
return ECC_BAD_ARG_E;
(void)mp;
return sp_ecc_map_256(P->x, P->y, P->z);
#endif
}
#endif /* !WOLFSSL_SP_MATH || WOLFSSL_PUBLIC_ECC_ADD_DBL */
#if !defined(FREESCALE_LTC_ECC)
#if !defined(FP_ECC) || !defined(WOLFSSL_SP_MATH)
/**
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 WOLFSSL_SP_MATH
#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;
#ifdef WOLFSSL_SMALL_STACK
mp_int* mu = NULL;
#ifdef WOLFSSL_SMALL_STACK_CACHE
ecc_key key;
#endif
#else
mp_int mu[1];
#endif
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));
#ifdef WOLFSSL_SMALL_STACK
mu = (mp_int*)XMALLOC(sizeof(mp_int), heap, DYNAMIC_TYPE_ECC);
if (mu == NULL)
return MEMORY_E;
#endif
#ifdef WOLFSSL_SMALL_STACK_CACHE
key.t1 = (mp_int*)XMALLOC(sizeof(mp_int), heap, DYNAMIC_TYPE_ECC);
key.t2 = (mp_int*)XMALLOC(sizeof(mp_int), heap, DYNAMIC_TYPE_ECC);
#ifdef ALT_ECC_SIZE
key.x = (mp_int*)XMALLOC(sizeof(mp_int), heap, DYNAMIC_TYPE_ECC);
key.y = (mp_int*)XMALLOC(sizeof(mp_int), heap, DYNAMIC_TYPE_ECC);
key.z = (mp_int*)XMALLOC(sizeof(mp_int), heap, DYNAMIC_TYPE_ECC);
#endif
if (key.t1 == NULL || key.t2 == NULL
#ifdef ALT_ECC_SIZE
|| key.x == NULL || key.y == NULL || key.z == NULL
#endif
) {
#ifdef ALT_ECC_SIZE
XFREE(key.z, heap, DYNAMIC_TYPE_ECC);
XFREE(key.y, heap, DYNAMIC_TYPE_ECC);
XFREE(key.x, heap, DYNAMIC_TYPE_ECC);
#endif
XFREE(key.t2, heap, DYNAMIC_TYPE_ECC);
XFREE(key.t1, heap, DYNAMIC_TYPE_ECC);
XFREE(mu, heap, DYNAMIC_TYPE_ECC);
return MEMORY_E;
}
#endif /* WOLFSSL_SMALL_STACK_CACHE */
/* init montgomery reduction */
if ((err = mp_montgomery_setup(modulus, &mp)) != MP_OKAY) {
#ifdef WOLFSSL_SMALL_STACK_CACHE
#ifdef ALT_ECC_SIZE
XFREE(key.z, heap, DYNAMIC_TYPE_ECC);
XFREE(key.y, heap, DYNAMIC_TYPE_ECC);
XFREE(key.x, heap, DYNAMIC_TYPE_ECC);
#endif
XFREE(key.t2, heap, DYNAMIC_TYPE_ECC);
XFREE(key.t1, heap, DYNAMIC_TYPE_ECC);
#endif /* WOLFSSL_SMALL_STACK_CACHE */
#ifdef WOLFSSL_SMALL_STACK
XFREE(mu, heap, DYNAMIC_TYPE_ECC);
#endif
return err;
}
if ((err = mp_init(mu)) != MP_OKAY) {
#ifdef WOLFSSL_SMALL_STACK_CACHE
#ifdef ALT_ECC_SIZE
XFREE(key.z, heap, DYNAMIC_TYPE_ECC);
XFREE(key.y, heap, DYNAMIC_TYPE_ECC);
XFREE(key.x, heap, DYNAMIC_TYPE_ECC);
#endif
XFREE(key.t2, heap, DYNAMIC_TYPE_ECC);
XFREE(key.t1, heap, DYNAMIC_TYPE_ECC);
#endif /* WOLFSSL_SMALL_STACK_CACHE */
#ifdef WOLFSSL_SMALL_STACK
XFREE(mu, heap, DYNAMIC_TYPE_ECC);
#endif
return err;
}
if ((err = mp_montgomery_calc_normalization(mu, modulus)) != MP_OKAY) {
mp_clear(mu);
#ifdef WOLFSSL_SMALL_STACK_CACHE
#ifdef ALT_ECC_SIZE
XFREE(key.z, heap, DYNAMIC_TYPE_ECC);
XFREE(key.y, heap, DYNAMIC_TYPE_ECC);
XFREE(key.x, heap, DYNAMIC_TYPE_ECC);
#endif
XFREE(key.t2, heap, DYNAMIC_TYPE_ECC);
XFREE(key.t1, heap, DYNAMIC_TYPE_ECC);
#endif /* WOLFSSL_SMALL_STACK_CACHE */
#ifdef WOLFSSL_SMALL_STACK
XFREE(mu, heap, DYNAMIC_TYPE_ECC);
#endif
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;
}
#ifdef WOLFSSL_SMALL_STACK_CACHE
M[i]->key = &key;
#endif
}
/* 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);
#ifdef WOLFSSL_SMALL_STACK_CACHE
R->key = &key;
#endif
#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);
}
#ifdef WOLFSSL_SMALL_STACK_CACHE
R->key = NULL;
#ifdef ALT_ECC_SIZE
XFREE(key.z, heap, DYNAMIC_TYPE_ECC);
XFREE(key.y, heap, DYNAMIC_TYPE_ECC);
XFREE(key.x, heap, DYNAMIC_TYPE_ECC);
#endif
XFREE(key.t2, heap, DYNAMIC_TYPE_ECC);
XFREE(key.t1, heap, DYNAMIC_TYPE_ECC);
#endif /* WOLFSSL_SMALL_STACK_CACHE */
#ifdef WOLFSSL_SMALL_STACK
XFREE(mu, heap, DYNAMIC_TYPE_ECC);
#endif
return err;
#else
if (k == NULL || G == NULL || R == NULL || modulus == NULL) {
return ECC_BAD_ARG_E;
}
(void)a;
return sp_ecc_mulmod_256(k, G, R, map, heap);
#endif
}
#endif /* !FP_ECC || !WOLFSSL_SP_MATH */
#endif /* !FREESCALE_LTC_ECC */
/** 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 /* !WOLFSSL_ATECC508A */
/**
* 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;
(void)heap;
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;
}
/** 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 (ecc_sets[curve_idx].name &&
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;
#ifdef WOLFSSL_SMALL_STACK
mp_int* a = NULL;
mp_int* b = NULL;
#else
mp_int a[1], b[1];
#endif
if (param == NULL || curveParam == NULL)
return BAD_FUNC_ARG;
#ifdef WOLFSSL_SMALL_STACK
a = (mp_int*)XMALLOC(sizeof(mp_int), NULL, DYNAMIC_TYPE_ECC);
if (a == NULL)
return MEMORY_E;
b = (mp_int*)XMALLOC(sizeof(mp_int), NULL, DYNAMIC_TYPE_ECC);
if (b == NULL) {
XFREE(a, NULL, DYNAMIC_TYPE_ECC);
return MEMORY_E;
}
#endif
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, MP_RADIX_HEX);
if (err == MP_OKAY) {
if (mp_cmp(a, b) != MP_EQ) {
err = -1;
} else {
err = MP_EQ;
}
}
mp_clear(a);
mp_clear(b);
#ifdef WOLFSSL_SMALL_STACK
XFREE(b, NULL, DYNAMIC_TYPE_ECC);
XFREE(a, NULL, DYNAMIC_TYPE_ECC);
#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 WOLFSSL_ASYNC_CRYPT
static WC_INLINE int wc_ecc_alloc_mpint(ecc_key* key, mp_int** mp)
{
if (key == NULL || mp == NULL)
return BAD_FUNC_ARG;
if (*mp == NULL) {
*mp = (mp_int*)XMALLOC(sizeof(mp_int), key->heap, DYNAMIC_TYPE_BIGINT);
if (*mp == NULL) {
return MEMORY_E;
}
XMEMSET(*mp, 0, sizeof(mp_int));
}
return 0;
}
static WC_INLINE void wc_ecc_free_mpint(ecc_key* key, mp_int** mp)
{
if (key && mp && *mp) {
mp_clear(*mp);
XFREE(*mp, key->heap, DYNAMIC_TYPE_BIGINT);
*mp = NULL;
}
}
static int wc_ecc_alloc_async(ecc_key* key)
{
int err = wc_ecc_alloc_mpint(key, &key->r);
if (err == 0)
err = wc_ecc_alloc_mpint(key, &key->s);
return err;
}
static void wc_ecc_free_async(ecc_key* key)
{
wc_ecc_free_mpint(key, &key->r);
wc_ecc_free_mpint(key, &key->s);
#ifdef HAVE_CAVIUM_V
wc_ecc_free_mpint(key, &key->e);
wc_ecc_free_mpint(key, &key->signK);
#endif /* HAVE_CAVIUM_V */
}
#endif /* WOLFSSL_ASYNC_CRYPT */
#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;
}
#ifdef WOLF_CRYPTO_DEV
if (private_key->devId != INVALID_DEVID) {
err = wc_CryptoDev_Ecdh(private_key, public_key, out, outlen);
if (err != NOT_COMPILED_IN)
return err;
}
#endif
/* type valid? */
if (private_key->type != ECC_PRIVATEKEY &&
private_key->type != ECC_PRIVATEKEY_ONLY) {
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_raw, 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;
#ifndef WOLFSSL_SP_MATH
ecc_point* result = NULL;
word32 x = 0;
#endif
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
#ifdef WOLFSSL_HAVE_SP_ECC
#ifndef WOLFSSL_SP_NO_256
if (private_key->idx != ECC_CUSTOM_IDX &&
ecc_sets[private_key->idx].id == ECC_SECP256R1) {
err = sp_ecc_secret_gen_256(k, point, out, outlen, private_key->heap);
}
else
#endif
#endif
#ifdef WOLFSSL_SP_MATH
{
