wolf SSL
wolfSSL SSL/TLS library, support up to TLS1.3
Dependents: CyaSSL-Twitter-OAuth4Tw Example-client-tls-cert TwitterReader TweetTest ... more
Diff: wolfcrypt/src/ecc.c
- Revision:
- 0:d92f9d21154c
- Child:
- 3:6f956bdb3073
--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/wolfcrypt/src/ecc.c Fri Jun 26 00:39:20 2015 +0000
@@ -0,0 +1,5187 @@
+/* ecc.c
+ *
+ * Copyright (C) 2006-2015 wolfSSL Inc.
+ *
+ * This file is part of wolfSSL. (formerly known as CyaSSL)
+ *
+ * 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 02110-1301, USA
+ */
+
+
+#ifdef HAVE_CONFIG_H
+ #include <config.h>
+#endif
+
+/* in case user set HAVE_ECC there */
+#include <wolfssl/wolfcrypt/settings.h>
+
+#ifdef HAVE_ECC
+
+#include <wolfssl/wolfcrypt/ecc.h>
+#include <wolfssl/wolfcrypt/asn.h>
+#include <wolfssl/wolfcrypt/error-crypt.h>
+
+#ifdef HAVE_ECC_ENCRYPT
+ #include <wolfssl/wolfcrypt/hmac.h>
+ #include <wolfssl/wolfcrypt/aes.h>
+#endif
+
+#ifdef NO_INLINE
+ #include <wolfssl/wolfcrypt/misc.h>
+#else
+ #include <wolfcrypt/src/misc.c>
+#endif
+
+/* map
+
+ ptmul -> mulmod
+
+*/
+
+
+/* p256 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(NO_ECC256) || defined(HAVE_ALL_CURVES)
+ #define ECC256
+#endif
+#if defined(HAVE_ECC384) || defined(HAVE_ALL_CURVES)
+ #define ECC384
+#endif
+#if defined(HAVE_ECC521) || defined(HAVE_ALL_CURVES)
+ #define ECC521
+#endif
+
+
+
+/* This holds the key settings. ***MUST*** be organized by size from
+ smallest to largest. */
+
+const ecc_set_type ecc_sets[] = {
+#ifdef ECC112
+{
+ 14,
+ "SECP112R1",
+ "DB7C2ABF62E35E668076BEAD208B",
+ "DB7C2ABF62E35E668076BEAD2088",
+ "659EF8BA043916EEDE8911702B22",
+ "DB7C2ABF62E35E7628DFAC6561C5",
+ "09487239995A5EE76B55F9C2F098",
+ "A89CE5AF8724C0A23E0E0FF77500"
+},
+#endif
+#ifdef ECC128
+{
+ 16,
+ "SECP128R1",
+ "FFFFFFFDFFFFFFFFFFFFFFFFFFFFFFFF",
+ "FFFFFFFDFFFFFFFFFFFFFFFFFFFFFFFC",
+ "E87579C11079F43DD824993C2CEE5ED3",
+ "FFFFFFFE0000000075A30D1B9038A115",
+ "161FF7528B899B2D0C28607CA52C5B86",
+ "CF5AC8395BAFEB13C02DA292DDED7A83",
+},
+#endif
+#ifdef ECC160
+{
+ 20,
+ "SECP160R1",
+ "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF7FFFFFFF",
+ "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF7FFFFFFC",
+ "1C97BEFC54BD7A8B65ACF89F81D4D4ADC565FA45",
+ "0100000000000000000001F4C8F927AED3CA752257",
+ "4A96B5688EF573284664698968C38BB913CBFC82",
+ "23A628553168947D59DCC912042351377AC5FB32",
+},
+#endif
+#ifdef ECC192
+{
+ 24,
+ "ECC-192",
+ "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFFFFFFFFFFFF",
+ "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFFFFFFFFFFFC",
+ "64210519E59C80E70FA7E9AB72243049FEB8DEECC146B9B1",
+ "FFFFFFFFFFFFFFFFFFFFFFFF99DEF836146BC9B1B4D22831",
+ "188DA80EB03090F67CBF20EB43A18800F4FF0AFD82FF1012",
+ "7192B95FFC8DA78631011ED6B24CDD573F977A11E794811",
+},
+#endif
+#ifdef ECC224
+{
+ 28,
+ "ECC-224",
+ "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF000000000000000000000001",
+ "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFFFFFFFFFFFFFFFFFFFE",
+ "B4050A850C04B3ABF54132565044B0B7D7BFD8BA270B39432355FFB4",
+ "FFFFFFFFFFFFFFFFFFFFFFFFFFFF16A2E0B8F03E13DD29455C5C2A3D",
+ "B70E0CBD6BB4BF7F321390B94A03C1D356C21122343280D6115C1D21",
+ "BD376388B5F723FB4C22DFE6CD4375A05A07476444D5819985007E34",
+},
+#endif
+#ifdef ECC256
+{
+ 32,
+ "ECC-256",
+ "FFFFFFFF00000001000000000000000000000000FFFFFFFFFFFFFFFFFFFFFFFF",
+ "FFFFFFFF00000001000000000000000000000000FFFFFFFFFFFFFFFFFFFFFFFC",
+ "5AC635D8AA3A93E7B3EBBD55769886BC651D06B0CC53B0F63BCE3C3E27D2604B",
+ "FFFFFFFF00000000FFFFFFFFFFFFFFFFBCE6FAADA7179E84F3B9CAC2FC632551",
+ "6B17D1F2E12C4247F8BCE6E563A440F277037D812DEB33A0F4A13945D898C296",
+ "4FE342E2FE1A7F9B8EE7EB4A7C0F9E162BCE33576B315ECECBB6406837BF51F5",
+},
+#endif
+#ifdef ECC384
+{
+ 48,
+ "ECC-384",
+ "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFFFF0000000000000000FFFFFFFF",
+ "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFFFF0000000000000000FFFFFFFC",
+ "B3312FA7E23EE7E4988E056BE3F82D19181D9C6EFE8141120314088F5013875AC656398D8A2ED19D2A85C8EDD3EC2AEF",
+ "FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFC7634D81F4372DDF581A0DB248B0A77AECEC196ACCC52973",
+ "AA87CA22BE8B05378EB1C71EF320AD746E1D3B628BA79B9859F741E082542A385502F25DBF55296C3A545E3872760AB7",
+ "3617DE4A96262C6F5D9E98BF9292DC29F8F41DBD289A147CE9DA3113B5F0B8C00A60B1CE1D7E819D7A431D7C90EA0E5F",
+},
+#endif
+#ifdef ECC521
+{
+ 66,
+ "ECC-521",
+ "1FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF",
+ "1FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFC",
+ "51953EB9618E1C9A1F929A21A0B68540EEA2DA725B99B315F3B8B489918EF109E156193951EC7E937B1652C0BD3BB1BF073573DF883D2C34F1EF451FD46B503F00",
+ "1FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFA51868783BF2F966B7FCC0148F709A5D03BB5C9B8899C47AEBB6FB71E91386409",
+ "C6858E06B70404E9CD9E3ECB662395B4429C648139053FB521F828AF606B4D3DBAA14B5E77EFE75928FE1DC127A2FFA8DE3348B3C1856A429BF97E7E31C2E5BD66",
+ "11839296A789A3BC0045C8A5FB42C7D1BD998F54449579B446817AFBD17273E662C97EE72995EF42640C550B9013FAD0761353C7086A272C24088BE94769FD16650",
+},
+#endif
+{
+ 0,
+ NULL, NULL, NULL, NULL, NULL, NULL, NULL
+}
+};
+
+
+ecc_point* ecc_new_point(void);
+void ecc_del_point(ecc_point* p);
+int ecc_map(ecc_point*, mp_int*, mp_digit*);
+int ecc_projective_add_point(ecc_point* P, ecc_point* Q, ecc_point* R,
+ mp_int* modulus, mp_digit* mp);
+int ecc_projective_dbl_point(ecc_point* P, ecc_point* R, mp_int* modulus,
+ mp_digit* mp);
+static int ecc_mulmod(mp_int* k, ecc_point *G, ecc_point *R, mp_int* modulus,
+ int map);
+static int ecc_check_pubkey_order(ecc_key* key, mp_int* prime, mp_int* order);
+#ifdef ECC_SHAMIR
+static int ecc_mul2add(ecc_point* A, mp_int* kA, ecc_point* B, mp_int* kB,
+ ecc_point* C, mp_int* modulus);
+#endif
+
+int mp_jacobi(mp_int* a, mp_int* p, int* c);
+int mp_sqrtmod_prime(mp_int* n, mp_int* prime, mp_int* ret);
+int mp_submod(mp_int* a, mp_int* b, mp_int* c, mp_int* d);
+
+#ifdef HAVE_COMP_KEY
+static int wc_ecc_export_x963_compressed(ecc_key*, byte* out, word32* outLen);
+#endif
+
+/* helper for either lib */
+static int get_digit_count(mp_int* a)
+{
+ if (a == NULL)
+ return 0;
+
+ return a->used;
+}
+
+/* helper for either lib */
+static mp_digit get_digit(mp_int* a, int n)
+{
+ if (a == NULL)
+ return 0;
+
+ return (n >= a->used || n < 0) ? 0 : a->dp[n];
+}
+
+
+#if defined(USE_FAST_MATH)
+
+/* fast math accelerated version, but not for fp ecc yet */
+
+/**
+ Add two ECC points
+ P The point to add
+ Q The point to add
+ R [out] The destination of the double
+ 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* modulus, mp_digit* mp)
+{
+ fp_int t1, t2, x, y, z;
+ int err;
+
+ if (P == NULL || Q == NULL || R == NULL || modulus == NULL || mp == NULL)
+ return ECC_BAD_ARG_E;
+
+ if ((err = mp_init_multi(&t1, &t2, &x, &y, &z, NULL)) != MP_OKAY) {
+ return err;
+ }
+
+ /* should we dbl instead? */
+ fp_sub(modulus, Q->y, &t1);
+ if ( (fp_cmp(P->x, Q->x) == FP_EQ) &&
+ (get_digit_count(Q->z) && fp_cmp(P->z, Q->z) == FP_EQ) &&
+ (fp_cmp(P->y, Q->y) == FP_EQ || fp_cmp(P->y, &t1) == FP_EQ)) {
+ return ecc_projective_dbl_point(P, R, modulus, mp);
+ }
+
+ fp_copy(P->x, &x);
+ fp_copy(P->y, &y);
+ fp_copy(P->z, &z);
+
+ /* if Z is one then these are no-operations */
+ if (get_digit_count(Q->z)) {
+ /* T1 = Z' * Z' */
+ fp_sqr(Q->z, &t1);
+ fp_montgomery_reduce(&t1, modulus, *mp);
+ /* X = X * T1 */
+ fp_mul(&t1, &x, &x);
+ fp_montgomery_reduce(&x, modulus, *mp);
+ /* T1 = Z' * T1 */
+ fp_mul(Q->z, &t1, &t1);
+ fp_montgomery_reduce(&t1, modulus, *mp);
+ /* Y = Y * T1 */
+ fp_mul(&t1, &y, &y);
+ fp_montgomery_reduce(&y, modulus, *mp);
+ }
+
+ /* T1 = Z*Z */
+ fp_sqr(&z, &t1);
+ fp_montgomery_reduce(&t1, modulus, *mp);
+ /* T2 = X' * T1 */
+ fp_mul(Q->x, &t1, &t2);
+ fp_montgomery_reduce(&t2, modulus, *mp);
+ /* T1 = Z * T1 */
+ fp_mul(&z, &t1, &t1);
+ fp_montgomery_reduce(&t1, modulus, *mp);
+ /* T1 = Y' * T1 */
+ fp_mul(Q->y, &t1, &t1);
+ fp_montgomery_reduce(&t1, modulus, *mp);
+
+ /* Y = Y - T1 */
+ fp_sub(&y, &t1, &y);
+ if (fp_cmp_d(&y, 0) == FP_LT) {
+ fp_add(&y, modulus, &y);
+ }
+ /* T1 = 2T1 */
+ fp_add(&t1, &t1, &t1);
+ if (fp_cmp(&t1, modulus) != FP_LT) {
+ fp_sub(&t1, modulus, &t1);
+ }
+ /* T1 = Y + T1 */
+ fp_add(&t1, &y, &t1);
+ if (fp_cmp(&t1, modulus) != FP_LT) {
+ fp_sub(&t1, modulus, &t1);
+ }
+ /* X = X - T2 */
+ fp_sub(&x, &t2, &x);
+ if (fp_cmp_d(&x, 0) == FP_LT) {
+ fp_add(&x, modulus, &x);
+ }
+ /* T2 = 2T2 */
+ fp_add(&t2, &t2, &t2);
+ if (fp_cmp(&t2, modulus) != FP_LT) {
+ fp_sub(&t2, modulus, &t2);
+ }
+ /* T2 = X + T2 */
+ fp_add(&t2, &x, &t2);
+ if (fp_cmp(&t2, modulus) != FP_LT) {
+ fp_sub(&t2, modulus, &t2);
+ }
+
+ /* if Z' != 1 */
+ if (get_digit_count(Q->z)) {