err = WC_KEY_SIZE_E;
(void)curve;
}
#else
{
/* 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);
}
#endif
#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;
#if defined(HAVE_CAVIUM_V) || defined(HAVE_INTEL_QA)
#ifdef HAVE_CAVIUM_V
/* verify the curve is supported by hardware */
if (NitroxEccIsCurveSupported(private_key))
#endif
{
word32 keySz = private_key->dp->size;
/* sync public key x/y */
err = wc_mp_to_bigint_sz(&private_key->k, &private_key->k.raw, keySz);
if (err == MP_OKAY)
err = wc_mp_to_bigint_sz(point->x, &point->x->raw, keySz);
if (err == MP_OKAY)
err = wc_mp_to_bigint_sz(point->y, &point->y->raw, keySz);
#ifdef HAVE_CAVIUM_V
/* allocate buffer for output */
if (err == MP_OKAY)
err = wc_ecc_alloc_mpint(private_key, &private_key->e);
if (err == MP_OKAY)
err = wc_bigint_alloc(&private_key->e->raw,
NitroxEccGetSize(private_key)*2);
if (err == MP_OKAY)
err = NitroxEcdh(private_key,
&private_key->k.raw, &point->x->raw, &point->y->raw,
private_key->e->raw.buf, &private_key->e->raw.len,
&curve->prime->raw);
#else
if (err == MP_OKAY)
err = wc_ecc_curve_load(private_key->dp, &curve, ECC_CURVE_FIELD_BF);
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);
#endif
return err;
}
#elif defined(WOLFSSL_ASYNC_CRYPT_TEST)
if (wc_AsyncTestInit(&private_key->asyncDev, ASYNC_TEST_ECC_SHARED_SEC)) {
WC_ASYNC_TEST* testDev = &private_key->asyncDev.test;
testDev->eccSharedSec.private_key = private_key;
testDev->eccSharedSec.public_point = point;
testDev->eccSharedSec.out = out;
testDev->eccSharedSec.outLen = outlen;
return WC_PENDING_E;
}
#endif
/* use sync in other cases */
err = wc_ecc_shared_secret_gen_sync(private_key, point, out, outlen, curve);
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(curve, 2);
if (private_key == NULL || point == NULL || out == NULL ||
outlen == NULL) {
return BAD_FUNC_ARG;
}
ALLOC_CURVE_SPECS(2);
/* load curve info */
err = wc_ecc_curve_load(private_key->dp, &curve,
(ECC_CURVE_FIELD_PRIME | ECC_CURVE_FIELD_AF));
if (err != MP_OKAY) {
FREE_CURVE_SPECS();
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);
FREE_CURVE_SPECS();
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 &&
private_key->type != ECC_PRIVATEKEY_ONLY) {
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;
#if defined(WOLFSSL_ASYNC_CRYPT) && defined(WC_ASYNC_ENABLE_ECC)
if (private_key->asyncDev.marker == WOLFSSL_ASYNC_MARKER_ECC) {
#ifdef HAVE_CAVIUM_V
/* verify the curve is supported by hardware */
if (NitroxEccIsCurveSupported(private_key)) {
/* copy output */
*outlen = private_key->dp->size;
XMEMCPY(out, private_key->e->raw.buf, *outlen);
}
#endif /* HAVE_CAVIUM_V */
}
#endif /* WOLFSSL_ASYNC_CRYPT */
err = 0;
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;
}
/* cleanup */
#ifdef WOLFSSL_ASYNC_CRYPT
wc_ecc_free_async(private_key);
#endif
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;
}
#ifndef WOLFSSL_SP_MATH
/* 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;
DECLARE_VAR(buf, byte, ECC_MAXSIZE_GEN, rng->heap);
/*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);
/* 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);
}
}
/* 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;
}
ForceZero(buf, ECC_MAXSIZE);
FREE_VAR(buf, rng->heap);
return err;
}
#endif
#endif /* !WOLFSSL_ATECC508A */
static WC_INLINE void wc_ecc_reset(ecc_key* key)
{
/* make sure required key variables are reset */
key->state = ECC_STATE_NONE;
}
/* create the public ECC key from a private key
*
* key an initialized private key to generate public part from
* curveIn [in]curve for key, can be NULL
* pubOut [out]ecc_point holding the public key, if NULL then public key part
* is cached in key instead.
*
* Note this function is local to the file because of the argument type
* ecc_curve_spec. Having this argument allows for not having to load the
* curve type multiple times when generating a key with wc_ecc_make_key().
*
* returns MP_OKAY on success
*/
static int wc_ecc_make_pub_ex(ecc_key* key, ecc_curve_spec* curveIn,
ecc_point* pubOut)
{
int err = MP_OKAY;
#ifndef WOLFSSL_ATECC508A
#ifndef WOLFSSL_SP_MATH
ecc_point* base = NULL;
#endif
ecc_point* pub;
DECLARE_CURVE_SPECS(curve, ECC_CURVE_FIELD_COUNT);
#endif
if (key == NULL) {
return BAD_FUNC_ARG;
}
#ifndef WOLFSSL_ATECC508A
/* if ecc_point passed in then use it as output for public key point */
if (pubOut != NULL) {
pub = pubOut;
}
else {
/* caching public key making it a ECC_PRIVATEKEY instead of
ECC_PRIVATEKEY_ONLY */
pub = &key->pubkey;
key->type = ECC_PRIVATEKEY_ONLY;
}
/* avoid loading the curve unless it is not passed in */
if (curveIn != NULL) {
curve = curveIn;
}
else {
ALLOC_CURVE_SPECS(ECC_CURVE_FIELD_COUNT);
/* load curve info */
if (err == MP_OKAY)
err = wc_ecc_curve_load(key->dp, &curve, ECC_CURVE_FIELD_ALL);
}
if (err == MP_OKAY) {
#ifndef ALT_ECC_SIZE
err = mp_init_multi(pub->x, pub->y, pub->z, NULL, NULL, NULL);
#else
pub->x = (mp_int*)&pub->xyz[0];
pub->y = (mp_int*)&pub->xyz[1];
pub->z = (mp_int*)&pub->xyz[2];
alt_fp_init(pub->x);
alt_fp_init(pub->y);
alt_fp_init(pub->z);
#endif
}
#ifdef WOLFSSL_HAVE_SP_ECC
#ifndef WOLFSSL_SP_NO_256
if (key->idx != ECC_CUSTOM_IDX && ecc_sets[key->idx].id == ECC_SECP256R1) {
if (err == MP_OKAY)
err = sp_ecc_mulmod_base_256(&key->k, pub, 1, key->heap);
}
else
#endif
#endif
#ifdef WOLFSSL_SP_MATH
err = WC_KEY_SIZE_E;
#else
{
if (err == MP_OKAY) {
base = wc_ecc_new_point_h(key->heap);
if (base == NULL)
err = MEMORY_E;
}
/* 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);
/* make the public key */
if (err == MP_OKAY) {
err = wc_ecc_mulmod_ex(&key->k, base, pub, curve->Af, curve->prime,
1, key->heap);
}
wc_ecc_del_point_h(base, key->heap);
}
#endif
#ifdef WOLFSSL_VALIDATE_ECC_KEYGEN
/* validate the public key, order * pubkey = point at infinity */
if (err == MP_OKAY)
err = ecc_check_pubkey_order(key, pub, curve->Af, curve->prime,
curve->order);
#endif /* WOLFSSL_VALIDATE_KEYGEN */
if (err != MP_OKAY) {
/* clean up if failed */
#ifndef ALT_ECC_SIZE
mp_clear(pub->x);
mp_clear(pub->y);
mp_clear(pub->z);
#endif
}
/* free up local curve */
if (curveIn == NULL) {
wc_ecc_curve_free(curve);
#ifndef WOLFSSL_ATECC508A
FREE_CURVE_SPECS();
#endif
}
#else
(void)curveIn;
#endif /* WOLFSSL_ATECC508A */
/* change key state if public part is cached */
if (key->type == ECC_PRIVATEKEY_ONLY && pubOut == NULL) {
key->type = ECC_PRIVATEKEY;
}
return err;
}
/* create the public ECC key from a private key
*
* key an initialized private key to generate public part from
* pubOut [out]ecc_point holding the public key, if NULL then public key part
* is cached in key instead.
*
*
* returns MP_OKAY on success
*/
int wc_ecc_make_pub(ecc_key* key, ecc_point* pubOut)
{
WOLFSSL_ENTER("wc_ecc_make_pub");
return wc_ecc_make_pub_ex(key, NULL, pubOut);
}
int wc_ecc_make_key_ex(WC_RNG* rng, int keysize, ecc_key* key, int curve_id)
{
int err;
#ifndef WOLFSSL_ATECC508A
#ifndef WOLFSSL_SP_MATH
DECLARE_CURVE_SPECS(curve, ECC_CURVE_FIELD_COUNT);
#endif
#endif
if (key == NULL || rng == NULL) {
return BAD_FUNC_ARG;
}
/* make sure required variables are reset */
wc_ecc_reset(key);
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
if (wc_AsyncTestInit(&key->asyncDev, ASYNC_TEST_ECC_MAKE)) {
WC_ASYNC_TEST* testDev = &key->asyncDev.test;
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_raw);
if (err != ATCA_SUCCESS) {
err = BAD_COND_E;
}
/* populate key->pubkey */
err = mp_read_unsigned_bin(key->pubkey.x, key->pubkey_raw,
ECC_MAX_CRYPTO_HW_SIZE);
if (err == MP_OKAY)
err = mp_read_unsigned_bin(key->pubkey.y,
key->pubkey_raw + ECC_MAX_CRYPTO_HW_SIZE,
ECC_MAX_CRYPTO_HW_SIZE);
#else
#ifdef WOLFSSL_HAVE_SP_ECC
#ifndef WOLFSSL_SP_NO_256
if (key->idx != ECC_CUSTOM_IDX && ecc_sets[key->idx].id == ECC_SECP256R1) {
err = sp_ecc_make_key_256(rng, &key->k, &key->pubkey, key->heap);
if (err == MP_OKAY)
key->type = ECC_PRIVATEKEY;
}
else
#endif
#endif
#ifdef WOLFSSL_SP_MATH
err = WC_KEY_SIZE_E;
#else
{
ALLOC_CURVE_SPECS(ECC_CURVE_FIELD_COUNT);
/* setup the key variables */
err = mp_init(&key->k);
/* load curve info */
if (err == MP_OKAY)
err = wc_ecc_curve_load(key->dp, &curve, ECC_CURVE_FIELD_ALL);
/* generate k */
if (err == MP_OKAY)
err = wc_ecc_gen_k(rng, key->dp->size, &key->k, curve->order);
/* generate public key from k */
if (err == MP_OKAY)
err = wc_ecc_make_pub_ex(key, curve, NULL);
if (err == MP_OKAY)
key->type = ECC_PRIVATEKEY;
/* cleanup these on failure case only */
if (err != MP_OKAY) {
/* clean up */
mp_forcezero(&key->k);
}
/* cleanup allocations */
wc_ecc_curve_free(curve);
#ifndef WOLFSSL_ATECC508A
FREE_CURVE_SPECS();
#endif
}
#endif
#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);
}
/* 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;
#if defined(PLUTON_CRYPTO_ECC) || defined(WOLF_CRYPTO_DEV)
key->devId = devId;
#else
(void)devId;
#endif
#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);
#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
#if defined(WOLFSSL_ATECC508A) || defined(PLUTON_CRYPTO_ECC)
static int wc_ecc_sign_hash_hw(const byte* in, word32 inlen,
mp_int* r, mp_int* s, byte* out, word32 *outlen, WC_RNG* rng,
ecc_key* key)
{
int err;
#ifdef PLUTON_CRYPTO_ECC
if (key->devId != INVALID_DEVID) /* use hardware */
#endif
{
word32 keysize = (word32)key->dp->size;
/* Check args */
if (keysize > ECC_MAX_CRYPTO_HW_SIZE || inlen != keysize ||
*outlen < keysize*2) {
return ECC_BAD_ARG_E;
}
#if defined(WOLFSSL_ATECC508A)
/* 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;
}
#elif defined(PLUTON_CRYPTO_ECC)
{
/* perform ECC sign */
word32 raw_sig_size = *outlen;
err = Crypto_EccSign(in, inlen, out, &raw_sig_size);
if (err != CRYPTO_RES_SUCCESS || raw_sig_size != keysize*2){
return BAD_COND_E;
}
}
#endif
/* Load R and S */
err = mp_read_unsigned_bin(r, &out[0], keysize);
if (err != MP_OKAY) {
return err;
}
err = mp_read_unsigned_bin(s, &out[keysize], keysize);
if (err != MP_OKAY) {
return err;
}
/* Check for zeros */
if (mp_iszero(r) || mp_iszero(s)) {
return MP_ZERO_E;
}
}
#ifdef PLUTON_CRYPTO_ECC
else {
err = wc_ecc_sign_hash_ex(in, inlen, rng, key, r, s);
}
#endif
(void)rng;
return err;
}
#endif /* WOLFSSL_ATECC508A || PLUTON_CRYPTO_ECC */
/**
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;
#if !defined(WOLFSSL_ASYNC_CRYPT) && !defined(WOLFSSL_SMALL_STACK)
mp_int r_lcl, s_lcl;
#endif
if (in == NULL || out == NULL || outlen == NULL || key == NULL ||
rng == NULL) {
return ECC_BAD_ARG_E;
}
#ifdef WOLF_CRYPTO_DEV
if (key->devId != INVALID_DEVID) {
err = wc_CryptoDev_EccSign(in, inlen, out, outlen, rng, key);
if (err != NOT_COMPILED_IN)
return err;
}
#endif
#ifdef WOLFSSL_ASYNC_CRYPT
err = wc_ecc_alloc_async(key);
if (err != 0)
return err;
r = key->r;
s = key->s;
#elif !defined(WOLFSSL_SMALL_STACK)
r = &r_lcl;
s = &s_lcl;
#else
r = (mp_int*)XMALLOC(sizeof(mp_int), key->heap, DYNAMIC_TYPE_ECC);
if (r == NULL)
return MEMORY_E;
s = (mp_int*)XMALLOC(sizeof(mp_int), key->heap, DYNAMIC_TYPE_ECC);
if (s == NULL) {
XFREE(r, key->heap, DYNAMIC_TYPE_ECC);
return MEMORY_E;
}
#endif
switch(key->state) {
case ECC_STATE_NONE:
case ECC_STATE_SIGN_DO:
key->state = ECC_STATE_SIGN_DO;
if ((err = mp_init_multi(r, s, NULL, NULL, NULL, NULL)) != MP_OKAY){
break;
}
/* hardware crypto */
#if defined(WOLFSSL_ATECC508A) || defined(PLUTON_CRYPTO_ECC)
err = wc_ecc_sign_hash_hw(in, inlen, r, s, out, outlen, rng, key);
#else
err = wc_ecc_sign_hash_ex(in, inlen, rng, key, r, s);
#endif
if (err < 0) {
break;
}
FALL_THROUGH;
case ECC_STATE_SIGN_ENCODE:
key->state = ECC_STATE_SIGN_ENCODE;
#if defined(WOLFSSL_ASYNC_CRYPT) && defined(WC_ASYNC_ENABLE_ECC)
if (key->asyncDev.marker == WOLFSSL_ASYNC_MARKER_ECC) {
#ifdef HAVE_CAVIUM_V
/* Nitrox requires r and s in sep buffer, so split it */
NitroxEccRsSplit(key, &r->raw, &s->raw);
#endif
#ifndef WOLFSSL_ASYNC_CRYPT_TEST
/* only do this if not simulator, since it overwrites result */
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);
/* done with R/S */
mp_clear(r);
mp_clear(s);
#if !defined(WOLFSSL_ASYNC_CRYPT) && defined(WOLFSSL_SMALL_STACK)
XFREE(s, key->heap, DYNAMIC_TYPE_ECC);
XFREE(r, key->heap, DYNAMIC_TYPE_ECC);
#endif
break;
default:
err = BAD_STATE_E;
break;
}
/* if async pending then return and skip done cleanup below */
if (err == WC_PENDING_E) {
key->state++;
return err;
}
/* cleanup */
#ifdef WOLFSSL_ASYNC_CRYPT
wc_ecc_free_async(key);
#endif
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;
#ifndef WOLFSSL_SP_MATH
mp_int* e;
#if (!defined(WOLFSSL_ASYNC_CRYPT) || !defined(HAVE_CAVIUM_V)) && \
!defined(WOLFSSL_SMALL_STACK)
mp_int e_lcl;
#endif
DECLARE_CURVE_SPECS(curve, 1);
#endif /* !WOLFSSL_SP_MATH */
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 && key->type != ECC_PRIVATEKEY_ONLY) {
return ECC_BAD_ARG_E;
}
/* is the IDX valid ? */
if (wc_ecc_is_valid_idx(key->idx) != 1) {
return ECC_BAD_ARG_E;
}
#ifdef WOLFSSL_SP_MATH
if (key->idx != ECC_CUSTOM_IDX && ecc_sets[key->idx].id == ECC_SECP256R1)
return sp_ecc_sign_256(in, inlen, rng, &key->k, r, s, key->heap);
else
return WC_KEY_SIZE_E;
#else
#ifdef WOLFSSL_HAVE_SP_ECC
#if defined(WOLFSSL_ASYNC_CRYPT) && defined(WC_ASYNC_ENABLE_ECC) && \
defined(WOLFSSL_ASYNC_CRYPT_TEST)
if (key->asyncDev.marker != WOLFSSL_ASYNC_MARKER_ECC)
#endif
{
#ifndef WOLFSSL_SP_NO_256
if (key->idx != ECC_CUSTOM_IDX && ecc_sets[key->idx].id == ECC_SECP256R1)
return sp_ecc_sign_256(in, inlen, rng, &key->k, r, s, key->heap);
#endif
}
#endif /* WOLFSSL_HAVE_SP_ECC */
#if defined(WOLFSSL_ASYNC_CRYPT) && defined(WC_ASYNC_ENABLE_ECC) && \
defined(WOLFSSL_ASYNC_CRYPT_TEST)
if (key->asyncDev.marker == WOLFSSL_ASYNC_MARKER_ECC) {
if (wc_AsyncTestInit(&key->asyncDev, ASYNC_TEST_ECC_SIGN)) {
WC_ASYNC_TEST* testDev = &key->asyncDev.test;
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