+ /* Z = Z * Z' */
+ fp_mul(&z, Q->z, &z);
+ fp_montgomery_reduce(&z, modulus, *mp);
+ }
+
+ /* Z = Z * X */
+ fp_mul(&z, &x, &z);
+ fp_montgomery_reduce(&z, modulus, *mp);
+
+ /* T1 = T1 * X */
+ fp_mul(&t1, &x, &t1);
+ fp_montgomery_reduce(&t1, modulus, *mp);
+ /* X = X * X */
+ fp_sqr(&x, &x);
+ fp_montgomery_reduce(&x, modulus, *mp);
+ /* T2 = T2 * x */
+ fp_mul(&t2, &x, &t2);
+ fp_montgomery_reduce(&t2, modulus, *mp);
+ /* T1 = T1 * X */
+ fp_mul(&t1, &x, &t1);
+ fp_montgomery_reduce(&t1, modulus, *mp);
+
+ /* X = Y*Y */
+ fp_sqr(&y, &x);
+ fp_montgomery_reduce(&x, modulus, *mp);
+ /* X = X - T2 */
+ fp_sub(&x, &t2, &x);
+ if (fp_cmp_d(&x, 0) == FP_LT) {
+ fp_add(&x, modulus, &x);
+ }
+
+ /* T2 = T2 - X */
+ fp_sub(&t2, &x, &t2);
+ if (fp_cmp_d(&t2, 0) == FP_LT) {
+ fp_add(&t2, modulus, &t2);
+ }
+ /* T2 = T2 - X */
+ fp_sub(&t2, &x, &t2);
+ if (fp_cmp_d(&t2, 0) == FP_LT) {
+ fp_add(&t2, modulus, &t2);
+ }
+ /* T2 = T2 * Y */
+ fp_mul(&t2, &y, &t2);
+ fp_montgomery_reduce(&t2, modulus, *mp);
+ /* Y = T2 - T1 */
+ fp_sub(&t2, &t1, &y);
+ if (fp_cmp_d(&y, 0) == FP_LT) {
+ fp_add(&y, modulus, &y);
+ }
+ /* Y = Y/2 */
+ if (fp_isodd(&y)) {
+ fp_add(&y, modulus, &y);
+ }
+ fp_div_2(&y, &y);
+
+ fp_copy(&x, R->x);
+ fp_copy(&y, R->y);
+ fp_copy(&z, R->z);
+
+ return MP_OKAY;
+}
+
+
+/**
+ Double an ECC point
+ P The point to double
+ R [out] The destination of the double
+ 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* modulus,
+ mp_digit* mp)
+{
+ fp_int t1, t2;
+ int err;
+
+ if (P == NULL || R == NULL || modulus == NULL || mp == NULL)
+ return ECC_BAD_ARG_E;
+
+ if (P != R) {
+ fp_copy(P->x, R->x);
+ fp_copy(P->y, R->y);
+ fp_copy(P->z, R->z);
+ }
+
+ if ((err = mp_init_multi(&t1, &t2, NULL, NULL, NULL, NULL)) != MP_OKAY) {
+ return err;
+ }
+
+ /* t1 = Z * Z */
+ fp_sqr(R->z, &t1);
+ fp_montgomery_reduce(&t1, modulus, *mp);
+ /* Z = Y * Z */
+ fp_mul(R->z, R->y, R->z);
+ fp_montgomery_reduce(R->z, modulus, *mp);
+ /* Z = 2Z */
+ fp_add(R->z, R->z, R->z);
+ if (fp_cmp(R->z, modulus) != FP_LT) {
+ fp_sub(R->z, modulus, R->z);
+ }
+
+ /* &t2 = X - T1 */
+ fp_sub(R->x, &t1, &t2);
+ if (fp_cmp_d(&t2, 0) == FP_LT) {
+ fp_add(&t2, modulus, &t2);
+ }
+ /* T1 = X + T1 */
+ fp_add(&t1, R->x, &t1);
+ if (fp_cmp(&t1, modulus) != FP_LT) {
+ fp_sub(&t1, modulus, &t1);
+ }
+ /* T2 = T1 * T2 */
+ fp_mul(&t1, &t2, &t2);
+ fp_montgomery_reduce(&t2, modulus, *mp);
+ /* T1 = 2T2 */
+ fp_add(&t2, &t2, &t1);
+ if (fp_cmp(&t1, modulus) != FP_LT) {
+ fp_sub(&t1, modulus, &t1);
+ }
+ /* T1 = T1 + T2 */
+ fp_add(&t1, &t2, &t1);
+ if (fp_cmp(&t1, modulus) != FP_LT) {
+ fp_sub(&t1, modulus, &t1);
+ }
+
+ /* Y = 2Y */
+ fp_add(R->y, R->y, R->y);
+ if (fp_cmp(R->y, modulus) != FP_LT) {
+ fp_sub(R->y, modulus, R->y);
+ }
+ /* Y = Y * Y */
+ fp_sqr(R->y, R->y);
+ fp_montgomery_reduce(R->y, modulus, *mp);
+ /* T2 = Y * Y */
+ fp_sqr(R->y, &t2);
+ fp_montgomery_reduce(&t2, modulus, *mp);
+ /* T2 = T2/2 */
+ if (fp_isodd(&t2)) {
+ fp_add(&t2, modulus, &t2);
+ }
+ fp_div_2(&t2, &t2);
+ /* Y = Y * X */
+ fp_mul(R->y, R->x, R->y);
+ fp_montgomery_reduce(R->y, modulus, *mp);
+
+ /* X = T1 * T1 */
+ fp_sqr(&t1, R->x);
+ fp_montgomery_reduce(R->x, modulus, *mp);
+ /* X = X - Y */
+ fp_sub(R->x, R->y, R->x);
+ if (fp_cmp_d(R->x, 0) == FP_LT) {
+ fp_add(R->x, modulus, R->x);
+ }
+ /* X = X - Y */
+ fp_sub(R->x, R->y, R->x);
+ if (fp_cmp_d(R->x, 0) == FP_LT) {
+ fp_add(R->x, modulus, R->x);
+ }
+
+ /* Y = Y - X */
+ fp_sub(R->y, R->x, R->y);
+ if (fp_cmp_d(R->y, 0) == FP_LT) {
+ fp_add(R->y, modulus, R->y);
+ }
+ /* Y = Y * T1 */
+ fp_mul(R->y, &t1, R->y);
+ fp_montgomery_reduce(R->y, modulus, *mp);
+ /* Y = Y - T2 */
+ fp_sub(R->y, &t2, R->y);
+ if (fp_cmp_d(R->y, 0) == FP_LT) {
+ fp_add(R->y, modulus, R->y);
+ }
+
+ return MP_OKAY;
+}
+
+#else /* USE_FAST_MATH */
+
+/**
+ Add two ECC points
+ P The point to add
+ Q The point to add
+ R [out] The destination of the double
+ 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* modulus, mp_digit* mp)
+{
+ mp_int t1;
+ mp_int t2;
+ mp_int x;
+ mp_int y;
+ mp_int z;
+ int err;
+
+ if (P == NULL || Q == NULL || R == NULL || modulus == NULL || mp == NULL)
+ return ECC_BAD_ARG_E;
+
+ if ((err = mp_init_multi(&t1, &t2, &x, &y, &z, NULL)) != MP_OKAY) {
+ return err;
+ }
+
+ /* should we dbl instead? */
+ 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);
+ mp_clear(&x);
+ mp_clear(&y);
+ mp_clear(&z);
+
+ return ecc_projective_dbl_point(P, R, modulus, mp);
+ }
+ }
+
+ 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 (get_digit_count(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_cmp_d(&y, 0) == MP_LT)
+ 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_cmp_d(&x, 0) == MP_LT)
+ 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 (get_digit_count(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_cmp_d(&x, 0) == MP_LT)
+ 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_cmp_d(&t2, 0) == MP_LT)
+ 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_cmp_d(&t2, 0) == MP_LT)
+ 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_cmp_d(&y, 0) == MP_LT)
+ err = mp_add(&y, modulus, &y);
+ }
+ /* Y = Y/2 */
+ if (err == MP_OKAY) {
+ if (mp_isodd(&y))
+ err = mp_add(&y, modulus, &y);
+ }
+ if (err == MP_OKAY)
+ err = mp_div_2(&y, &y);
+
+ 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);
+
+ /* clean up */
+ mp_clear(&t1);
+ mp_clear(&t2);
+ mp_clear(&x);
+ mp_clear(&y);
+ mp_clear(&z);
+
+ return err;
+}
+
+
+/**
+ Double an ECC point
+ P The point to double
+ R [out] The destination of the double
+ 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* modulus,
+ mp_digit* mp)
+{
+ mp_int t1;
+ mp_int t2;
+ int err;
+
+ if (P == NULL || R == NULL || modulus == NULL || mp == NULL)
+ return ECC_BAD_ARG_E;
+
+ if ((err = mp_init_multi(&t1, &t2, NULL, NULL, NULL, NULL)) != MP_OKAY) {
+ return err;
+ }
+
+ if (P != R) {
+ err = mp_copy(P->x, R->x);
+ if (err == MP_OKAY)
+ err = mp_copy(P->y, R->y);
+ if (err == MP_OKAY)
+ err = mp_copy(P->z, R->z);
+ }
+
+ /* t1 = Z * Z */
+ if (err == MP_OKAY)
+ err = mp_sqr(R->z, &t1);
+ if (err == MP_OKAY)
+ err = mp_montgomery_reduce(&t1, modulus, *mp);
+
+ /* Z = Y * Z */
+ if (err == MP_OKAY)
+ err = mp_mul(R->z, R->y, R->z);
+ if (err == MP_OKAY)
+ err = mp_montgomery_reduce(R->z, modulus, *mp);
+
+ /* Z = 2Z */
+ if (err == MP_OKAY)
+ err = mp_add(R->z, R->z, R->z);
+ if (err == MP_OKAY) {
+ if (mp_cmp(R->z, modulus) != MP_LT)
+ err = mp_sub(R->z, modulus, R->z);
+ }
+
+ /* T2 = X - T1 */
+ if (err == MP_OKAY)
+ err = mp_sub(R->x, &t1, &t2);
+ if (err == MP_OKAY) {
+ if (mp_cmp_d(&t2, 0) == MP_LT)
+ err = mp_add(&t2, modulus, &t2);
+ }
+ /* T1 = X + T1 */
+ if (err == MP_OKAY)
+ err = mp_add(&t1, R->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(R->y, R->y, R->y);
+ if (err == MP_OKAY) {
+ if (mp_cmp(R->y, modulus) != MP_LT)
+ err = mp_sub(R->y, modulus, R->y);
+ }
+ /* Y = Y * Y */
+ if (err == MP_OKAY)
+ err = mp_sqr(R->y, R->y);
+ if (err == MP_OKAY)
+ err = mp_montgomery_reduce(R->y, modulus, *mp);
+
+ /* T2 = Y * Y */
+ if (err == MP_OKAY)
+ err = mp_sqr(R->y, &t2);
+ if (err == MP_OKAY)
+ err = mp_montgomery_reduce(&t2, modulus, *mp);
+
+ /* T2 = T2/2 */
+ if (err == MP_OKAY) {
+ if (mp_isodd(&t2))
+ 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(R->y, R->x, R->y);
+ if (err == MP_OKAY)
+ err = mp_montgomery_reduce(R->y, modulus, *mp);
+
+ /* X = T1 * T1 */
+ if (err == MP_OKAY)
+ err = mp_sqr(&t1, R->x);
+ if (err == MP_OKAY)
+ err = mp_montgomery_reduce(R->x, modulus, *mp);
+
+ /* X = X - Y */
+ if (err == MP_OKAY)
+ err = mp_sub(R->x, R->y, R->x);
+ if (err == MP_OKAY) {
+ if (mp_cmp_d(R->x, 0) == MP_LT)
+ err = mp_add(R->x, modulus, R->x);
+ }
+ /* X = X - Y */
+ if (err == MP_OKAY)
+ err = mp_sub(R->x, R->y, R->x);
+ if (err == MP_OKAY) {
+ if (mp_cmp_d(R->x, 0) == MP_LT)
+ err = mp_add(R->x, modulus, R->x);
+ }
+ /* Y = Y - X */
+ if (err == MP_OKAY)
+ err = mp_sub(R->y, R->x, R->y);
+ if (err == MP_OKAY) {
+ if (mp_cmp_d(R->y, 0) == MP_LT)
+ err = mp_add(R->y, modulus, R->y);
+ }
+ /* Y = Y * T1 */
+ if (err == MP_OKAY)
+ err = mp_mul(R->y, &t1, R->y);
+ if (err == MP_OKAY)
+ err = mp_montgomery_reduce(R->y, modulus, *mp);
+
+ /* Y = Y - T2 */
+ if (err == MP_OKAY)
+ err = mp_sub(R->y, &t2, R->y);
+ if (err == MP_OKAY) {
+ if (mp_cmp_d(R->y, 0) == MP_LT)
+ err = mp_add(R->y, modulus, R->y);
+ }
+
+ /* clean up */
+ mp_clear(&t1);
+ mp_clear(&t2);
+
+ return err;
+}
+
+#endif /* USE_FAST_MATH */
+
+/**
+ Map a projective jacbobian point back to affine space
+ P [in/out] The point to map
+ modulus The modulus of the field the ECC curve is in
+ mp The "b" value from montgomery_setup()
+ return MP_OKAY on success
+*/
+int ecc_map(ecc_point* P, mp_int* modulus, mp_digit* mp)
+{
+ mp_int t1;
+ mp_int t2;
+ int err;
+
+ if (P == NULL || mp == NULL || modulus == NULL)
+ return ECC_BAD_ARG_E;
+
+ /* special case for point at infinity */
+ if (mp_cmp_d(P->z, 0) == MP_EQ) {
+ mp_set(P->x, 0);
+ mp_set(P->y, 0);
+ mp_set(P->z, 1);
+ return MP_OKAY;
+ }
+
+ if ((err = mp_init_multi(&t1, &t2, NULL, NULL, NULL, NULL)) != MP_OKAY) {
+ return MEMORY_E;
+ }
+
+ /* first map z back to normal */
+ err = mp_montgomery_reduce(P->z, modulus, *mp);
+
+ /* get 1/z */
+ if (err == MP_OKAY)
+ err = mp_invmod(P->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(P->x, &t2, P->x);
+ if (err == MP_OKAY)
+ err = mp_montgomery_reduce(P->x, modulus, *mp);
+ if (err == MP_OKAY)
+ err = mp_mul(P->y, &t1, P->y);
+ if (err == MP_OKAY)
+ err = mp_montgomery_reduce(P->y, modulus, *mp);
+
+ if (err == MP_OKAY)
+ mp_set(P->z, 1);
+
+ /* clean up */
+ mp_clear(&t1);
+ mp_clear(&t2);
+
+ return err;
+}
+
+
+#ifndef ECC_TIMING_RESISTANT
+
+/* size of sliding window, don't change this! */
+#define WINSIZE 4
+
+/**
+ Perform a point multiplication
+ k The scalar to multiply by
+ G The base point
+ R [out] Destination for kG
+ 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* modulus, int map)
+#else
+static int ecc_mulmod(mp_int* k, ecc_point *G, ecc_point *R, mp_int* modulus,
+ int map)
+#endif
+{
+ ecc_point *tG, *M[8];
+ int i, j, err;
+ mp_int mu;
+ mp_digit mp;
+ mp_digit buf;
+ int first = 1, bitbuf = 0, bitcpy = 0, bitcnt = 0, mode = 0,
+ digidx = 0;
+
+ if (k == NULL || G == NULL || R == NULL || modulus == NULL)
+ return ECC_BAD_ARG_E;
+
+ /* init montgomery reduction */
+ if ((err = mp_montgomery_setup(modulus, &mp)) != MP_OKAY) {
+ return err;
+ }
+ if ((err = mp_init(&mu)) != MP_OKAY) {
+ return err;
+ }
+ if ((err = mp_montgomery_calc_normalization(&mu, modulus)) != MP_OKAY) {
+ mp_clear(&mu);
+ return err;
+ }
+
+ /* alloc ram for window temps */
+ for (i = 0; i < 8; i++) {
+ M[i] = ecc_new_point();
+ if (M[i] == NULL) {
+ for (j = 0; j < i; j++) {
+ ecc_del_point(M[j]);
+ }
+ mp_clear(&mu);
+ return MEMORY_E;
+ }
+ }
+
+ /* make a copy of G incase R==G */
+ tG = ecc_new_point();
+ 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);
+ }
+ }
+ mp_clear(&mu);
+
+ /* 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], modulus, &mp);
+ if (err == MP_OKAY)
+ err = ecc_projective_dbl_point(M[0], M[0], modulus, &mp);
+ if (err == MP_OKAY)
+ err = ecc_projective_dbl_point(M[0], M[0], 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-8], 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, 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-8]->x, R->x);
+ if (err != MP_OKAY) break;
+
+ err = mp_copy(M[bitbuf-8]->y, R->y);
+ if (err != MP_OKAY) break;
+
+ err = mp_copy(M[bitbuf-8]->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, 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] guaranted */
+ err = ecc_projective_add_point(R,M[bitbuf-8],R,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, 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, modulus, &mp);
+ if (err != MP_OKAY) break;
+ }
+ }
+ }
+ }
+ }
+
+ /* map R back from projective space */
+ if (err == MP_OKAY && map)
+ err = ecc_map(R, modulus, &mp);
+
+ mp_clear(&mu);
+ ecc_del_point(tG);
+ for (i = 0; i < 8; i++) {
+ ecc_del_point(M[i]);
+ }
+ return err;
+}
+
+#undef WINSIZE
+
+#else /* ECC_TIMING_RESISTANT */
+
+/**
+ Perform a point multiplication (timing resistant)
+ k The scalar to multiply by
+ G The base point
+ R [out] Destination for kG
+ 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* modulus, int map)
+#else
+static int ecc_mulmod(mp_int* k, ecc_point *G, ecc_point *R, mp_int* modulus,
+ int map)
+#endif
+{
+ ecc_point *tG, *M[3];
+ int i, j, err;
+ mp_int mu;
+ mp_digit mp;
+ mp_digit buf;
+ int bitcnt = 0, mode = 0, digidx = 0;
+
+ if (k == NULL || G == NULL || R == NULL || modulus == NULL)
+ return ECC_BAD_ARG_E;
+
+ /* init montgomery reduction */
+ if ((err = mp_montgomery_setup(modulus, &mp)) != MP_OKAY) {
+ return err;
+ }
+ if ((err = mp_init(&mu)) != MP_OKAY) {
+ return err;
+ }
+ if ((err = mp_montgomery_calc_normalization(&mu, modulus)) != MP_OKAY) {
+ mp_clear(&mu);
+ return err;
+ }
+
+ /* alloc ram for window temps */
+ for (i = 0; i < 3; i++) {
+ M[i] = ecc_new_point();
+ if (M[i] == NULL) {
+ for (j = 0; j < i; j++) {
+ ecc_del_point(M[j]);
+ }
+ mp_clear(&mu);
+ return MEMORY_E;
+ }
+ }
+
+ /* make a copy of G incase R==G */
+ tG = ecc_new_point();
+ if (tG == NULL)
+ err = MEMORY_E;
+
+ /* tG = G and convert to montgomery */
+ if (err == MP_OKAY) {
+ 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);
+ }
+ mp_clear(&mu);
+
+ /* 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], 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 ltiplicand */
+ i = (buf >> (DIGIT_BIT - 1)) & 1;
+ buf <<= 1;
+
+ if (mode == 0 && i == 0) {
+ /* dummy operations */
+ if (err == MP_OKAY)
+ err = ecc_projective_add_point(M[0], M[1], M[2], modulus,
+ &mp);
+ if (err == MP_OKAY)
+ err = ecc_projective_dbl_point(M[1], M[2], modulus, &mp);
+ if (err == MP_OKAY)
+ continue;
+ }
+
+ if (mode == 0 && i == 1) {
+ mode = 1;
+ /* dummy operations */
+ if (err == MP_OKAY)
+ err = ecc_projective_add_point(M[0], M[1], M[2], modulus,
+ &mp);
+ if (err == MP_OKAY)
+ err = ecc_projective_dbl_point(M[1], M[2], modulus, &mp);
+ if (err == MP_OKAY)
+ continue;
+ }
+
+ if (err == MP_OKAY)
+ err = ecc_projective_add_point(M[0], M[1], M[i^1], modulus, &mp);
+ if (err == MP_OKAY)
+ err = ecc_projective_dbl_point(M[i], M[i], modulus, &mp);
+ if (err != MP_OKAY)
+ break;
+ } /* 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);
+
+ /* map R back from projective space */
+ if (err == MP_OKAY && map)
+ err = ecc_map(R, modulus, &mp);
+
+ /* done */
+ mp_clear(&mu);
+ ecc_del_point(tG);
+ for (i = 0; i < 3; i++) {
+ ecc_del_point(M[i]);
+ }
+ return err;
+}
+
+#endif /* ECC_TIMING_RESISTANT */
+
+
+#ifdef ALT_ECC_SIZE
+
+static void alt_fp_init(fp_int* a)
+{
+ a->size = FP_SIZE_ECC;
+ fp_zero(a);
+}
+
+#endif /* ALT_ECC_SIZE */
+
+
+/**
+ Allocate a new ECC point
+ return A newly allocated point or NULL on error
+*/
+ecc_point* ecc_new_point(void)
+{
+ ecc_point* p;
+
+ p = (ecc_point*)XMALLOC(sizeof(ecc_point), 0, DYNAMIC_TYPE_ECC);
+ if (p == NULL) {
+ return NULL;
+ }
+ XMEMSET(p, 0, sizeof(ecc_point));
+
+#ifndef USE_FAST_MATH
+ p->x->dp = NULL;
+ p->y->dp = NULL;
+ p->z->dp = NULL;
+#endif
+
+#ifndef ALT_ECC_SIZE
+ if (mp_init_multi(p->x, p->y, p->z, NULL, NULL, NULL) != MP_OKAY) {
+ XFREE(p, 0, 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;
+}
+
+/** Free an ECC point from memory
+ p The point to free
+*/
+void ecc_del_point(ecc_point* p)
+{
+ /* prevents free'ing null arguments */
+ if (p != NULL) {
+ mp_clear(p->x);
+ mp_clear(p->y);
+ mp_clear(p->z);
+ XFREE(p, 0, DYNAMIC_TYPE_ECC);
+ }
+}
+
+
+/** Returns whether an ECC idx is valid or not
+ n The idx number to check
+ return 1 if valid, 0 if not
+*/
+static int 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 >= -1) && (n < x)) {
+ return 1;
+ }
+ return 0;
+}
+
+
+/**
+ Create an ECC shared secret between two keys
+ private_key The private ECC 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)
+{
+ word32 x = 0;
+ ecc_point* result;
+ mp_int prime;
+ int err;
+
+ if (private_key == NULL || public_key == NULL || out == NULL ||
+ outlen == NULL)
+ return BAD_FUNC_ARG;
+
+ /* type valid? */
+ if (private_key->type != ECC_PRIVATEKEY) {
+ return ECC_BAD_ARG_E;
+ }
+
+ if (ecc_is_valid_idx(private_key->idx) == 0 ||
+ ecc_is_valid_idx(public_key->idx) == 0)
+ return ECC_BAD_ARG_E;
+
+ if (XSTRNCMP(private_key->dp->name, public_key->dp->name, ECC_MAXNAME) != 0)
+ return ECC_BAD_ARG_E;
+
+ /* make new point */
+ result = ecc_new_point();
+ if (result == NULL) {
+ return MEMORY_E;
+ }
+
+ if ((err = mp_init(&prime)) != MP_OKAY) {
+ ecc_del_point(result);
+ return err;
+ }
+
+ err = mp_read_radix(&prime, (char *)private_key->dp->prime, 16);
+
+ if (err == MP_OKAY)
+ err = ecc_mulmod(&private_key->k, &public_key->pubkey, result, &prime,1);
+
+ if (err == MP_OKAY) {
+ x = mp_unsigned_bin_size(&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;
+ }
+
+ mp_clear(&prime);
+ ecc_del_point(result);
+
+ return err;
+}
+
+
+/* return 1 if point is at infinity, 0 if not, < 0 on error */
+static int 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;
+}
+
+
+int wc_ecc_make_key_ex(RNG* rng, ecc_key* key, const ecc_set_type* dp);
+
+/**
+ 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(RNG* rng, int keysize, ecc_key* key)
+{
+ int x, err;
+
+ if (key == NULL || rng == NULL)
+ return ECC_BAD_ARG_E;
+
+ /* find key size */
+ for (x = 0; (keysize > ecc_sets[x].size) && (ecc_sets[x].size != 0); x++)