ALLOC_CURVE_SPECS(1);
#if defined(WOLFSSL_ASYNC_CRYPT) && defined(HAVE_CAVIUM_V)
err = wc_ecc_alloc_mpint(key, &key->e);
if (err != 0) {
FREE_CURVE_SPECS();
return err;
}
e = key->e;
#elif !defined(WOLFSSL_SMALL_STACK)
e = &e_lcl;
#else
e = (mp_int*)XMALLOC(sizeof(mp_int), key->heap, DYNAMIC_TYPE_ECC);
if (e == NULL) {
FREE_CURVE_SPECS();
return MEMORY_E;
}
#endif
/* get the hash and load it as a bignum into 'e' */
/* init the bignums */
if ((err = mp_init(e)) != MP_OKAY) {
#ifdef WOLFSSL_SMALL_STACK
XFREE(e, key->heap, DYNAMIC_TYPE_ECC);
#endif
FREE_CURVE_SPECS();
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;
#ifdef WOLFSSL_SMALL_STACK
ecc_key* pubkey = NULL;
#else
ecc_key pubkey[1];
#endif
#if defined(WOLFSSL_ASYNC_CRYPT) && defined(WC_ASYNC_ENABLE_ECC)
if (key->asyncDev.marker == WOLFSSL_ASYNC_MARKER_ECC) {
#if defined(HAVE_CAVIUM_V) || defined(HAVE_INTEL_QA)
#ifdef HAVE_CAVIUM_V
if (NitroxEccIsCurveSupported(key))
#endif
{
word32 keySz = key->dp->size;
mp_int* k;
#ifdef HAVE_CAVIUM_V
err = wc_ecc_alloc_mpint(key, &key->signK);
if (err != 0)
return err;
k = key->signK;
#else
mp_int k_lcl;
k = &k_lcl;
#endif
err = mp_init(k);
/* make sure r and s are allocated */
#ifdef HAVE_CAVIUM_V
/* Nitrox V needs single buffer for R and S */
if (err == MP_OKAY)
err = wc_bigint_alloc(&key->r->raw, NitroxEccGetSize(key)*2);
/* Nitrox V only needs Prime and Order */
if (err == MP_OKAY)
err = wc_ecc_curve_load(key->dp, &curve,
(ECC_CURVE_FIELD_PRIME | ECC_CURVE_FIELD_ORDER));
#else
if (err == MP_OKAY)
err = wc_bigint_alloc(&key->r->raw, key->dp->size);
if (err == MP_OKAY)
err = wc_ecc_curve_load(key->dp, &curve, ECC_CURVE_FIELD_ALL);
#endif
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_sz(e, &e->raw, keySz);
if (err == MP_OKAY)
err = wc_mp_to_bigint_sz(&key->k, &key->k.raw, keySz);
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_sz(k, &k->raw, keySz);
#ifdef HAVE_CAVIUM_V
if (err == MP_OKAY)
err = NitroxEcdsaSign(key, &e->raw, &key->k.raw, &k->raw,
&r->raw, &s->raw, &curve->prime->raw, &curve->order->raw);
#else
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);
#endif
#ifndef HAVE_CAVIUM_V
mp_clear(e);
mp_clear(k);
#endif
wc_ecc_curve_free(curve);
FREE_CURVE_SPECS();
return err;
}
#endif /* HAVE_CAVIUM_V || HAVE_INTEL_QA */
}
#endif /* WOLFSSL_ASYNC_CRYPT */
#ifdef WOLFSSL_SMALL_STACK
pubkey = (ecc_key*)XMALLOC(sizeof(ecc_key), key->heap, DYNAMIC_TYPE_ECC);
if (pubkey == NULL)
err = MEMORY_E;
#endif
/* don't use async for key, since we don't support async return here */
if (err == MP_OKAY && (err = wc_ecc_init_ex(pubkey, key->heap,
INVALID_DEVID)) == MP_OKAY) {
#ifdef WOLFSSL_SMALL_STACK
mp_int* b = NULL;
#else
mp_int b[1];
#endif
#ifdef WOLFSSL_SMALL_STACK
if (err == MP_OKAY) {
b = (mp_int*)XMALLOC(sizeof(mp_int), key->heap,
DYNAMIC_TYPE_ECC);
if (b == NULL)
err = MEMORY_E;
}
#endif
if (err == MP_OKAY) {
err = mp_init(b);
}
#ifdef WOLFSSL_CUSTOM_CURVES
/* if custom curve, apply params to pubkey */
if (err == MP_OKAY && key->idx == ECC_CUSTOM_IDX) {
err = wc_ecc_set_custom_curve(pubkey, key->dp);
}
#endif
if (err == MP_OKAY) {
/* Generate blinding value - non-zero value. */
do {
if (++loop_check > 64) {
err = RNG_FAILURE_E;
break;
}
err = wc_ecc_gen_k(rng, key->dp->size, b, curve->order);
}
while (err == MP_ZERO_E);
loop_check = 0;
}
for (; err == MP_OKAY;) {
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
= b.(e/k.b + x.r/k.b) */
/* k = k.b */
err = mp_mulmod(&pubkey->k, b, curve->order, &pubkey->k);
if (err != MP_OKAY) break;
/* k = 1/k.b */
err = mp_invmod(&pubkey->k, curve->order, &pubkey->k);
if (err != MP_OKAY) break;
/* s = x.r */
err = mp_mulmod(&key->k, r, curve->order, s);
if (err != MP_OKAY) break;
/* s = x.r/k.b */
err = mp_mulmod(&pubkey->k, s, curve->order, s);
if (err != MP_OKAY) break;
/* e = e/k.b */
err = mp_mulmod(&pubkey->k, e, curve->order, e);
if (err != MP_OKAY) break;
/* s = e/k.b + x.r/k.b
= (e + x.r)/k.b */
err = mp_add(e, s, s);
if (err != MP_OKAY) break;
/* s = b.(e + x.r)/k.b
= (e + x.r)/k */
err = mp_mulmod(s, b, curve->order, s);
if (err != MP_OKAY) break;
/* s = (e + xr)/k */
err = mp_mod(s, curve->order, s);
if (err != MP_OKAY) break;
if (mp_iszero(s) == MP_NO)
break;
}
}
mp_clear(b);
mp_free(b);
#ifdef WOLFSSL_SMALL_STACK
XFREE(b, key->heap, DYNAMIC_TYPE_ECC);
#endif
wc_ecc_free(pubkey);
#ifdef WOLFSSL_SMALL_STACK
XFREE(pubkey, key->heap, DYNAMIC_TYPE_ECC);
#endif
}
}
mp_clear(e);
wc_ecc_curve_free(curve);
#ifdef WOLFSSL_SMALL_STACK
XFREE(e, key->heap, DYNAMIC_TYPE_ECC);
#endif
FREE_CURVE_SPECS();
#endif /* WOLFSSL_SP_MATH */
return err;
}
#endif /* WOLFSSL_ATECC508A */
#endif /* HAVE_ECC_SIGN */
#ifdef WOLFSSL_CUSTOM_CURVES
void wc_ecc_free_curve(const ecc_set_type* curve, void* heap)
{
if (curve->prime != NULL)
XFREE((void*)curve->prime, heap, DYNAMIC_TYPE_ECC_BUFFER);
if (curve->Af != NULL)
XFREE((void*)curve->Af, heap, DYNAMIC_TYPE_ECC_BUFFER);
if (curve->Bf != NULL)
XFREE((void*)curve->Bf, heap, DYNAMIC_TYPE_ECC_BUFFER);
if (curve->order != NULL)
XFREE((void*)curve->order, heap, DYNAMIC_TYPE_ECC_BUFFER);
if (curve->Gx != NULL)
XFREE((void*)curve->Gx, heap, DYNAMIC_TYPE_ECC_BUFFER);
if (curve->Gy != NULL)
XFREE((void*)curve->Gy, heap, DYNAMIC_TYPE_ECC_BUFFER);
XFREE((void*)curve, heap, DYNAMIC_TYPE_ECC_BUFFER);
(void)heap;
}
#endif /* WOLFSSL_CUSTOM_CURVES */
/**
Free an ECC key from memory
key The key you wish to free
*/
int wc_ecc_free(ecc_key* key)
{
if (key == NULL) {
return 0;
}
#ifdef WOLFSSL_ASYNC_CRYPT
#ifdef WC_ASYNC_ENABLE_ECC
wolfAsync_DevCtxFree(&key->asyncDev, WOLFSSL_ASYNC_MARKER_ECC);
#endif
wc_ecc_free_async(key);
#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 WOLFSSL_CUSTOM_CURVES
if (key->deallocSet && key->dp != NULL)
wc_ecc_free_curve(key->dp, key->heap);
#endif
return 0;
}
#if !defined(WOLFSSL_SP_MATH) && !defined(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
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
{
#ifdef WOLFSSL_SMALL_STACK
ecc_point** precomp = NULL;
#ifdef WOLFSSL_SMALL_STACK_CACHE
ecc_key key;
#endif
#else
ecc_point* precomp[SHAMIR_PRECOMP_SZ];
#endif
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 = 0;
/* 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_ECC_BUFFER);
if (tA == NULL) {
return GEN_MEM_ERR;
}
tB = (unsigned char*)XMALLOC(ECC_BUFSIZE, heap, DYNAMIC_TYPE_ECC_BUFFER);
if (tB == NULL) {
XFREE(tA, heap, DYNAMIC_TYPE_ECC_BUFFER);
return GEN_MEM_ERR;
}
#ifdef WOLFSSL_SMALL_STACK
precomp = (ecc_point**)XMALLOC(sizeof(ecc_point*) * SHAMIR_PRECOMP_SZ, heap,
DYNAMIC_TYPE_ECC_BUFFER);
if (precomp == NULL) {
XFREE(tB, heap, DYNAMIC_TYPE_ECC_BUFFER);
XFREE(tA, heap, DYNAMIC_TYPE_ECC_BUFFER);
return GEN_MEM_ERR;
}
#endif
#ifdef WOLFSSL_SMALL_STACK_CACHE
key.t1 = (mp_int*)XMALLOC(sizeof(mp_int), heap, DYNAMIC_TYPE_ECC);
key.t2 = (mp_int*)XMALLOC(sizeof(mp_int), heap, DYNAMIC_TYPE_ECC);
#ifdef ALT_ECC_SIZE
key.x = (mp_int*)XMALLOC(sizeof(mp_int), heap, DYNAMIC_TYPE_ECC);
key.y = (mp_int*)XMALLOC(sizeof(mp_int), heap, DYNAMIC_TYPE_ECC);
key.z = (mp_int*)XMALLOC(sizeof(mp_int), heap, DYNAMIC_TYPE_ECC);
#endif
if (key.t1 == NULL || key.t2 == NULL
#ifdef ALT_ECC_SIZE