+ ;
+ keysize = ecc_sets[x].size;
+
+ if (keysize > ECC_MAXSIZE || ecc_sets[x].size == 0) {
+ return BAD_FUNC_ARG;
+ }
+ err = wc_ecc_make_key_ex(rng, key, &ecc_sets[x]);
+ key->idx = x;
+
+ return err;
+}
+
+int wc_ecc_make_key_ex(RNG* rng, ecc_key* key, const ecc_set_type* dp)
+{
+ int err;
+ ecc_point* base;
+ mp_int prime;
+ mp_int order;
+#ifdef WOLFSSL_SMALL_STACK
+ byte* buf;
+#else
+ byte buf[ECC_MAXSIZE];
+#endif
+ int keysize;
+ int po_init = 0; /* prime order Init flag for clear */
+
+ if (key == NULL || rng == NULL || dp == NULL)
+ return ECC_BAD_ARG_E;
+
+#ifdef WOLFSSL_SMALL_STACK
+ buf = (byte*)XMALLOC(ECC_MAXSIZE, NULL, DYNAMIC_TYPE_TMP_BUFFER);
+ if (buf == NULL)
+ return MEMORY_E;
+#endif
+
+ key->idx = -1;
+ key->dp = dp;
+ keysize = dp->size;
+
+ /* allocate ram */
+ base = NULL;
+
+ /* make up random string */
+ err = wc_RNG_GenerateBlock(rng, buf, keysize);
+ if (err == 0)
+ buf[0] |= 0x0c;
+
+ /* setup the key variables */
+ if (err == 0) {
+#ifndef ALT_ECC_SIZE
+ err = mp_init_multi(key->pubkey.x, key->pubkey.y, key->pubkey.z,
+ &key->k, &prime, &order);
+#else
+ key->pubkey.x = (mp_int*)&key->pubkey.xyz[0];
+ key->pubkey.y = (mp_int*)&key->pubkey.xyz[1];
+ key->pubkey.z = (mp_int*)&key->pubkey.xyz[2];
+ alt_fp_init(key->pubkey.x);
+ alt_fp_init(key->pubkey.y);
+ alt_fp_init(key->pubkey.z);
+ err = mp_init_multi(&key->k, &prime, &order, NULL, NULL, NULL);
+#endif
+ if (err != MP_OKAY)
+ err = MEMORY_E;
+ else
+ po_init = 1;
+ }
+
+ if (err == MP_OKAY) {
+ base = ecc_new_point();
+ if (base == NULL)
+ err = MEMORY_E;
+ }
+
+ /* read in the specs for this key */
+ if (err == MP_OKAY)
+ err = mp_read_radix(&prime, (char *)key->dp->prime, 16);
+ if (err == MP_OKAY)
+ err = mp_read_radix(&order, (char *)key->dp->order, 16);
+ if (err == MP_OKAY)
+ err = mp_read_radix(base->x, (char *)key->dp->Gx, 16);
+ if (err == MP_OKAY)
+ err = mp_read_radix(base->y, (char *)key->dp->Gy, 16);
+
+ if (err == MP_OKAY)
+ mp_set(base->z, 1);
+ if (err == MP_OKAY)
+ err = mp_read_unsigned_bin(&key->k, (byte*)buf, keysize);
+
+ /* the key should be smaller than the order of base point */
+ if (err == MP_OKAY) {
+ if (mp_cmp(&key->k, &order) != MP_LT)
+ err = mp_mod(&key->k, &order, &key->k);
+ }
+ /* make the public key */
+ if (err == MP_OKAY)
+ err = ecc_mulmod(&key->k, base, &key->pubkey, &prime, 1);
+
+#ifdef WOLFSSL_VALIDATE_ECC_KEYGEN
+ /* validate the public key, order * pubkey = point at infinity */
+ if (err == MP_OKAY)
+ err = ecc_check_pubkey_order(key, &prime, &order);
+#endif /* WOLFSSL_VALIDATE_KEYGEN */
+
+ if (err == MP_OKAY)
+ key->type = ECC_PRIVATEKEY;
+
+ if (err != MP_OKAY) {
+ /* clean up */
+ mp_clear(key->pubkey.x);
+ mp_clear(key->pubkey.y);
+ mp_clear(key->pubkey.z);
+ mp_clear(&key->k);
+ }
+ ecc_del_point(base);
+ if (po_init) {
+ mp_clear(&prime);
+ mp_clear(&order);
+ }
+
+ ForceZero(buf, ECC_MAXSIZE);
+#ifdef WOLFSSL_SMALL_STACK
+ XFREE(buf, NULL, DYNAMIC_TYPE_TMP_BUFFER);
+#endif
+
+ return err;
+}
+
+
+/* Setup dynamic pointers is using normal math for proper freeing */
+int wc_ecc_init(ecc_key* key)
+{
+ (void)key;
+
+#ifndef USE_FAST_MATH
+ key->pubkey.x->dp = NULL;
+ key->pubkey.y->dp = NULL;
+ key->pubkey.z->dp = NULL;
+
+ key->k.dp = NULL;
+#endif
+
+#ifdef ALT_ECC_SIZE
+ if (mp_init(&key->k) != MP_OKAY)
+ return MEMORY_E;
+
+ key->pubkey.x = (mp_int*)&key->pubkey.xyz[0];
+ key->pubkey.y = (mp_int*)&key->pubkey.xyz[1];
+ key->pubkey.z = (mp_int*)&key->pubkey.xyz[2];
+ alt_fp_init(key->pubkey.x);
+ alt_fp_init(key->pubkey.y);
+ alt_fp_init(key->pubkey.z);
+#endif
+
+ return 0;
+}
+
+
+/**
+ 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,
+ RNG* rng, ecc_key* key)
+{
+ mp_int r;
+ mp_int s;
+ mp_int e;
+ mp_int p;
+ int err;
+
+ if (in == NULL || out == NULL || outlen == NULL || key == NULL || rng ==NULL)
+ return ECC_BAD_ARG_E;
+
+ /* is this a private key? */
+ if (key->type != ECC_PRIVATEKEY) {
+ return ECC_BAD_ARG_E;
+ }
+
+ /* is the IDX valid ? */
+ if (ecc_is_valid_idx(key->idx) != 1) {
+ return ECC_BAD_ARG_E;
+ }
+
+ /* get the hash and load it as a bignum into 'e' */
+ /* init the bignums */
+ if ((err = mp_init_multi(&r, &s, &p, &e, NULL, NULL)) != MP_OKAY) {
+ return err;
+ }
+ err = mp_read_radix(&p, (char *)key->dp->order, 16);
+
+ if (err == MP_OKAY) {
+ /* we may need to truncate if hash is longer than key size */
+ word32 orderBits = mp_count_bits(&p);
+
+ /* truncate down to byte size, may be all that's needed */
+ if ( (WOLFSSL_BIT_SIZE * inlen) > orderBits)
+ inlen = (orderBits + WOLFSSL_BIT_SIZE - 1)/WOLFSSL_BIT_SIZE;
+ err = mp_read_unsigned_bin(&e, (byte*)in, inlen);
+
+ /* may still need bit truncation too */
+ if (err == MP_OKAY && (WOLFSSL_BIT_SIZE * inlen) > orderBits)
+ mp_rshb(&e, WOLFSSL_BIT_SIZE - (orderBits & 0x7));
+ }
+
+ /* make up a key and export the public copy */
+ if (err == MP_OKAY) {
+ int loop_check = 0;
+ ecc_key pubkey;
+ wc_ecc_init(&pubkey);
+ for (;;) {
+ if (++loop_check > 64) {
+ err = RNG_FAILURE_E;
+ break;
+ }
+ err = wc_ecc_make_key_ex(rng, &pubkey, key->dp);
+ if (err != MP_OKAY) break;
+
+ /* find r = x1 mod n */
+ err = mp_mod(pubkey.pubkey.x, &p, &r);
+ if (err != MP_OKAY) break;
+
+ if (mp_iszero(&r) == MP_YES) {
+ mp_clear(pubkey.pubkey.x);
+ mp_clear(pubkey.pubkey.y);
+ mp_clear(pubkey.pubkey.z);
+ mp_clear(&pubkey.k);
+ }
+ else {
+ /* find s = (e + xr)/k */
+ err = mp_invmod(&pubkey.k, &p, &pubkey.k);
+ if (err != MP_OKAY) break;
+
+ err = mp_mulmod(&key->k, &r, &p, &s); /* s = xr */
+ if (err != MP_OKAY) break;
+
+ err = mp_add(&e, &s, &s); /* s = e + xr */
+ if (err != MP_OKAY) break;
+
+ err = mp_mod(&s, &p, &s); /* s = e + xr */
+ if (err != MP_OKAY) break;
+
+ err = mp_mulmod(&s, &pubkey.k, &p, &s); /* s = (e + xr)/k */
+ if (err != MP_OKAY) break;
+
+ if (mp_iszero(&s) == MP_NO)
+ break;
+ }
+ }
+ wc_ecc_free(&pubkey);
+ }
+
+ /* store as SEQUENCE { r, s -- integer } */
+ if (err == MP_OKAY)
+ err = StoreECC_DSA_Sig(out, outlen, &r, &s);
+
+ mp_clear(&r);
+ mp_clear(&s);
+ mp_clear(&p);
+ mp_clear(&e);
+
+ return err;
+}
+
+
+/**
+ Free an ECC key from memory
+ key The key you wish to free
+*/
+void wc_ecc_free(ecc_key* key)
+{
+ if (key == NULL)
+ return;
+
+ mp_clear(key->pubkey.x);
+ mp_clear(key->pubkey.y);
+ mp_clear(key->pubkey.z);
+ mp_clear(&key->k);
+}
+
+
+#ifdef USE_FAST_MATH
+ #define GEN_MEM_ERR FP_MEM
+#else
+ #define GEN_MEM_ERR MP_MEM
+#endif
+
+#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)
+ 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* modulus)
+#else
+static int ecc_mul2add(ecc_point* A, mp_int* kA,
+ ecc_point* B, mp_int* kB,
+ ecc_point* C, mp_int* modulus)
+#endif
+{
+ ecc_point* precomp[16];
+ unsigned bitbufA, bitbufB, lenA, lenB, len, x, y, nA, nB, nibble;
+ unsigned char* tA;
+ unsigned char* tB;
+ int err = MP_OKAY, first;
+ int muInit = 0;
+ int tableInit = 0;
+ mp_digit mp;
+ mp_int mu;
+
+ /* 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, NULL, DYNAMIC_TYPE_TMP_BUFFER);
+ if (tA == NULL) {
+ return GEN_MEM_ERR;
+ }
+ tB = (unsigned char*)XMALLOC(ECC_BUFSIZE, NULL, DYNAMIC_TYPE_TMP_BUFFER);
+ if (tB == NULL) {
+ XFREE(tA, NULL, DYNAMIC_TYPE_TMP_BUFFER);
+ return GEN_MEM_ERR;
+ }
+ XMEMSET(tA, 0, ECC_BUFSIZE);
+ XMEMSET(tB, 0, ECC_BUFSIZE);
+
+ /* get sizes */
+ lenA = mp_unsigned_bin_size(kA);
+ lenB = mp_unsigned_bin_size(kB);
+ len = MAX(lenA, lenB);
+
+ /* sanity check */
+ if ((lenA > ECC_BUFSIZE) || (lenB > ECC_BUFSIZE)) {
+ err = BAD_FUNC_ARG;
+ }
+
+ if (err == MP_OKAY) {
+ /* extract and justify kA */
+ err = mp_to_unsigned_bin(kA, (len - lenA) + tA);
+
+ /* extract and justify kB */
+ if (err == MP_OKAY)
+ err = mp_to_unsigned_bin(kB, (len - lenB) + tB);
+
+ /* allocate the table */
+ if (err == MP_OKAY) {
+ for (x = 0; x < 16; x++) {
+ precomp[x] = ecc_new_point();
+ if (precomp[x] == NULL) {
+ for (y = 0; y < x; ++y) {
+ ecc_del_point(precomp[y]);
+ }
+ err = GEN_MEM_ERR;
+ break;
+ }
+ }
+ }
+ }
+
+ if (err == MP_OKAY)
+ tableInit = 1;
+
+ if (err == MP_OKAY)
+ /* init montgomery reduction */
+ err = mp_montgomery_setup(modulus, &mp);
+
+ if (err == MP_OKAY)
+ err = mp_init(&mu);
+ if (err == MP_OKAY)
+ muInit = 1;
+
+ 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);
+
+ if (err == MP_OKAY)
+ /* precomp [i,0](A + B) table */
+ err = ecc_projective_dbl_point(precomp[1], precomp[2], modulus, &mp);
+
+ if (err == MP_OKAY)
+ err = ecc_projective_add_point(precomp[1], precomp[2], precomp[3],
+ modulus, &mp);
+ if (err == MP_OKAY)
+ /* precomp [0,i](A + B) table */
+ err = ecc_projective_dbl_point(precomp[1<<2], precomp[2<<2], modulus, &mp);
+
+ if (err == MP_OKAY)
+ err = ecc_projective_add_point(precomp[1<<2], precomp[2<<2], precomp[3<<2],