|| key.x == NULL || key.y == NULL || key.z == NULL
#endif
) {
#ifdef ALT_ECC_SIZE
XFREE(key.z, heap, DYNAMIC_TYPE_ECC);
XFREE(key.y, heap, DYNAMIC_TYPE_ECC);
XFREE(key.x, heap, DYNAMIC_TYPE_ECC);
#endif
XFREE(key.t2, heap, DYNAMIC_TYPE_ECC);
XFREE(key.t1, heap, DYNAMIC_TYPE_ECC);
XFREE(precomp, heap, DYNAMIC_TYPE_ECC_BUFFER);
XFREE(tB, heap, DYNAMIC_TYPE_ECC_BUFFER);
XFREE(tA, heap, DYNAMIC_TYPE_ECC_BUFFER);
return MEMORY_E;
}
C->key = &key;
#endif /* WOLFSSL_SMALL_STACK_CACHE */
/* init variables */
XMEMSET(tA, 0, ECC_BUFSIZE);
XMEMSET(tB, 0, ECC_BUFSIZE);
#ifndef WOLFSSL_SMALL_STACK
XMEMSET(precomp, 0, sizeof(precomp));
#else
XMEMSET(precomp, 0, sizeof(ecc_point*) * SHAMIR_PRECOMP_SZ);
#endif
/* 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 < SHAMIR_PRECOMP_SZ; x++) {
precomp[x] = wc_ecc_new_point_h(heap);
if (precomp[x] == NULL) {
err = GEN_MEM_ERR;
break;
}
#ifdef WOLFSSL_SMALL_STACK_CACHE
precomp[x]->key = &key;
#endif
}
}
}
if (err == MP_OKAY)
/* init montgomery reduction */
err = mp_montgomery_setup(modulus, &mp);
if (err == MP_OKAY) {
#ifdef WOLFSSL_SMALL_STACK
mp_int* mu = NULL;
#else
mp_int mu[1];
#endif
#ifdef WOLFSSL_SMALL_STACK
mu = (mp_int*)XMALLOC(sizeof(mp_int), heap, DYNAMIC_TYPE_ECC);
if (mu == NULL)
err = MEMORY_E;
#endif
if (err == MP_OKAY) {
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);
#ifdef WOLFSSL_SMALL_STACK
XFREE(mu, heap, DYNAMIC_TYPE_ECC);
#endif
}
}
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 < SHAMIR_PRECOMP_SZ; x++) {
wc_ecc_del_point_h(precomp[x], heap);
}
ForceZero(tA, ECC_BUFSIZE);
ForceZero(tB, ECC_BUFSIZE);
#ifdef WOLFSSL_SMALL_STACK_CACHE
#ifdef ALT_ECC_SIZE
XFREE(key.z, heap, DYNAMIC_TYPE_ECC);
XFREE(key.y, heap, DYNAMIC_TYPE_ECC);
XFREE(key.x, heap, DYNAMIC_TYPE_ECC);
#endif
XFREE(key.t2, heap, DYNAMIC_TYPE_ECC);
XFREE(key.t1, heap, DYNAMIC_TYPE_ECC);
C->key = NULL;
#endif
#ifdef WOLFSSL_SMALL_STACK
XFREE(precomp, heap, DYNAMIC_TYPE_ECC_BUFFER);
#endif
XFREE(tB, heap, DYNAMIC_TYPE_ECC_BUFFER);
XFREE(tA, heap, DYNAMIC_TYPE_ECC_BUFFER);
return err;
}
#endif /* ECC_SHAMIR */
#endif /* !WOLFSSL_SP_MATH && !WOLFSSL_ATECC508A */
#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
#ifndef WOLFSSL_SMALL_STACK
mp_int r_lcl[1], s_lcl[1];
#endif
#endif
if (sig == NULL || hash == NULL || res == NULL || key == NULL) {
return ECC_BAD_ARG_E;
}
#ifdef WOLF_CRYPTO_DEV
if (key->devId != INVALID_DEVID) {
err = wc_CryptoDev_EccVerify(sig, siglen, hash, hashlen, res, key);
if (err != NOT_COMPILED_IN)
return err;
}
#endif
#ifdef WOLFSSL_ASYNC_CRYPT
err = wc_ecc_alloc_async(key);
if (err != 0)
return err;
r = key->r;
s = key->s;
#else
#ifndef WOLFSSL_SMALL_STACK
r = r_lcl;
s = s_lcl;
#else
r = (mp_int*)XMALLOC(sizeof(mp_int), key->heap, DYNAMIC_TYPE_ECC);
if (r == NULL)
return MEMORY_E;
s = (mp_int*)XMALLOC(sizeof(mp_int), key->heap, DYNAMIC_TYPE_ECC);
if (s == NULL) {
XFREE(r, key->heap, DYNAMIC_TYPE_ECC);
return MEMORY_E;
}
#endif
#endif
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. */
/* 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);
#ifndef WOLFSSL_ASYNC_CRYPT
/* done with R/S */
mp_clear(r);
mp_clear(s);
#ifdef WOLFSSL_SMALL_STACK
XFREE(s, key->heap, DYNAMIC_TYPE_ECC);
XFREE(r, key->heap, DYNAMIC_TYPE_ECC);
#endif
#endif
if (err < 0) {
break;
}
FALL_THROUGH;
case ECC_STATE_VERIFY_RES:
key->state = ECC_STATE_VERIFY_RES;
err = 0;
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 */
#ifdef WOLFSSL_ASYNC_CRYPT
wc_ecc_free_async(key);
#endif
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;
#ifdef WOLFSSL_ATECC508A
byte sigRS[ATECC_KEY_SIZE*2];
#elif !defined(WOLFSSL_SP_MATH)
int did_init = 0;
ecc_point *mG = NULL, *mQ = NULL;
#ifdef WOLFSSL_SMALL_STACK
mp_int* v = NULL;
mp_int* w = NULL;
mp_int* u1 = NULL;
mp_int* u2 = NULL;
#if !defined(WOLFSSL_ASYNC_CRYPT) || !defined(HAVE_CAVIUM_V)
mp_int* e_lcl = NULL;
#endif
#else /* WOLFSSL_SMALL_STACK */
mp_int v[1];
mp_int w[1];
mp_int u1[1];
mp_int u2[1];
#if !defined(WOLFSSL_ASYNC_CRYPT) || !defined(HAVE_CAVIUM_V)
mp_int e_lcl[1];
#endif
#endif /* WOLFSSL_SMALL_STACK */
mp_int* e;
DECLARE_CURVE_SPECS(curve, ECC_CURVE_FIELD_COUNT);
#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) {
if (wc_AsyncTestInit(&key->asyncDev, ASYNC_TEST_ECC_VERIFY)) {
WC_ASYNC_TEST* testDev = &key->asyncDev.test;
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_raw, (bool*)res);
if (err != ATCA_SUCCESS) {
return BAD_COND_E;
}
(void)hashlen;
#else
/* checking if private key with no public part */
if (key->type == ECC_PRIVATEKEY_ONLY) {
WOLFSSL_MSG("Verify called with private key, generating public part");
err = wc_ecc_make_pub_ex(key, NULL, NULL);
if (err != MP_OKAY) {
WOLFSSL_MSG("Unable to extract public key");
return err;
}
}
#ifdef WOLFSSL_SP_MATH
if (key->idx != ECC_CUSTOM_IDX && ecc_sets[key->idx].id == ECC_SECP256R1) {
return sp_ecc_verify_256(hash, hashlen, key->pubkey.x, key->pubkey.y,
key->pubkey.z, r, s, res, key->heap);
}
else
return WC_KEY_SIZE_E;
#else
#ifdef WOLFSSL_HAVE_SP_ECC
#ifndef WOLFSSL_SP_NO_256
#if defined(WOLFSSL_ASYNC_CRYPT) && defined(WC_ASYNC_ENABLE_ECC) && \
defined(WOLFSSL_ASYNC_CRYPT_TEST)
if (key->asyncDev.marker != WOLFSSL_ASYNC_MARKER_ECC)
#endif
{
if (key->idx != ECC_CUSTOM_IDX && ecc_sets[key->idx].id == ECC_SECP256R1)
return sp_ecc_verify_256(hash, hashlen, key->pubkey.x, key->pubkey.y,
key->pubkey.z,r, s, res, key->heap);
}
#endif /* WOLFSSL_SP_NO_256 */
#endif /* WOLFSSL_HAVE_SP_ECC */
ALLOC_CURVE_SPECS(ECC_CURVE_FIELD_COUNT);
#if defined(WOLFSSL_ASYNC_CRYPT) && defined(HAVE_CAVIUM_V)
err = wc_ecc_alloc_mpint(key, &key->e);
if (err != 0) {
FREE_CURVE_SPECS();
return err;
}
e = key->e;
#else
#ifdef WOLFSSL_SMALL_STACK
e_lcl = (mp_int*)XMALLOC(sizeof(mp_int), key->heap, DYNAMIC_TYPE_ECC);
if (e_lcl == NULL) {
FREE_CURVE_SPECS();
return MEMORY_E;
}
#endif
e = e_lcl;
#endif
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) {
#if defined(HAVE_CAVIUM_V) || defined(HAVE_INTEL_QA)
#ifdef HAVE_CAVIUM_V
if (NitroxEccIsCurveSupported(key))
#endif
{
word32 keySz = key->dp->size;
err = wc_mp_to_bigint_sz(e, &e->raw, keySz);
if (err == MP_OKAY)
err = wc_mp_to_bigint_sz(key->pubkey.x, &key->pubkey.x->raw, keySz);
if (err == MP_OKAY)
err = wc_mp_to_bigint_sz(key->pubkey.y, &key->pubkey.y->raw, keySz);
if (err == MP_OKAY)
#ifdef HAVE_CAVIUM_V
err = NitroxEcdsaVerify(key, &e->raw, &key->pubkey.x->raw,
&key->pubkey.y->raw, &r->raw, &s->raw,
&curve->prime->raw, &curve->order->raw, res);
#else
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);
#endif
#ifndef HAVE_CAVIUM_V
mp_clear(e);
#endif
wc_ecc_curve_free(curve);
FREE_CURVE_SPECS();
return err;
}
#endif /* HAVE_CAVIUM_V || HAVE_INTEL_QA */
}
#endif /* WOLFSSL_ASYNC_CRYPT */
#ifdef WOLFSSL_SMALL_STACK
if (err == MP_OKAY) {
v = (mp_int*)XMALLOC(sizeof(mp_int), key->heap, DYNAMIC_TYPE_ECC);
if (v == NULL)
err = MEMORY_E;
}
if (err == MP_OKAY) {
w = (mp_int*)XMALLOC(sizeof(mp_int), key->heap, DYNAMIC_TYPE_ECC);
if (w == NULL)
err = MEMORY_E;
}
if (err == MP_OKAY) {
u1 = (mp_int*)XMALLOC(sizeof(mp_int), key->heap, DYNAMIC_TYPE_ECC);
if (u1 == NULL)
err = MEMORY_E;
}
if (err == MP_OKAY) {
u2 = (mp_int*)XMALLOC(sizeof(mp_int), key->heap, DYNAMIC_TYPE_ECC);
if (u2 == NULL)
err = MEMORY_E;
}
#endif
/* 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
#ifndef ECC_SHAMIR
{
mp_digit mp = 0;
/* 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);
}
#ifdef WOLFSSL_SMALL_STACK
XFREE(u2, key->heap, DYNAMIC_TYPE_ECC);
XFREE(u1, key->heap, DYNAMIC_TYPE_ECC);
XFREE(w, key->heap, DYNAMIC_TYPE_ECC);
XFREE(v, key->heap, DYNAMIC_TYPE_ECC);
#if !defined(WOLFSSL_ASYNC_CRYPT) || !defined(HAVE_CAVIUM_V)
XFREE(e_lcl, key->heap, DYNAMIC_TYPE_ECC);
#endif
#endif
wc_ecc_curve_free(curve);
FREE_CURVE_SPECS();
#endif /* WOLFSSL_SP_MATH */
#endif /* WOLFSSL_ATECC508A */
return err;
}
#endif /* HAVE_ECC_VERIFY */
#ifdef HAVE_ECC_KEY_IMPORT
/* import point from der */
int wc_ecc_import_point_der(byte* in, word32 inLen, const int curve_idx,
ecc_point* point)
{
int err = 0;
#ifndef WOLFSSL_ATECC508A
int compressed = 0;
int keysize;
byte pointType;
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 point type (4, 2, or 3) */
pointType = in[0];
if (pointType != ECC_POINT_UNCOMP && pointType != ECC_POINT_COMP_EVEN &&
pointType != ECC_POINT_COMP_ODD) {
err = ASN_PARSE_E;
}
if (pointType == ECC_POINT_COMP_EVEN || pointType == ECC_POINT_COMP_ODD) {
#ifdef HAVE_COMP_KEY
compressed = 1;
#else
err = NOT_COMPILED_IN;
#endif
}
/* adjust to skip first byte */
inLen -= 1;
in += 1;
/* calculate key size based on inLen / 2 */
keysize = inLen>>1;
#ifdef WOLFSSL_ATECC508A
/* populate key->pubkey_raw */
XMEMCPY(key->pubkey_raw, (byte*)in, sizeof(key->pubkey_raw));
#endif
/* read data */
if (err == MP_OKAY)
err = mp_read_unsigned_bin(point->x, (byte*)in, keysize);
#ifdef HAVE_COMP_KEY
if (err == MP_OKAY && compressed == 1) { /* build y */
#ifndef WOLFSSL_SP_MATH
int did_init = 0;
mp_int t1, t2;
DECLARE_CURVE_SPECS(curve, 3);
ALLOC_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 && pointType == ECC_POINT_COMP_ODD) ||
(mp_isodd(&t2) == MP_NO && pointType == ECC_POINT_COMP_EVEN)) {
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);
FREE_CURVE_SPECS();
#else
sp_ecc_uncompress_256(point->x, pointType, point->y);
#endif
}
#endif
if (err == MP_OKAY && compressed == 0)
err = mp_read_unsigned_bin(point->y, (byte*)in + keysize, keysize);
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);
}
#else
err = NOT_COMPILED_IN;
(void)in;
(void)inLen;
(void)curve_idx;
(void)point;
#endif /* !WOLFSSL_ATECC508A */
return err;
}
#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 point type */
out[0] = ECC_POINT_UNCOMP;
#ifdef WOLFSSL_SMALL_STACK
buf = (byte*)XMALLOC(ECC_BUFSIZE, NULL, DYNAMIC_TYPE_ECC_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_ECC_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;
#ifdef WOLFSSL_SMALL_STACK
byte* buf;
#else
byte buf[ECC_BUFSIZE];
#endif
word32 pubxlen, pubylen;
/* 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 (key->type == ECC_PRIVATEKEY_ONLY)
return ECC_PRIVATEONLY_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;
}
/* 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 point type */
out[0] = ECC_POINT_UNCOMP;
#ifdef WOLFSSL_SMALL_STACK
buf = (byte*)XMALLOC(ECC_BUFSIZE, NULL, DYNAMIC_TYPE_ECC_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_ECC_BUFFER);
#endif
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)
{
#ifndef WOLFSSL_SP_MATH
int err;
#ifdef WOLFSSL_SMALL_STACK
mp_int* t1 = NULL;
mp_int* t2 = NULL;
#else
mp_int t1[1], t2[1];
#endif
#ifdef WOLFSSL_SMALL_STACK
t1 = (mp_int*)XMALLOC(sizeof(mp_int), NULL, DYNAMIC_TYPE_ECC);
if (t1 == NULL)
return MEMORY_E;
t2 = (mp_int*)XMALLOC(sizeof(mp_int), NULL, DYNAMIC_TYPE_ECC);
if (t2 == NULL) {
XFREE(t1, NULL, DYNAMIC_TYPE_ECC);
return MEMORY_E;
}
#endif
if ((err = mp_init_multi(t1, t2, NULL, NULL, NULL, NULL)) != MP_OKAY) {
#ifdef WOLFSSL_SMALL_STACK
XFREE(t2, NULL, DYNAMIC_TYPE_ECC);
XFREE(t1, NULL, DYNAMIC_TYPE_ECC);
#endif
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);
#ifdef WOLFSSL_SMALL_STACK
XFREE(t2, NULL, DYNAMIC_TYPE_ECC);
XFREE(t1, NULL, DYNAMIC_TYPE_ECC);
#endif
return err;
#else
(void)a;
(void)b;
(void)prime;
return sp_ecc_is_point_256(ecp->x, ecp->y);
#endif
}
#ifndef WOLFSSL_SP_MATH
/* 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(curve, 2);
if (key == NULL)
return BAD_FUNC_ARG;
ALLOC_CURVE_SPECS(2);
res = wc_ecc_new_point_h(key->heap);
if (res == NULL)
err = MEMORY_E;
#ifdef WOLFSSL_HAVE_SP_ECC
#ifndef WOLFSSL_SP_NO_256
if (key->idx != ECC_CUSTOM_IDX && ecc_sets[key->idx].id == ECC_SECP256R1) {
if (err == MP_OKAY)
err = sp_ecc_mulmod_base_256(&key->k, res, 1, key->heap);
}
else
#endif
#endif
{
base = wc_ecc_new_point_h(key->heap);
if (base == NULL)
err = MEMORY_E;
if (err == MP_OKAY) {
/* 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)
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);
FREE_CURVE_SPECS();
return err;
}
#endif
#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(curve, 2);
#endif
if (key == NULL)
return BAD_FUNC_ARG;
#ifdef WOLFSSL_ATECC508A
/* TODO: Implement equiv call to ATECC508A */
err = BAD_COND_E;
#else
ALLOC_CURVE_SPECS(2);
/* 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);
FREE_CURVE_SPECS();
#endif /* WOLFSSL_ATECC508A */
return err;
}
#endif /* WOLFSSL_VALIDATE_ECC_IMPORT */
#if defined(WOLFSSL_VALIDATE_ECC_KEYGEN) || !defined(WOLFSSL_SP_MATH)
/* validate order * pubkey = point at infinity, 0 on success */
static int ecc_check_pubkey_order(ecc_key* key, ecc_point* pubkey, 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 {
#ifdef WOLFSSL_HAVE_SP_ECC
#ifndef WOLFSSL_SP_NO_256
if (key->idx != ECC_CUSTOM_IDX &&
ecc_sets[key->idx].id == ECC_SECP256R1) {
err = sp_ecc_mulmod_256(order, pubkey, inf, 1, key->heap);
}
else
#endif
#endif
#ifndef WOLFSSL_SP_MATH
err = wc_ecc_mulmod_ex(order, pubkey, inf, a, prime, 1, key->heap);
if (err == MP_OKAY && !wc_ecc_point_is_at_infinity(inf))
err = ECC_INF_E;
#else
(void)a;
(void)prime;
err = WC_KEY_SIZE_E;
#endif
}
wc_ecc_del_point_h(inf, key->heap);
return err;
}
#endif
#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_SP_MATH
#ifndef WOLFSSL_ATECC508A
mp_int* b = NULL;
#ifdef USE_ECC_B_PARAM
DECLARE_CURVE_SPECS(curve, 4);
#else
#ifndef WOLFSSL_SMALL_STACK
mp_int b_lcl;
#endif
DECLARE_CURVE_SPECS(curve, 3);
#endif /* USE_ECC_B_PARAM */
#endif /* WOLFSSL_ATECC508A */
if (key == NULL)
return BAD_FUNC_ARG;
#ifdef WOLFSSL_ATECC508A
if (key->slot == ATECC_INVALID_SLOT)
return ECC_BAD_ARG_E;
err = 0; /* consider key check success on ECC508A */
#else
#ifdef USE_ECC_B_PARAM
ALLOC_CURVE_SPECS(4);
#else
ALLOC_CURVE_SPECS(3);
#ifndef WOLFSSL_SMALL_STACK
b = &b_lcl;
#else
b = (mp_int*)XMALLOC(sizeof(mp_int), key->heap, DYNAMIC_TYPE_ECC);
if (b == NULL) {
FREE_CURVE_SPECS();
return MEMORY_E;
}
#endif
XMEMSET(b, 0, sizeof(mp_int));
#endif
/* SP 800-56Ar3, section 5.6.2.3.3, process step 1 */
/* pubkey point cannot be at infinity */
if (wc_ecc_point_is_at_infinity(&key->pubkey)) {
#ifdef WOLFSSL_SMALL_STACK
XFREE(b, key->heap, DYNAMIC_TYPE_ECC);
#endif
FREE_CURVE_SPECS();
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, MP_RADIX_HEX);
#else
b = curve->Bf;
#endif