+ 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)], modulus, &mp);
+ }
+ }
+ }
+
+ if (err == MP_OKAY) {
+ nibble = 3;
+ first = 1;
+ bitbufA = tA[0];
+ bitbufB = tB[0];
+
+ /* for every byte of the multiplicands */
+ for (x = -1;; ) {
+ /* grab a nibble */
+ if (++nibble == 4) {
+ ++x; if (x == len) break;
+ bitbufA = tA[x];
+ bitbufB = tB[x];
+ nibble = 0;
+ }
+
+ /* 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, modulus, &mp);
+ if (err == MP_OKAY)
+ err = ecc_projective_dbl_point(C, C, 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,
+ modulus, &mp);
+ else
+ break;
+ }
+ }
+ }
+ }
+
+ if (err == MP_OKAY)
+ /* reduce to affine */
+ err = ecc_map(C, modulus, &mp);
+
+ /* clean up */
+ if (muInit)
+ mp_clear(&mu);
+
+ if (tableInit) {
+ for (x = 0; x < 16; x++) {
+ ecc_del_point(precomp[x]);
+ }
+ }
+ ForceZero(tA, ECC_BUFSIZE);
+ ForceZero(tB, ECC_BUFSIZE);
+ XFREE(tA, NULL, DYNAMIC_TYPE_TMP_BUFFER);
+ XFREE(tB, NULL, DYNAMIC_TYPE_TMP_BUFFER);
+
+ return err;
+}
+
+
+#endif /* ECC_SHAMIR */
+
+
+
+/* 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)
+ stat 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* stat, ecc_key* key)
+{
+ ecc_point *mG, *mQ;
+ mp_int r;
+ mp_int s;
+ mp_int v;
+ mp_int w;
+ mp_int u1;
+ mp_int u2;
+ mp_int e;
+ mp_int p;
+ mp_int m;
+ int err;
+
+ if (sig == NULL || hash == NULL || stat == NULL || key == NULL)
+ return ECC_BAD_ARG_E;
+
+ /* default to invalid signature */
+ *stat = 0;
+
+ /* is the IDX valid ? */
+ if (ecc_is_valid_idx(key->idx) != 1) {
+ return ECC_BAD_ARG_E;
+ }
+
+ /* allocate ints */
+ if ((err = mp_init_multi(&v, &w, &u1, &u2, &p, &e)) != MP_OKAY) {
+ return MEMORY_E;
+ }
+
+ if ((err = mp_init(&m)) != MP_OKAY) {
+ mp_clear(&v);
+ mp_clear(&w);
+ mp_clear(&u1);
+ mp_clear(&u2);
+ mp_clear(&p);
+ mp_clear(&e);
+ return MEMORY_E;
+ }
+
+ /* allocate points */
+ mG = ecc_new_point();
+ mQ = ecc_new_point();
+ if (mQ == NULL || mG == NULL)
+ err = MEMORY_E;
+
+ /* 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. */
+ XMEMSET(&r, 0, sizeof(r));
+ XMEMSET(&s, 0, sizeof(s));
+ if (err == MP_OKAY)
+ err = DecodeECC_DSA_Sig(sig, siglen, &r, &s);
+
+ /* get the order */
+ if (err == MP_OKAY)
+ err = mp_read_radix(&p, (char *)key->dp->order, 16);
+
+ /* get the modulus */
+ if (err == MP_OKAY)
+ err = mp_read_radix(&m, (char *)key->dp->prime, 16);
+
+ /* check for zero */
+ if (err == MP_OKAY) {
+ if (mp_iszero(&r) || mp_iszero(&s) || mp_cmp(&r, &p) != MP_LT ||
+ mp_cmp(&s, &p) != 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(&p);
+
+ /* 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));
+ }
+
+ /* w = s^-1 mod n */
+ if (err == MP_OKAY)
+ err = mp_invmod(&s, &p, &w);
+
+ /* u1 = ew */
+ if (err == MP_OKAY)
+ err = mp_mulmod(&e, &w, &p, &u1);
+
+ /* u2 = rw */
+ if (err == MP_OKAY)
+ err = mp_mulmod(&r, &w, &p, &u2);
+
+ /* find mG and mQ */
+ if (err == MP_OKAY)
+ err = mp_read_radix(mG->x, (char *)key->dp->Gx, 16);
+
+ if (err == MP_OKAY)
+ err = mp_read_radix(mG->y, (char *)key->dp->Gy, 16);
+ if (err == MP_OKAY)
+ 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);
+
+#ifndef ECC_SHAMIR
+ {
+ mp_digit mp;
+
+ /* compute u1*mG + u2*mQ = mG */
+ if (err == MP_OKAY)
+ err = ecc_mulmod(&u1, mG, mG, &m, 0);
+ if (err == MP_OKAY)
+ err = ecc_mulmod(&u2, mQ, mQ, &m, 0);
+
+ /* find the montgomery mp */
+ if (err == MP_OKAY)
+ err = mp_montgomery_setup(&m, &mp);
+
+ /* add them */
+ if (err == MP_OKAY)
+ err = ecc_projective_add_point(mQ, mG, mG, &m, &mp);
+
+ /* reduce */
+ if (err == MP_OKAY)
+ err = ecc_map(mG, &m, &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, &m);
+#endif /* ECC_SHAMIR */
+
+ /* v = X_x1 mod n */
+ if (err == MP_OKAY)
+ err = mp_mod(mG->x, &p, &v);
+
+ /* does v == r */
+ if (err == MP_OKAY) {
+ if (mp_cmp(&v, &r) == MP_EQ)
+ *stat = 1;
+ }
+
+ ecc_del_point(mG);
+ ecc_del_point(mQ);
+
+ mp_clear(&r);
+ mp_clear(&s);
+ mp_clear(&v);
+ mp_clear(&w);
+ mp_clear(&u1);
+ mp_clear(&u2);
+ mp_clear(&p);
+ mp_clear(&e);
+ mp_clear(&m);
+
+ return err;
+}
+
+
+/* export public ECC key in ANSI X9.63 format */
+int wc_ecc_export_x963(ecc_key* key, byte* out, word32* outLen)
+{
+#ifdef WOLFSSL_SMALL_STACK
+ byte* buf;
+#else
+ byte buf[ECC_BUFSIZE];
+#endif
+ word32 numlen;
+ int ret = MP_OKAY;
+
+ /* 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 (ecc_is_valid_idx(key->idx) == 0) {
+ return ECC_BAD_ARG_E;
+ }
+ numlen = key->dp->size;
+
+ if (*outLen < (1 + 2*numlen)) {
+ *outLen = 1 + 2*numlen;
+ return BUFFER_E;
+ }
+
+ /* store byte 0x04 */
+ out[0] = 0x04;
+
+#ifdef WOLFSSL_SMALL_STACK
+ buf = (byte*)XMALLOC(ECC_BUFSIZE, NULL, DYNAMIC_TYPE_TMP_BUFFER);
+ if (buf == NULL)
+ return MEMORY_E;
+#endif
+
+ do {
+ /* pad and store x */
+ XMEMSET(buf, 0, ECC_BUFSIZE);
+ ret = mp_to_unsigned_bin(key->pubkey.x,
+ buf + (numlen - mp_unsigned_bin_size(key->pubkey.x)));
+ if (ret != MP_OKAY)
+ break;
+ XMEMCPY(out+1, buf, numlen);
+
+ /* pad and store y */
+ XMEMSET(buf, 0, ECC_BUFSIZE);
+ ret = mp_to_unsigned_bin(key->pubkey.y,
+ buf + (numlen - mp_unsigned_bin_size(key->pubkey.y)));
+ if (ret != MP_OKAY)
+ break;
+ XMEMCPY(out+1+numlen, buf, numlen);
+
+ *outLen = 1 + 2*numlen;
+ } while (0);
+
+#ifdef WOLFSSL_SMALL_STACK
+ XFREE(buf, NULL, DYNAMIC_TYPE_TMP_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);
+#endif
+
+ return NOT_COMPILED_IN;
+}
+
+
+/* is ec point on curve descriped by dp ? */
+static int ecc_is_point(const ecc_set_type* dp, ecc_point* ecp, mp_int* prime)
+{
+ mp_int b, t1, t2;
+ int err;
+
+ if ((err = mp_init_multi(&b, &t1, &t2, NULL, NULL, NULL)) != MP_OKAY) {
+ return err;
+ }
+
+ /* load b */
+ err = mp_read_radix(&b, dp->Bf, 16);
+
+ /* 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);
+
+ /* 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);
+
+ while (err == MP_OKAY && mp_cmp_d(&t1, 0) == MP_LT) {
+ 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(&b);
+ mp_clear(&t1);
+ mp_clear(&t2);
+
+ return err;
+}
+
+
+/* validate privkey * generator == pubkey, 0 on success */
+static int ecc_check_privkey_gen(ecc_key* key, mp_int* prime)
+{
+ ecc_point* base = NULL;
+ ecc_point* res = NULL;
+ int err;
+
+ if (key == NULL)
+ return BAD_FUNC_ARG;
+
+ base = ecc_new_point();
+ if (base == NULL)
+ return MEMORY_E;
+
+ /* set up base generator */
+ err = mp_read_radix(base->x, (char*)key->dp->Gx, 16);
+ if (err == MP_OKAY)
+ err = mp_read_radix(base->y, (char*)key->dp->Gy, 16);
+ if (err == MP_OKAY)
+ mp_set(base->z, 1);
+
+ if (err == MP_OKAY) {
+ res = ecc_new_point();
+ if (res == NULL)
+ err = MEMORY_E;
+ else {
+ err = ecc_mulmod(&key->k, base, res, prime, 1);
+ 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;
+ }
+ }
+ }
+ }
+
+ ecc_del_point(res);
+ ecc_del_point(base);
+
+ return err;
+}
+
+
+#ifdef WOLFSSL_VALIDATE_ECC_IMPORT
+
+/* check privkey generator helper, creates prime needed */
+static int ecc_check_privkey_gen_helper(ecc_key* key)
+{
+ mp_int prime;
+ int err;
+
+ if (key == NULL)
+ return BAD_FUNC_ARG;
+
+ err = mp_init(&prime);
+ if (err != MP_OKAY)
+ return err;
+
+ err = mp_read_radix(&prime, (char*)key->dp->prime, 16);
+
+ if (err == MP_OKAY);
+ err = ecc_check_privkey_gen(key, &prime);
+
+ mp_clear(&prime);
+
+ return err;
+}
+
+#endif /* WOLFSSL_VALIDATE_ECC_IMPORT */
+
+
+/* validate order * pubkey = point at infinity, 0 on success */
+static int ecc_check_pubkey_order(ecc_key* key, mp_int* prime, mp_int* order)
+{
+ ecc_point* inf = NULL;
+ int err;
+
+ if (key == NULL)
+ return BAD_FUNC_ARG;
+
+ inf = ecc_new_point();
+ if (inf == NULL)
+ err = MEMORY_E;
+ else {
+ err = ecc_mulmod(order, &key->pubkey, inf, prime, 1);
+ if (err == MP_OKAY && !ecc_point_is_at_infinity(inf))
+ err = ECC_INF_E;
+ }
+
+ ecc_del_point(inf);
+
+ return err;
+}
+
+
+/* perform sanity checks on ec key validity, 0 on success */
+int wc_ecc_check_key(ecc_key* key)
+{
+ mp_int prime; /* used by multiple calls so let's cache */
+ mp_int order; /* other callers have, so let's gen here */
+ int err;
+
+ if (key == NULL)
+ return BAD_FUNC_ARG;
+
+ /* pubkey point cannot be at inifinity */
+ if (ecc_point_is_at_infinity(&key->pubkey))
+ return ECC_INF_E;
+
+ err = mp_init_multi(&prime, &order, NULL, NULL, NULL, NULL);
+ if (err != MP_OKAY)
+ return err;
+
+ err = mp_read_radix(&prime, (char*)key->dp->prime, 16);
+
+ /* make sure point is actually on curve */
+ if (err == MP_OKAY)
+ err = ecc_is_point(key->dp, &key->pubkey, &prime);
+
+ if (err == MP_OKAY)
+ err = mp_read_radix(&order, (char*)key->dp->order, 16);
+
+ /* pubkey * order must be at infinity */
+ if (err == MP_OKAY)
+ err = ecc_check_pubkey_order(key, &prime, &order);
+
+ /* private * base generator must equal pubkey */
+ if (err == MP_OKAY && key->type == ECC_PRIVATEKEY)