/* SP 800-56Ar3, section 5.6.2.3.3, process step 2 */
/* 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;
/* SP 800-56Ar3, section 5.6.2.3.3, process steps 3 */
/* make sure point is actually on curve */
if (err == MP_OKAY)
err = wc_ecc_is_point(&key->pubkey, curve->Af, b, curve->prime);
/* SP 800-56Ar3, section 5.6.2.3.3, process steps 4 */
/* pubkey * order must be at infinity */
if (err == MP_OKAY)
err = ecc_check_pubkey_order(key, &key->pubkey, curve->Af, curve->prime,
curve->order);
/* SP 800-56Ar3, section 5.6.2.1.4, method (b) for ECC */
/* 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);
#ifdef WOLFSSL_SMALL_STACK
XFREE(b, key->heap, DYNAMIC_TYPE_ECC);
#endif
#endif
FREE_CURVE_SPECS();
#endif /* WOLFSSL_ATECC508A */
#else
if (key == NULL)
return BAD_FUNC_ARG;
/* pubkey point cannot be at infinity */
if (key->idx != ECC_CUSTOM_IDX && ecc_sets[key->idx].id == ECC_SECP256R1) {
err = sp_ecc_check_key_256(key->pubkey.x, key->pubkey.y, &key->k,
key->heap);
}
else
err = WC_KEY_SIZE_E;
#endif
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;
int compressed = 0;
int keysize = 0;
byte pointType;
if (in == NULL || key == NULL)
return BAD_FUNC_ARG;
/* must be odd */
if ((inLen & 1) == 0) {
return ECC_BAD_ARG_E;
}
/* make sure required variables are reset */
wc_ecc_reset(key);
/* 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 point type (4, 2, or 3) */
pointType = in[0];
if (pointType != ECC_POINT_UNCOMP && pointType != ECC_POINT_COMP_EVEN &&
pointType != ECC_POINT_COMP_ODD) {
err = ASN_PARSE_E;
}
if (pointType == ECC_POINT_COMP_EVEN || pointType == ECC_POINT_COMP_ODD) {
#ifdef HAVE_COMP_KEY
compressed = 1;
#else
err = NOT_COMPILED_IN;
#endif
}
/* adjust to skip first byte */
inLen -= 1;
in += 1;
if (err == MP_OKAY) {
#ifdef HAVE_COMP_KEY
/* adjust inLen if compressed */
if (compressed)
inLen = inLen*2 + 1; /* used uncompressed len */
#endif
/* determine key size */
keysize = (inLen>>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, keysize);
#ifdef HAVE_COMP_KEY
if (err == MP_OKAY && compressed == 1) { /* build y */
#ifndef WOLFSSL_SP_MATH
mp_int t1, t2;
int did_init = 0;
DECLARE_CURVE_SPECS(curve, 3);
ALLOC_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 && pointType == ECC_POINT_COMP_ODD) ||
(mp_isodd(&t2) == MP_NO && pointType == ECC_POINT_COMP_EVEN)) {
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);
FREE_CURVE_SPECS();
#else
sp_ecc_uncompress_256(key->pubkey.x, pointType, key->pubkey.y);
#endif
}
#endif /* HAVE_COMP_KEY */
if (err == MP_OKAY && compressed == 0)
err = mp_read_unsigned_bin(key->pubkey.y, (byte*)in + keysize, keysize);
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);
}
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 (key->type == ECC_PRIVATEKEY_ONLY) {
return ECC_PRIVATEONLY_E;
}
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);
#ifdef WOLFSSL_ATECC508A
/* TODO: Implement equiv call to ATECC508A */
return BAD_COND_E;
#else
/* private key, d */
err = mp_to_unsigned_bin(&key->k, d +
(numLen - mp_unsigned_bin_size(&key->k)));
if (err != MP_OKAY)
return err;
#endif /* WOLFSSL_ATECC508A */
}
/* 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;
word32 idx = 0;
if (key == NULL || priv == NULL)
return BAD_FUNC_ARG;
/* public optional, NULL if only importing private */
if (pub != NULL) {
ret = wc_ecc_import_x963_ex(pub, pubSz, key, curve_id);
if (ret < 0)
ret = wc_EccPublicKeyDecode(pub, &idx, key, pubSz);
key->type = ECC_PRIVATEKEY;
}
else {
/* make sure required variables are reset */
wc_ecc_reset(key);
/* set key size */
ret = wc_ecc_set_curve(key, privSz, curve_id);
key->type = ECC_PRIVATEKEY_ONLY;
}
if (ret != 0)
return ret;
#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 ((pub != NULL) && (ret == MP_OKAY))
/* public key needed to perform key validation */
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;
#ifdef WOLFSSL_SMALL_STACK
mp_int* rtmp = NULL;
mp_int* stmp = NULL;
#else
mp_int rtmp[1];
mp_int stmp[1];
#endif
if (r == NULL || s == NULL || out == NULL || outlen == NULL)
return ECC_BAD_ARG_E;
#ifdef WOLFSSL_SMALL_STACK
rtmp = (mp_int*)XMALLOC(sizeof(mp_int), NULL, DYNAMIC_TYPE_ECC);
if (rtmp == NULL)
return MEMORY_E;
stmp = (mp_int*)XMALLOC(sizeof(mp_int), NULL, DYNAMIC_TYPE_ECC);
if (stmp == NULL) {
XFREE(rtmp, NULL, DYNAMIC_TYPE_ECC);
return MEMORY_E;
}
#endif
err = mp_init_multi(rtmp, stmp, NULL, NULL, NULL, NULL);
if (err != MP_OKAY) {
#ifdef WOLFSSL_SMALL_STACK
XFREE(stmp, NULL, DYNAMIC_TYPE_ECC);
XFREE(rtmp, NULL, DYNAMIC_TYPE_ECC);
#endif
return err;
}
err = mp_read_radix(rtmp, r, MP_RADIX_HEX);
if (err == MP_OKAY)
err = mp_read_radix(stmp, s, MP_RADIX_HEX);
/* 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);
#ifdef WOLFSSL_SMALL_STACK
XFREE(stmp, NULL, DYNAMIC_TYPE_ECC);
XFREE(rtmp, NULL, DYNAMIC_TYPE_ECC);
#endif
return err;
}
/**
Convert ECC R,S raw unsigned bin to signature
r R component of signature
rSz R size
s S component of signature
sSz S size
out DER-encoded ECDSA signature
outlen [in/out] output buffer size, output signature size
return MP_OKAY on success
*/
int wc_ecc_rs_raw_to_sig(const byte* r, word32 rSz, const byte* s, word32 sSz,
byte* out, word32* outlen)
{
int err;
#ifdef WOLFSSL_SMALL_STACK
mp_int* rtmp = NULL;
mp_int* stmp = NULL;
#else
mp_int rtmp[1];
mp_int stmp[1];
#endif
if (r == NULL || s == NULL || out == NULL || outlen == NULL)
return ECC_BAD_ARG_E;
#ifdef WOLFSSL_SMALL_STACK
rtmp = (mp_int*)XMALLOC(sizeof(mp_int), NULL, DYNAMIC_TYPE_ECC);
if (rtmp == NULL)
return MEMORY_E;
stmp = (mp_int*)XMALLOC(sizeof(mp_int), NULL, DYNAMIC_TYPE_ECC);
if (stmp == NULL) {
XFREE(rtmp, NULL, DYNAMIC_TYPE_ECC);
return MEMORY_E;
}
#endif
err = mp_init_multi(rtmp, stmp, NULL, NULL, NULL, NULL);
if (err != MP_OKAY) {
#ifdef WOLFSSL_SMALL_STACK
XFREE(stmp, NULL, DYNAMIC_TYPE_ECC);
XFREE(rtmp, NULL, DYNAMIC_TYPE_ECC);
#endif
return err;
}
err = mp_read_unsigned_bin(rtmp, r, rSz);
if (err == MP_OKAY)
err = mp_read_unsigned_bin(stmp, s, sSz);
/* 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);
#ifdef WOLFSSL_SMALL_STACK
XFREE(stmp, NULL, DYNAMIC_TYPE_ECC);
XFREE(rtmp, NULL, DYNAMIC_TYPE_ECC);
#endif
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;
#ifdef WOLFSSL_SMALL_STACK
mp_int* rtmp = NULL;
mp_int* stmp = NULL;
#else
mp_int rtmp[1];
mp_int stmp[1];
#endif
if (sig == NULL || r == NULL || rLen == NULL || s == NULL || sLen == NULL)
return ECC_BAD_ARG_E;
#ifdef WOLFSSL_SMALL_STACK
rtmp = (mp_int*)XMALLOC(sizeof(mp_int), NULL, DYNAMIC_TYPE_ECC);
if (rtmp == NULL)
return MEMORY_E;
stmp = (mp_int*)XMALLOC(sizeof(mp_int), NULL, DYNAMIC_TYPE_ECC);
if (stmp == NULL) {
XFREE(rtmp, NULL, DYNAMIC_TYPE_ECC);
return MEMORY_E;
}
#endif
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);
#ifdef WOLFSSL_SMALL_STACK
XFREE(stmp, NULL, DYNAMIC_TYPE_ECC);
XFREE(rtmp, NULL, DYNAMIC_TYPE_ECC);
#endif
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 encType)
{
int err = MP_OKAY;
/* if d is NULL, only import as public key using Qx,Qy */
if (key == NULL || qx == NULL || qy == NULL) {
return BAD_FUNC_ARG;
}
/* make sure required variables are reset */
wc_ecc_reset(key);
/* 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;