+ err = ecc_check_privkey_gen(key, &prime);
+
+ mp_clear(&order);
+ mp_clear(&prime);
+
+ return err;
+}
+
+
+/* import public ECC key in ANSI X9.63 format */
+int wc_ecc_import_x963(const byte* in, word32 inLen, ecc_key* key)
+{
+ int x, err;
+ int compressed = 0;
+
+ if (in == NULL || key == NULL)
+ return ECC_BAD_ARG_E;
+
+ /* must be odd */
+ if ((inLen & 1) == 0) {
+ return ECC_BAD_ARG_E;
+ }
+
+ /* 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->pubkey.x, key->pubkey.y, key->pubkey.z, &key->k,
+ NULL, NULL);
+#endif
+ if (err != MP_OKAY)
+ return MEMORY_E;
+
+ /* check for 4, 2, or 3 */
+ if (in[0] != 0x04 && in[0] != 0x02 && in[0] != 0x03) {
+ err = ASN_PARSE_E;
+ }
+
+ if (in[0] == 0x02 || in[0] == 0x03) {
+#ifdef HAVE_COMP_KEY
+ compressed = 1;
+#else
+ err = NOT_COMPILED_IN;
+#endif
+ }
+
+ if (err == MP_OKAY) {
+ /* determine the idx */
+
+ if (compressed)
+ inLen = (inLen-1)*2 + 1; /* used uncompressed len */
+
+ for (x = 0; ecc_sets[x].size != 0; x++) {
+ if ((unsigned)ecc_sets[x].size >= ((inLen-1)>>1)) {
+ break;
+ }
+ }
+ if (ecc_sets[x].size == 0) {
+ err = ASN_PARSE_E;
+ } else {
+ /* set the idx */
+ key->idx = x;
+ key->dp = &ecc_sets[x];
+ key->type = ECC_PUBLICKEY;
+ }
+ }
+
+ /* read data */
+ if (err == MP_OKAY)
+ err = mp_read_unsigned_bin(key->pubkey.x, (byte*)in+1, (inLen-1)>>1);
+
+#ifdef HAVE_COMP_KEY
+ if (err == MP_OKAY && compressed == 1) { /* build y */
+ mp_int t1, t2, prime, a, b;
+
+ if (mp_init_multi(&t1, &t2, &prime, &a, &b, NULL) != MP_OKAY)
+ err = MEMORY_E;
+
+ /* load prime */
+ if (err == MP_OKAY)
+ err = mp_read_radix(&prime, (char *)key->dp->prime, 16);
+
+ /* load a */
+ if (err == MP_OKAY)
+ err = mp_read_radix(&a, (char *)key->dp->Af, 16);
+
+ /* load b */
+ if (err == MP_OKAY)
+ err = mp_read_radix(&b, (char *)key->dp->Bf, 16);
+
+ /* 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, &prime, &t1);
+
+ /* compute x^3 + a*x */
+ if (err == MP_OKAY)
+ err = mp_mulmod(&a, key->pubkey.x, &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, &b, &t1);
+
+ /* compute sqrt(x^3 + a*x + b) */
+ if (err == MP_OKAY)
+ err = mp_sqrtmod_prime(&t1, &prime, &t2);
+
+ /* adjust y */
+ if (err == MP_OKAY) {
+ if ((mp_isodd(&t2) && in[0] == 0x03) ||
+ (!mp_isodd(&t2) && in[0] == 0x02)) {
+ err = mp_mod(&t2, &prime, key->pubkey.y);
+ }
+ else {
+ err = mp_submod(&prime, &t2, &prime, key->pubkey.y);
+ }
+ }
+
+ mp_clear(&a);
+ mp_clear(&b);
+ mp_clear(&prime);
+ mp_clear(&t2);
+ mp_clear(&t1);
+ }
+#endif
+
+ if (err == MP_OKAY && compressed == 0)
+ err = mp_read_unsigned_bin(key->pubkey.y, (byte*)in+1+((inLen-1)>>1),
+ (inLen-1)>>1);
+ if (err == MP_OKAY)
+ 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;
+}
+
+
+/* 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 ECC_BAD_ARG_E;
+
+ if (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);
+ return mp_to_unsigned_bin(&key->k, out + (numlen -
+ mp_unsigned_bin_size(&key->k)));
+}
+
+
+/* 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)
+{
+ int ret = wc_ecc_import_x963(pub, pubSz, key);
+ if (ret != 0)
+ return ret;
+
+ key->type = ECC_PRIVATEKEY;
+
+ ret = mp_read_unsigned_bin(&key->k, priv, privSz);
+
+#ifdef WOLFSSL_VALIDATE_ECC_IMPORT
+ if (ret == MP_OKAY)
+ ret = ecc_check_privkey_gen_helper(key);
+#endif
+
+ return ret;
+}
+
+/**
+ Convert ECC R,S to signature
+ r R component of signature
+ s S component of signature
+ out DER-encoded ECDSA signature
+ outlen [in/out] output buffer size, output signature size
+ return MP_OKAY on success
+*/
+int wc_ecc_rs_to_sig(const char* r, const char* s, byte* out, word32* outlen)
+{
+ int err;
+ mp_int rtmp;
+ mp_int stmp;
+
+ if (r == NULL || s == NULL || out == NULL || outlen == NULL)
+ return ECC_BAD_ARG_E;
+
+ err = mp_init_multi(&rtmp, &stmp, NULL, NULL, NULL, NULL);
+ if (err != MP_OKAY)
+ return err;
+
+ err = mp_read_radix(&rtmp, r, 16);
+ if (err == MP_OKAY)
+ err = mp_read_radix(&stmp, s, 16);
+
+ /* convert mp_ints to ECDSA sig, initializes rtmp and stmp internally */
+ if (err == MP_OKAY)
+ err = StoreECC_DSA_Sig(out, outlen, &rtmp, &stmp);
+
+ if (err == MP_OKAY) {
+ if (mp_iszero(&rtmp) || mp_iszero(&stmp))
+ err = MP_ZERO_E;
+ }
+
+ mp_clear(&rtmp);
+ mp_clear(&stmp);
+
+ return err;
+}
+
+/**
+ Import raw ECC key
+ key The destination ecc_key structure
+ qx x component of base point, as ASCII hex string
+ qy y component of base point, as ASCII hex string
+ d private key, as ASCII hex string
+ 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 (key == NULL || qx == NULL || qy == NULL || d == NULL ||
+ curveName == NULL)
+ return ECC_BAD_ARG_E;
+
+ /* 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->pubkey.x, key->pubkey.y, key->pubkey.z, &key->k,
+ NULL, NULL);
+#endif
+ if (err != MP_OKAY)
+ return MEMORY_E;
+
+ /* read Qx */
+ if (err == MP_OKAY)
+ err = mp_read_radix(key->pubkey.x, qx, 16);
+
+ /* read Qy */
+ if (err == MP_OKAY)
+ err = mp_read_radix(key->pubkey.y, qy, 16);
+
+ if (err == MP_OKAY)
+ mp_set(key->pubkey.z, 1);
+
+ /* read and set the curve */
+ if (err == MP_OKAY) {
+ 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) {
+ err = ASN_PARSE_E;
+ } else {
+ /* set the curve */
+ key->idx = x;
+ key->dp = &ecc_sets[x];
+ key->type = ECC_PUBLICKEY;
+ }
+ }
+
+ /* import private key */
+ if (err == MP_OKAY) {
+ key->type = ECC_PRIVATEKEY;
+ err = mp_read_radix(&key->k, d, 16);
+ }
+
+#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;
+}
+
+
+/* key size in octets */
+int wc_ecc_size(ecc_key* key)
+{
+ if (key == NULL) return 0;
+
+ return key->dp->size;
+}
+
+
+/* worst case estimate, check actual return from wc_ecc_sign_hash for actual value
+ of signature size in octets */
+int wc_ecc_sig_size(ecc_key* key)
+{
+ int sz = wc_ecc_size(key);
+ if (sz <= 0)
+ return sz;
+
+ return sz * 2 + SIG_HEADER_SZ + 4; /* (4) worst case estimate */
+}
+
+
+#ifdef FP_ECC
+
+/* fixed point ECC cache */
+/* number of entries in the cache */
+#ifndef FP_ENTRIES
+ #define FP_ENTRIES 16
+#endif
+
+/* number of bits in LUT */
+#ifndef FP_LUT
+ #define FP_LUT 8U
+#endif
+
+#ifdef ECC_SHAMIR
+ /* Sharmir requires a bigger LUT, TAO */
+ #if (FP_LUT > 12) || (FP_LUT < 4)
+ #error FP_LUT must be between 4 and 12 inclusively
+ #endif
+#else
+ #if (FP_LUT > 12) || (FP_LUT < 2)
+ #error FP_LUT must be between 2 and 12 inclusively
+ #endif
+#endif
+
+
+/** Our FP cache */
+typedef struct {
+ ecc_point* g; /* cached COPY of base point */
+ ecc_point* LUT[1U<<FP_LUT]; /* fixed point lookup */
+ mp_int mu; /* copy of the montgomery constant */
+ int lru_count; /* amount of times this entry has been used */
+ int lock; /* flag to indicate cache eviction */
+ /* permitted (0) or not (1) */
+} fp_cache_t;
+
+/* if HAVE_THREAD_LS this cache is per thread, no locking needed */
+static THREAD_LS_T fp_cache_t fp_cache[FP_ENTRIES];
+
+#ifndef HAVE_THREAD_LS
+ static volatile int initMutex = 0; /* prevent multiple mutex inits */
+ static wolfSSL_Mutex ecc_fp_lock;
+#endif /* HAVE_THREAD_LS */
+
+/* simple table to help direct the generation of the LUT */
+static const struct {
+ int ham, terma, termb;
+} lut_orders[] = {
+ { 0, 0, 0 }, { 1, 0, 0 }, { 1, 0, 0 }, { 2, 1, 2 }, { 1, 0, 0 }, { 2, 1, 4 }, { 2, 2, 4 }, { 3, 3, 4 },
+ { 1, 0, 0 }, { 2, 1, 8 }, { 2, 2, 8 }, { 3, 3, 8 }, { 2, 4, 8 }, { 3, 5, 8 }, { 3, 6, 8 }, { 4, 7, 8 },
+ { 1, 0, 0 }, { 2, 1, 16 }, { 2, 2, 16 }, { 3, 3, 16 }, { 2, 4, 16 }, { 3, 5, 16 }, { 3, 6, 16 }, { 4, 7, 16 },
+ { 2, 8, 16 }, { 3, 9, 16 }, { 3, 10, 16 }, { 4, 11, 16 }, { 3, 12, 16 }, { 4, 13, 16 }, { 4, 14, 16 }, { 5, 15, 16 },
+ { 1, 0, 0 }, { 2, 1, 32 }, { 2, 2, 32 }, { 3, 3, 32 }, { 2, 4, 32 }, { 3, 5, 32 }, { 3, 6, 32 }, { 4, 7, 32 },
+ { 2, 8, 32 }, { 3, 9, 32 }, { 3, 10, 32 }, { 4, 11, 32 }, { 3, 12, 32 }, { 4, 13, 32 }, { 4, 14, 32 }, { 5, 15, 32 },
+ { 2, 16, 32 }, { 3, 17, 32 }, { 3, 18, 32 }, { 4, 19, 32 }, { 3, 20, 32 }, { 4, 21, 32 }, { 4, 22, 32 }, { 5, 23, 32 },
+ { 3, 24, 32 }, { 4, 25, 32 }, { 4, 26, 32 }, { 5, 27, 32 }, { 4, 28, 32 }, { 5, 29, 32 }, { 5, 30, 32 }, { 6, 31, 32 },
+#if FP_LUT > 6
+ { 1, 0, 0 }, { 2, 1, 64 }, { 2, 2, 64 }, { 3, 3, 64 }, { 2, 4, 64 }, { 3, 5, 64 }, { 3, 6, 64 }, { 4, 7, 64 },
+ { 2, 8, 64 }, { 3, 9, 64 }, { 3, 10, 64 }, { 4, 11, 64 }, { 3, 12, 64 }, { 4, 13, 64 }, { 4, 14, 64 }, { 5, 15, 64 },
+ { 2, 16, 64 }, { 3, 17, 64 }, { 3, 18, 64 }, { 4, 19, 64 }, { 3, 20, 64 }, { 4, 21, 64 }, { 4, 22, 64 }, { 5, 23, 64 },
+ { 3, 24, 64 }, { 4, 25, 64 }, { 4, 26, 64 }, { 5, 27, 64 }, { 4, 28, 64 }, { 5, 29, 64 }, { 5, 30, 64 }, { 6, 31, 64 },
+ { 2, 32, 64 }, { 3, 33, 64 }, { 3, 34, 64 }, { 4, 35, 64 }, { 3, 36, 64 }, { 4, 37, 64 }, { 4, 38, 64 }, { 5, 39, 64 },
+ { 3, 40, 64 }, { 4, 41, 64 }, { 4, 42, 64 }, { 5, 43, 64 }, { 4, 44, 64 }, { 5, 45, 64 }, { 5, 46, 64 }, { 6, 47, 64 },
+ { 3, 48, 64 }, { 4, 49, 64 }, { 4, 50, 64 }, { 5, 51, 64 }, { 4, 52, 64 }, { 5, 53, 64 }, { 5, 54, 64 }, { 6, 55, 64 },
+ { 4, 56, 64 }, { 5, 57, 64 }, { 5, 58, 64 }, { 6, 59, 64 }, { 5, 60, 64 }, { 6, 61, 64 }, { 6, 62, 64 }, { 7, 63, 64 },
+#if FP_LUT > 7
+ { 1, 0, 0 }, { 2, 1, 128 }, { 2, 2, 128 }, { 3, 3, 128 }, { 2, 4, 128 }, { 3, 5, 128 }, { 3, 6, 128 }, { 4, 7, 128 },
+ { 2, 8, 128 }, { 3, 9, 128 }, { 3, 10, 128 }, { 4, 11, 128 }, { 3, 12, 128 }, { 4, 13, 128 }, { 4, 14, 128 }, { 5, 15, 128 },
+ { 2, 16, 128 }, { 3, 17, 128 }, { 3, 18, 128 }, { 4, 19, 128 }, { 3, 20, 128 }, { 4, 21, 128 }, { 4, 22, 128 }, { 5, 23, 128 },
+ { 3, 24, 128 }, { 4, 25, 128 }, { 4, 26, 128 }, { 5, 27, 128 }, { 4, 28, 128 }, { 5, 29, 128 }, { 5, 30, 128 }, { 6, 31, 128 },
+ { 2, 32, 128 }, { 3, 33, 128 }, { 3, 34, 128 }, { 4, 35, 128 }, { 3, 36, 128 }, { 4, 37, 128 }, { 4, 38, 128 }, { 5, 39, 128 },
+ { 3, 40, 128 }, { 4, 41, 128 }, { 4, 42, 128 }, { 5, 43, 128 }, { 4, 44, 128 }, { 5, 45, 128 }, { 5, 46, 128 }, { 6, 47, 128 },
+ { 3, 48, 128 }, { 4, 49, 128 }, { 4, 50, 128 }, { 5, 51, 128 }, { 4, 52, 128 }, { 5, 53, 128 }, { 5, 54, 128 }, { 6, 55, 128 },
+ { 4, 56, 128 }, { 5, 57, 128 }, { 5, 58, 128 }, { 6, 59, 128 }, { 5, 60, 128 }, { 6, 61, 128 }, { 6, 62, 128 }, { 7, 63, 128 },
+ { 2, 64, 128 }, { 3, 65, 128 }, { 3, 66, 128 }, { 4, 67, 128 }, { 3, 68, 128 }, { 4, 69, 128 }, { 4, 70, 128 }, { 5, 71, 128 },
+ { 3, 72, 128 }, { 4, 73, 128 }, { 4, 74, 128 }, { 5, 75, 128 }, { 4, 76, 128 }, { 5, 77, 128 }, { 5, 78, 128 }, { 6, 79, 128 },
+ { 3, 80, 128 }, { 4, 81, 128 }, { 4, 82, 128 }, { 5, 83, 128 }, { 4, 84, 128 }, { 5, 85, 128 }, { 5, 86, 128 }, { 6, 87, 128 },
+ { 4, 88, 128 }, { 5, 89, 128 }, { 5, 90, 128 }, { 6, 91, 128 }, { 5, 92, 128 }, { 6, 93, 128 }, { 6, 94, 128 }, { 7, 95, 128 },
+ { 3, 96, 128 }, { 4, 97, 128 }, { 4, 98, 128 }, { 5, 99, 128 }, { 4, 100, 128 }, { 5, 101, 128 }, { 5, 102, 128 }, { 6, 103, 128 },
+ { 4, 104, 128 }, { 5, 105, 128 }, { 5, 106, 128 }, { 6, 107, 128 }, { 5, 108, 128 }, { 6, 109, 128 }, { 6, 110, 128 }, { 7, 111, 128 },
+ { 4, 112, 128 }, { 5, 113, 128 }, { 5, 114, 128 }, { 6, 115, 128 }, { 5, 116, 128 }, { 6, 117, 128 }, { 6, 118, 128 }, { 7, 119, 128 },
+ { 5, 120, 128 }, { 6, 121, 128 }, { 6, 122, 128 }, { 7, 123, 128 }, { 6, 124, 128 }, { 7, 125, 128 }, { 7, 126, 128 }, { 8, 127, 128 },
+#if FP_LUT > 8
+ { 1, 0, 0 }, { 2, 1, 256 }, { 2, 2, 256 }, { 3, 3, 256 }, { 2, 4, 256 }, { 3, 5, 256 }, { 3, 6, 256 }, { 4, 7, 256 },
+ { 2, 8, 256 }, { 3, 9, 256 }, { 3, 10, 256 }, { 4, 11, 256 }, { 3, 12, 256 }, { 4, 13, 256 }, { 4, 14, 256 }, { 5, 15, 256 },
+ { 2, 16, 256 }, { 3, 17, 256 }, { 3, 18, 256 }, { 4, 19, 256 }, { 3, 20, 256 }, { 4, 21, 256 }, { 4, 22, 256 }, { 5, 23, 256 },
+ { 3, 24, 256 }, { 4, 25, 256 }, { 4, 26, 256 }, { 5, 27, 256 }, { 4, 28, 256 }, { 5, 29, 256 }, { 5, 30, 256 }, { 6, 31, 256 },
+ { 2, 32, 256 }, { 3, 33, 256 }, { 3, 34, 256 }, { 4, 35, 256 }, { 3, 36, 256 }, { 4, 37, 256 }, { 4, 38, 256 }, { 5, 39, 256 },
+ { 3, 40, 256 }, { 4, 41, 256 }, { 4, 42, 256 }, { 5, 43, 256 }, { 4, 44, 256 }, { 5, 45, 256 }, { 5, 46, 256 }, { 6, 47, 256 },
+ { 3, 48, 256 }, { 4, 49, 256 }, { 4, 50, 256 }, { 5, 51, 256 }, { 4, 52, 256 }, { 5, 53, 256 }, { 5, 54, 256 }, { 6, 55, 256 },
+ { 4, 56, 256 }, { 5, 57, 256 }, { 5, 58, 256 }, { 6, 59, 256 }, { 5, 60, 256 }, { 6, 61, 256 }, { 6, 62, 256 }, { 7, 63, 256 },
+ { 2, 64, 256 }, { 3, 65, 256 }, { 3, 66, 256 }, { 4, 67, 256 }, { 3, 68, 256 }, { 4, 69, 256 }, { 4, 70, 256 }, { 5, 71, 256 },
+ { 3, 72, 256 }, { 4, 73, 256 }, { 4, 74, 256 }, { 5, 75, 256 }, { 4, 76, 256 }, { 5, 77, 256 }, { 5, 78, 256 }, { 6, 79, 256 },
+ { 3, 80, 256 }, { 4, 81, 256 }, { 4, 82, 256 }, { 5, 83, 256 }, { 4, 84, 256 }, { 5, 85, 256 }, { 5, 86, 256 }, { 6, 87, 256 },
+ { 4, 88, 256 }, { 5, 89, 256 }, { 5, 90, 256 }, { 6, 91, 256 }, { 5, 92, 256 }, { 6, 93, 256 }, { 6, 94, 256 }, { 7, 95, 256 },
+ { 3, 96, 256 }, { 4, 97, 256 }, { 4, 98, 256 }, { 5, 99, 256 }, { 4, 100, 256 }, { 5, 101, 256 }, { 5, 102, 256 }, { 6, 103, 256 },
+ { 4, 104, 256 }, { 5, 105, 256 }, { 5, 106, 256 }, { 6, 107, 256 }, { 5, 108, 256 }, { 6, 109, 256 }, { 6, 110, 256 }, { 7, 111, 256 },
+ { 4, 112, 256 }, { 5, 113, 256 }, { 5, 114, 256 }, { 6, 115, 256 }, { 5, 116, 256 }, { 6, 117, 256 }, { 6, 118, 256 }, { 7, 119, 256 },
+ { 5, 120, 256 }, { 6, 121, 256 }, { 6, 122, 256 }, { 7, 123, 256 }, { 6, 124, 256 }, { 7, 125, 256 }, { 7, 126, 256 }, { 8, 127, 256 },
+ { 2, 128, 256 }, { 3, 129, 256 }, { 3, 130, 256 }, { 4, 131, 256 }, { 3, 132, 256 }, { 4, 133, 256 }, { 4, 134, 256 }, { 5, 135, 256 },
+ { 3, 136, 256 }, { 4, 137, 256 }, { 4, 138, 256 }, { 5, 139, 256 }, { 4, 140, 256 }, { 5, 141, 256 }, { 5, 142, 256 }, { 6, 143, 256 },
+ { 3, 144, 256 }, { 4, 145, 256 }, { 4, 146, 256 }, { 5, 147, 256 }, { 4, 148, 256 }, { 5, 149, 256 }, { 5, 150, 256 }, { 6, 151, 256 },
+ { 4, 152, 256 }, { 5, 153, 256 }, { 5, 154, 256 }, { 6, 155, 256 }, { 5, 156, 256 }, { 6, 157, 256 }, { 6, 158, 256 }, { 7, 159, 256 },
+ { 3, 160, 256 }, { 4, 161, 256 }, { 4, 162, 256 }, { 5, 163, 256 }, { 4, 164, 256 }, { 5, 165, 256 }, { 5, 166, 256 }, { 6, 167, 256 },
+ { 4, 168, 256 }, { 5, 169, 256 }, { 5, 170, 256 }, { 6, 171, 256 }, { 5, 172, 256 }, { 6, 173, 256 }, { 6, 174, 256 }, { 7, 175, 256 },
+ { 4, 176, 256 }, { 5, 177, 256 }, { 5, 178, 256 }, { 6, 179, 256 }, { 5, 180, 256 }, { 6, 181, 256 }, { 6, 182, 256 }, { 7, 183, 256 },
+ { 5, 184, 256 }, { 6, 185, 256 }, { 6, 186, 256 }, { 7, 187, 256 }, { 6, 188, 256 }, { 7, 189, 256 }, { 7, 190, 256 }, { 8, 191, 256 },
+ { 3, 192, 256 }, { 4, 193, 256 }, { 4, 194, 256 }, { 5, 195, 256 }, { 4, 196, 256 }, { 5, 197, 256 }, { 5, 198, 256 }, { 6, 199, 256 },
+ { 4, 200, 256 }, { 5, 201, 256 }, { 5, 202, 256 }, { 6, 203, 256 }, { 5, 204, 256 }, { 6, 205, 256 }, { 6, 206, 256 }, { 7, 207, 256 },
+ { 4, 208, 256 }, { 5, 209, 256 }, { 5, 210, 256 }, { 6, 211, 256 }, { 5, 212, 256 }, { 6, 213, 256 }, { 6, 214, 256 }, { 7, 215, 256 },
+ { 5, 216, 256 }, { 6, 217, 256 }, { 6, 218, 256 }, { 7, 219, 256 }, { 6, 220, 256 }, { 7, 221, 256 }, { 7, 222, 256 }, { 8, 223, 256 },
+ { 4, 224, 256 }, { 5, 225, 256 }, { 5, 226, 256 }, { 6, 227, 256 }, { 5, 228, 256 }, { 6, 229, 256 }, { 6, 230, 256 }, { 7, 231, 256 },
+ { 5, 232, 256 }, { 6, 233, 256 }, { 6, 234, 256 }, { 7, 235, 256 }, { 6, 236, 256 }, { 7, 237, 256 }, { 7, 238, 256 }, { 8, 239, 256 },
+ { 5, 240, 256 }, { 6, 241, 256 }, { 6, 242, 256 }, { 7, 243, 256 }, { 6, 244, 256 }, { 7, 245, 256 }, { 7, 246, 256 }, { 8, 247, 256 },
+ { 6, 248, 256 }, { 7, 249, 256 }, { 7, 250, 256 }, { 8, 251, 256 }, { 7, 252, 256 }, { 8, 253, 256 }, { 8, 254, 256 }, { 9, 255, 256 },
+#if FP_LUT > 9
+ { 1, 0, 0 }, { 2, 1, 512 }, { 2, 2, 512 }, { 3, 3, 512 }, { 2, 4, 512 }, { 3, 5, 512 }, { 3, 6, 512 }, { 4, 7, 512 },
+ { 2, 8, 512 }, { 3, 9, 512 }, { 3, 10, 512 }, { 4, 11, 512 }, { 3, 12, 512 }, { 4, 13, 512 }, { 4, 14, 512 }, { 5, 15, 512 },
+ { 2, 16, 512 }, { 3, 17, 512 }, { 3, 18, 512 }, { 4, 19, 512 }, { 3, 20, 512 }, { 4, 21, 512 }, { 4, 22, 512 }, { 5, 23, 512 },
+ { 3, 24, 512 }, { 4, 25, 512 }, { 4, 26, 512 }, { 5, 27, 512 }, { 4, 28, 512 }, { 5, 29, 512 }, { 5, 30, 512 }, { 6, 31, 512 },
+ { 2, 32, 512 }, { 3, 33, 512 }, { 3, 34, 512 }, { 4, 35, 512 }, { 3, 36, 512 }, { 4, 37, 512 }, { 4, 38, 512 }, { 5, 39, 512 },
+ { 3, 40, 512 }, { 4, 41, 512 }, { 4, 42, 512 }, { 5, 43, 512 }, { 4, 44, 512 }, { 5, 45, 512 }, { 5, 46, 512 }, { 6, 47, 512 },
+ { 3, 48, 512 }, { 4, 49, 512 }, { 4, 50, 512 }, { 5, 51, 512 }, { 4, 52, 512 }, { 5, 53, 512 }, { 5, 54, 512 }, { 6, 55, 512 },
+ { 4, 56, 512 }, { 5, 57, 512 }, { 5, 58, 512 }, { 6, 59, 512 }, { 5, 60, 512 }, { 6, 61, 512 }, { 6, 62, 512 }, { 7, 63, 512 },
+ { 2, 64, 512 }, { 3, 65, 512 }, { 3, 66, 512 }, { 4, 67, 512 }, { 3, 68, 512 }, { 4, 69, 512 }, { 4, 70, 512 }, { 5, 71, 512 },
+ { 3, 72, 512 }, { 4, 73, 512 }, { 4, 74, 512 }, { 5, 75, 512 }, { 4, 76, 512 }, { 5, 77, 512 }, { 5, 78, 512 }, { 6, 79, 512 },
+ { 3, 80, 512 }, { 4, 81, 512 }, { 4, 82, 512 }, { 5, 83, 512 }, { 4, 84, 512 }, { 5, 85, 512 }, { 5, 86, 512 }, { 6, 87, 512 },
+ { 4, 88, 512 }, { 5, 89, 512 }, { 5, 90, 512 }, { 6, 91, 512 }, { 5, 92, 512 }, { 6, 93, 512 }, { 6, 94, 512 }, { 7, 95, 512 },
+ { 3, 96, 512 }, { 4, 97, 512 }, { 4, 98, 512 }, { 5, 99, 512 }, { 4, 100, 512 }, { 5, 101, 512 }, { 5, 102, 512 }, { 6, 103, 512 },
+ { 4, 104, 512 }, { 5, 105, 512 }, { 5, 106, 512 }, { 6, 107, 512 }, { 5, 108, 512 }, { 6, 109, 512 }, { 6, 110, 512 }, { 7, 111, 512 },
+ { 4, 112, 512 }, { 5, 113, 512 }, { 5, 114, 512 }, { 6, 115, 512 }, { 5, 116, 512 }, { 6, 117, 512 }, { 6, 118, 512 }, { 7, 119, 512 },