(void)d;
(void)encType;
#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) {
if (encType == ECC_TYPE_HEX_STR)
err = mp_read_radix(key->pubkey.x, qx, MP_RADIX_HEX);
else
err = mp_read_unsigned_bin(key->pubkey.x, (const byte*)qx,
key->dp->size);
}
/* read Qy */
if (err == MP_OKAY) {
if (encType == ECC_TYPE_HEX_STR)
err = mp_read_radix(key->pubkey.y, qy, MP_RADIX_HEX);
else
err = mp_read_unsigned_bin(key->pubkey.y, (const byte*)qy,
key->dp->size);
}
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;
if (encType == ECC_TYPE_HEX_STR)
err = mp_read_radix(&key->k, d, MP_RADIX_HEX);
else
err = mp_read_unsigned_bin(&key->k, (const byte*)d,
key->dp->size);
} 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,
ECC_TYPE_HEX_STR);
}
/* Import x, y and optional private (d) as unsigned binary */
int wc_ecc_import_unsigned(ecc_key* key, byte* qx, byte* qy,
byte* d, int curve_id)
{
return wc_ecc_import_raw_private(key, (const char*)qx, (const char*)qy,
(const char*)d, curve_id, ECC_TYPE_UNSIGNED_BIN);
}
/**
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,
ECC_TYPE_HEX_STR);
}
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;
}
int wc_ecc_sig_size_calc(int sz)
{
return (sz * 2) + SIG_HEADER_SZ + ECC_MAX_PAD_SZ;
}
/* 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 wc_ecc_sig_size_calc(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
#ifndef WOLFSSL_SP_MATH
/** 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;
}
#endif
#ifndef WOLFSSL_SP_MATH
/* 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,
MP_RADIX_HEX)) != 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_ECC_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] = (byte)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_ECC_BUFFER);
#endif
#undef KB_SIZE
return err;
}
#endif
#ifdef ECC_SHAMIR
#ifndef WOLFSSL_SP_MATH
/* 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,
MP_RADIX_HEX)) != 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,
MP_RADIX_HEX)) != 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_ECC_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] = (byte)z;
++x; --y;
}
/* store b */
#ifdef WOLFSSL_SMALL_STACK
kb[1] = (unsigned char*)XMALLOC(KB_SIZE, NULL, DYNAMIC_TYPE_ECC_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] = (byte)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_ECC_BUFFER);
XFREE(kb[1], NULL, DYNAMIC_TYPE_ECC_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
#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)
{
#ifndef WOLFSSL_SP_MATH
int idx, err = MP_OKAY;
mp_digit mp;
mp_int mu;
int mpSetup = 0;
if (k == NULL || G == NULL || R == NULL || a == NULL || modulus == NULL) {
return ECC_BAD_ARG_E;
}
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;
#else
if (k == NULL || G == NULL || R == NULL || a == NULL || modulus == NULL) {
return ECC_BAD_ARG_E;
}
return sp_ecc_mulmod_256(k, G, R, map, heap);
#endif
}
#ifndef WOLFSSL_SP_MATH
/* 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;
}
}
}
#endif
/** Free the Fixed Point cache */
void wc_ecc_fp_free(void)
{
#ifndef WOLFSSL_SP_MATH
#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
}
#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 = WC_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 = 0;
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_ECC_BUFFER);
if (sharedSecret == NULL)
return MEMORY_E;
keys = (byte*)XMALLOC(ECC_BUFSIZE, NULL, DYNAMIC_TYPE_ECC_BUFFER);
if (keys == NULL) {
XFREE(sharedSecret, NULL, DYNAMIC_TYPE_ECC_BUFFER);
return MEMORY_E;
}
#endif
do {
#if defined(WOLFSSL_ASYNC_CRYPT)
ret = wc_AsyncWait(ret, &privKey->asyncDev, WC_ASYNC_FLAG_CALL_AGAIN);
if (ret != 0)
break;
#endif
ret = wc_ecc_shared_secret(privKey, pubKey, sharedSecret, &sharedSz);
} while (ret == WC_PENDING_E);
if (ret == 0) {
switch (ctx->kdfAlgo) {
case ecHKDF_SHA256 :
ret = wc_HKDF(WC_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);
#if defined(WOLFSSL_ASYNC_CRYPT)
ret = wc_AsyncWait(ret, &aes.asyncDev, WC_ASYNC_FLAG_NONE);
#endif
}
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, WC_SHA256, macKey, WC_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_ECC_BUFFER);
XFREE(keys, NULL, DYNAMIC_TYPE_ECC_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 = 0;
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_ECC_BUFFER);
if (sharedSecret == NULL)
return MEMORY_E;
keys = (byte*)XMALLOC(ECC_BUFSIZE, NULL, DYNAMIC_TYPE_ECC_BUFFER);
if (keys == NULL) {
XFREE(sharedSecret, NULL, DYNAMIC_TYPE_ECC_BUFFER);
return MEMORY_E;
}
#endif
do {
#if defined(WOLFSSL_ASYNC_CRYPT)
ret = wc_AsyncWait(ret, &privKey->asyncDev, WC_ASYNC_FLAG_CALL_AGAIN);
if (ret != 0)
break;
#endif
ret = wc_ecc_shared_secret(privKey, pubKey, sharedSecret, &sharedSz);
} while (ret == WC_PENDING_E);
if (ret == 0) {
switch (ctx->kdfAlgo) {
case ecHKDF_SHA256 :
ret = wc_HKDF(WC_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[WC_SHA256_DIGEST_SIZE];
Hmac hmac;
ret = wc_HmacInit(&hmac, NULL, INVALID_DEVID);
if (ret == 0) {
ret = wc_HmacSetKey(&hmac, WC_SHA256, macKey, WC_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);
#if defined(WOLFSSL_ASYNC_CRYPT)
ret = wc_AsyncWait(ret, &aes.asyncDev, WC_ASYNC_FLAG_NONE);
#endif
}
break;
#endif
default:
ret = BAD_FUNC_ARG;
break;
}
}
if (ret == 0)
*outSz = msgSz - digestSz;
#ifdef WOLFSSL_SMALL_STACK
XFREE(sharedSecret, NULL, DYNAMIC_TYPE_ECC_BUFFER);
XFREE(keys, NULL, DYNAMIC_TYPE_ECC_BUFFER);
#endif
return ret;
}
#endif /* HAVE_ECC_ENCRYPT */
#ifdef HAVE_COMP_KEY
#ifndef WOLFSSL_ATECC508A
#ifndef WOLFSSL_SP_MATH
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)
{
#ifdef SQRTMOD_USE_MOD_EXP
int res;
mp_int e;
res = mp_init(&e);
if (res == MP_OKAY)
res = mp_add_d(prime, 1, &e);
if (res == MP_OKAY)
res = mp_div_2d(&e, 2, &e, NULL);
if (res == MP_OKAY)
res = mp_exptmod(n, &e, prime, ret);
mp_clear(&e);
return res;
#else
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
}
#endif
#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 ? ECC_POINT_COMP_ODD : ECC_POINT_COMP_EVEN;
/* 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 WC_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_HASHES);
if (hash == NULL)
return MEMORY_E;
#endif
ret = wc_HashInit(hash, type);
if (ret != 0) {
#ifdef WOLFSSL_SMALL_STACK
XFREE(hash, NULL, DYNAMIC_TYPE_HASHES);
#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_HASHES);
#endif
return ret;
}
ret = wc_HashUpdate(hash, type, counter, sizeof(counter));
if (ret != 0) {
#ifdef WOLFSSL_SMALL_STACK
XFREE(hash, NULL, DYNAMIC_TYPE_HASHES);
#endif
return ret;
}
if (sinfo) {
ret = wc_HashUpdate(hash, type, sinfo, sinfoSz);
if (ret != 0) {
#ifdef WOLFSSL_SMALL_STACK
XFREE(hash, NULL, DYNAMIC_TYPE_HASHES);
#endif
return ret;
}
}
ret = wc_HashFinal(hash, type, tmp);
if (ret != 0) {
#ifdef WOLFSSL_SMALL_STACK
XFREE(hash, NULL, DYNAMIC_TYPE_HASHES);
#endif
return ret;
}
copySz = min(remaining, digestSz);
XMEMCPY(outIdx, tmp, copySz);
remaining -= copySz;
outIdx += copySz;
}
#ifdef WOLFSSL_SMALL_STACK
XFREE(hash, NULL, DYNAMIC_TYPE_HASHES);
#endif
return 0;
}
#endif /* HAVE_X963_KDF */
#endif /* HAVE_ECC */