+ { 5, 120, 512 }, { 6, 121, 512 }, { 6, 122, 512 }, { 7, 123, 512 }, { 6, 124, 512 }, { 7, 125, 512 }, { 7, 126, 512 }, { 8, 127, 512 },
+ { 2, 128, 512 }, { 3, 129, 512 }, { 3, 130, 512 }, { 4, 131, 512 }, { 3, 132, 512 }, { 4, 133, 512 }, { 4, 134, 512 }, { 5, 135, 512 },
+ { 3, 136, 512 }, { 4, 137, 512 }, { 4, 138, 512 }, { 5, 139, 512 }, { 4, 140, 512 }, { 5, 141, 512 }, { 5, 142, 512 }, { 6, 143, 512 },
+ { 3, 144, 512 }, { 4, 145, 512 }, { 4, 146, 512 }, { 5, 147, 512 }, { 4, 148, 512 }, { 5, 149, 512 }, { 5, 150, 512 }, { 6, 151, 512 },
+ { 4, 152, 512 }, { 5, 153, 512 }, { 5, 154, 512 }, { 6, 155, 512 }, { 5, 156, 512 }, { 6, 157, 512 }, { 6, 158, 512 }, { 7, 159, 512 },
+ { 3, 160, 512 }, { 4, 161, 512 }, { 4, 162, 512 }, { 5, 163, 512 }, { 4, 164, 512 }, { 5, 165, 512 }, { 5, 166, 512 }, { 6, 167, 512 },
+ { 4, 168, 512 }, { 5, 169, 512 }, { 5, 170, 512 }, { 6, 171, 512 }, { 5, 172, 512 }, { 6, 173, 512 }, { 6, 174, 512 }, { 7, 175, 512 },
+ { 4, 176, 512 }, { 5, 177, 512 }, { 5, 178, 512 }, { 6, 179, 512 }, { 5, 180, 512 }, { 6, 181, 512 }, { 6, 182, 512 }, { 7, 183, 512 },
+ { 5, 184, 512 }, { 6, 185, 512 }, { 6, 186, 512 }, { 7, 187, 512 }, { 6, 188, 512 }, { 7, 189, 512 }, { 7, 190, 512 }, { 8, 191, 512 },
+ { 3, 192, 512 }, { 4, 193, 512 }, { 4, 194, 512 }, { 5, 195, 512 }, { 4, 196, 512 }, { 5, 197, 512 }, { 5, 198, 512 }, { 6, 199, 512 },
+ { 4, 200, 512 }, { 5, 201, 512 }, { 5, 202, 512 }, { 6, 203, 512 }, { 5, 204, 512 }, { 6, 205, 512 }, { 6, 206, 512 }, { 7, 207, 512 },
+ { 4, 208, 512 }, { 5, 209, 512 }, { 5, 210, 512 }, { 6, 211, 512 }, { 5, 212, 512 }, { 6, 213, 512 }, { 6, 214, 512 }, { 7, 215, 512 },
+ { 5, 216, 512 }, { 6, 217, 512 }, { 6, 218, 512 }, { 7, 219, 512 }, { 6, 220, 512 }, { 7, 221, 512 }, { 7, 222, 512 }, { 8, 223, 512 },
+ { 4, 224, 512 }, { 5, 225, 512 }, { 5, 226, 512 }, { 6, 227, 512 }, { 5, 228, 512 }, { 6, 229, 512 }, { 6, 230, 512 }, { 7, 231, 512 },
+ { 5, 232, 512 }, { 6, 233, 512 }, { 6, 234, 512 }, { 7, 235, 512 }, { 6, 236, 512 }, { 7, 237, 512 }, { 7, 238, 512 }, { 8, 239, 512 },
+ { 5, 240, 512 }, { 6, 241, 512 }, { 6, 242, 512 }, { 7, 243, 512 }, { 6, 244, 512 }, { 7, 245, 512 }, { 7, 246, 512 }, { 8, 247, 512 },
+ { 6, 248, 512 }, { 7, 249, 512 }, { 7, 250, 512 }, { 8, 251, 512 }, { 7, 252, 512 }, { 8, 253, 512 }, { 8, 254, 512 }, { 9, 255, 512 },
+ { 2, 256, 512 }, { 3, 257, 512 }, { 3, 258, 512 }, { 4, 259, 512 }, { 3, 260, 512 }, { 4, 261, 512 }, { 4, 262, 512 }, { 5, 263, 512 },
+ { 3, 264, 512 }, { 4, 265, 512 }, { 4, 266, 512 }, { 5, 267, 512 }, { 4, 268, 512 }, { 5, 269, 512 }, { 5, 270, 512 }, { 6, 271, 512 },
+ { 3, 272, 512 }, { 4, 273, 512 }, { 4, 274, 512 }, { 5, 275, 512 }, { 4, 276, 512 }, { 5, 277, 512 }, { 5, 278, 512 }, { 6, 279, 512 },
+ { 4, 280, 512 }, { 5, 281, 512 }, { 5, 282, 512 }, { 6, 283, 512 }, { 5, 284, 512 }, { 6, 285, 512 }, { 6, 286, 512 }, { 7, 287, 512 },
+ { 3, 288, 512 }, { 4, 289, 512 }, { 4, 290, 512 }, { 5, 291, 512 }, { 4, 292, 512 }, { 5, 293, 512 }, { 5, 294, 512 }, { 6, 295, 512 },
+ { 4, 296, 512 }, { 5, 297, 512 }, { 5, 298, 512 }, { 6, 299, 512 }, { 5, 300, 512 }, { 6, 301, 512 }, { 6, 302, 512 }, { 7, 303, 512 },
+ { 4, 304, 512 }, { 5, 305, 512 }, { 5, 306, 512 }, { 6, 307, 512 }, { 5, 308, 512 }, { 6, 309, 512 }, { 6, 310, 512 }, { 7, 311, 512 },
+ { 5, 312, 512 }, { 6, 313, 512 }, { 6, 314, 512 }, { 7, 315, 512 }, { 6, 316, 512 }, { 7, 317, 512 }, { 7, 318, 512 }, { 8, 319, 512 },
+ { 3, 320, 512 }, { 4, 321, 512 }, { 4, 322, 512 }, { 5, 323, 512 }, { 4, 324, 512 }, { 5, 325, 512 }, { 5, 326, 512 }, { 6, 327, 512 },
+ { 4, 328, 512 }, { 5, 329, 512 }, { 5, 330, 512 }, { 6, 331, 512 }, { 5, 332, 512 }, { 6, 333, 512 }, { 6, 334, 512 }, { 7, 335, 512 },
+ { 4, 336, 512 }, { 5, 337, 512 }, { 5, 338, 512 }, { 6, 339, 512 }, { 5, 340, 512 }, { 6, 341, 512 }, { 6, 342, 512 }, { 7, 343, 512 },
+ { 5, 344, 512 }, { 6, 345, 512 }, { 6, 346, 512 }, { 7, 347, 512 }, { 6, 348, 512 }, { 7, 349, 512 }, { 7, 350, 512 }, { 8, 351, 512 },
+ { 4, 352, 512 }, { 5, 353, 512 }, { 5, 354, 512 }, { 6, 355, 512 }, { 5, 356, 512 }, { 6, 357, 512 }, { 6, 358, 512 }, { 7, 359, 512 },
+ { 5, 360, 512 }, { 6, 361, 512 }, { 6, 362, 512 }, { 7, 363, 512 }, { 6, 364, 512 }, { 7, 365, 512 }, { 7, 366, 512 }, { 8, 367, 512 },
+ { 5, 368, 512 }, { 6, 369, 512 }, { 6, 370, 512 }, { 7, 371, 512 }, { 6, 372, 512 }, { 7, 373, 512 }, { 7, 374, 512 }, { 8, 375, 512 },
+ { 6, 376, 512 }, { 7, 377, 512 }, { 7, 378, 512 }, { 8, 379, 512 }, { 7, 380, 512 }, { 8, 381, 512 }, { 8, 382, 512 }, { 9, 383, 512 },
+ { 3, 384, 512 }, { 4, 385, 512 }, { 4, 386, 512 }, { 5, 387, 512 }, { 4, 388, 512 }, { 5, 389, 512 }, { 5, 390, 512 }, { 6, 391, 512 },
+ { 4, 392, 512 }, { 5, 393, 512 }, { 5, 394, 512 }, { 6, 395, 512 }, { 5, 396, 512 }, { 6, 397, 512 }, { 6, 398, 512 }, { 7, 399, 512 },
+ { 4, 400, 512 }, { 5, 401, 512 }, { 5, 402, 512 }, { 6, 403, 512 }, { 5, 404, 512 }, { 6, 405, 512 }, { 6, 406, 512 }, { 7, 407, 512 },
+ { 5, 408, 512 }, { 6, 409, 512 }, { 6, 410, 512 }, { 7, 411, 512 }, { 6, 412, 512 }, { 7, 413, 512 }, { 7, 414, 512 }, { 8, 415, 512 },
+ { 4, 416, 512 }, { 5, 417, 512 }, { 5, 418, 512 }, { 6, 419, 512 }, { 5, 420, 512 }, { 6, 421, 512 }, { 6, 422, 512 }, { 7, 423, 512 },
+ { 5, 424, 512 }, { 6, 425, 512 }, { 6, 426, 512 }, { 7, 427, 512 }, { 6, 428, 512 }, { 7, 429, 512 }, { 7, 430, 512 }, { 8, 431, 512 },
+ { 5, 432, 512 }, { 6, 433, 512 }, { 6, 434, 512 }, { 7, 435, 512 }, { 6, 436, 512 }, { 7, 437, 512 }, { 7, 438, 512 }, { 8, 439, 512 },
+ { 6, 440, 512 }, { 7, 441, 512 }, { 7, 442, 512 }, { 8, 443, 512 }, { 7, 444, 512 }, { 8, 445, 512 }, { 8, 446, 512 }, { 9, 447, 512 },
+ { 4, 448, 512 }, { 5, 449, 512 }, { 5, 450, 512 }, { 6, 451, 512 }, { 5, 452, 512 }, { 6, 453, 512 }, { 6, 454, 512 }, { 7, 455, 512 },
+ { 5, 456, 512 }, { 6, 457, 512 }, { 6, 458, 512 }, { 7, 459, 512 }, { 6, 460, 512 }, { 7, 461, 512 }, { 7, 462, 512 }, { 8, 463, 512 },
+ { 5, 464, 512 }, { 6, 465, 512 }, { 6, 466, 512 }, { 7, 467, 512 }, { 6, 468, 512 }, { 7, 469, 512 }, { 7, 470, 512 }, { 8, 471, 512 },
+ { 6, 472, 512 }, { 7, 473, 512 }, { 7, 474, 512 }, { 8, 475, 512 }, { 7, 476, 512 }, { 8, 477, 512 }, { 8, 478, 512 }, { 9, 479, 512 },
+ { 5, 480, 512 }, { 6, 481, 512 }, { 6, 482, 512 }, { 7, 483, 512 }, { 6, 484, 512 }, { 7, 485, 512 }, { 7, 486, 512 }, { 8, 487, 512 },
+ { 6, 488, 512 }, { 7, 489, 512 }, { 7, 490, 512 }, { 8, 491, 512 }, { 7, 492, 512 }, { 8, 493, 512 }, { 8, 494, 512 }, { 9, 495, 512 },
+ { 6, 496, 512 }, { 7, 497, 512 }, { 7, 498, 512 }, { 8, 499, 512 }, { 7, 500, 512 }, { 8, 501, 512 }, { 8, 502, 512 }, { 9, 503, 512 },
+ { 7, 504, 512 }, { 8, 505, 512 }, { 8, 506, 512 }, { 9, 507, 512 }, { 8, 508, 512 }, { 9, 509, 512 }, { 9, 510, 512 }, { 10, 511, 512 },
+#if FP_LUT > 10
+ { 1, 0, 0 }, { 2, 1, 1024 }, { 2, 2, 1024 }, { 3, 3, 1024 }, { 2, 4, 1024 }, { 3, 5, 1024 }, { 3, 6, 1024 }, { 4, 7, 1024 },
+ { 2, 8, 1024 }, { 3, 9, 1024 }, { 3, 10, 1024 }, { 4, 11, 1024 }, { 3, 12, 1024 }, { 4, 13, 1024 }, { 4, 14, 1024 }, { 5, 15, 1024 },
+ { 2, 16, 1024 }, { 3, 17, 1024 }, { 3, 18, 1024 }, { 4, 19, 1024 }, { 3, 20, 1024 }, { 4, 21, 1024 }, { 4, 22, 1024 }, { 5, 23, 1024 },
+ { 3, 24, 1024 }, { 4, 25, 1024 }, { 4, 26, 1024 }, { 5, 27, 1024 }, { 4, 28, 1024 }, { 5, 29, 1024 }, { 5, 30, 1024 }, { 6, 31, 1024 },
+ { 2, 32, 1024 }, { 3, 33, 1024 }, { 3, 34, 1024 }, { 4, 35, 1024 }, { 3, 36, 1024 }, { 4, 37, 1024 }, { 4, 38, 1024 }, { 5, 39, 1024 },
+ { 3, 40, 1024 }, { 4, 41, 1024 }, { 4, 42, 1024 }, { 5, 43, 1024 }, { 4, 44, 1024 }, { 5, 45, 1024 }, { 5, 46, 1024 }, { 6, 47, 1024 },
+ { 3, 48, 1024 }, { 4, 49, 1024 }, { 4, 50, 1024 }, { 5, 51, 1024 }, { 4, 52, 1024 }, { 5, 53, 1024 }, { 5, 54, 1024 }, { 6, 55, 1024 },
+ { 4, 56, 1024 }, { 5, 57, 1024 }, { 5, 58, 1024 }, { 6, 59, 1024 }, { 5, 60, 1024 }, { 6, 61, 1024 }, { 6, 62, 1024 }, { 7, 63, 1024 },
+ { 2, 64, 1024 }, { 3, 65, 1024 }, { 3, 66, 1024 }, { 4, 67, 1024 }, { 3, 68, 1024 }, { 4, 69, 1024 }, { 4, 70, 1024 }, { 5, 71, 1024 },
+ { 3, 72, 1024 }, { 4, 73, 1024 }, { 4, 74, 1024 }, { 5, 75, 1024 }, { 4, 76, 1024 }, { 5, 77, 1024 }, { 5, 78, 1024 }, { 6, 79, 1024 },
+ { 3, 80, 1024 }, { 4, 81, 1024 }, { 4, 82, 1024 }, { 5, 83, 1024 }, { 4, 84, 1024 }, { 5, 85, 1024 }, { 5, 86, 1024 }, { 6, 87, 1024 },
+ { 4, 88, 1024 }, { 5, 89, 1024 }, { 5, 90, 1024 }, { 6, 91, 1024 }, { 5, 92, 1024 }, { 6, 93, 1024 }, { 6, 94, 1024 }, { 7, 95, 1024 },
+ { 3, 96, 1024 }, { 4, 97, 1024 }, { 4, 98, 1024 }, { 5, 99, 1024 }, { 4, 100, 1024 }, { 5, 101, 1024 }, { 5, 102, 1024 }, { 6, 103, 1024 },
+ { 4, 104, 1024 }, { 5, 105, 1024 }, { 5, 106, 1024 }, { 6, 107, 1024 }, { 5, 108, 1024 }, { 6, 109, 1024 }, { 6, 110, 1024 }, { 7, 111, 1024 },
+ { 4, 112, 1024 }, { 5, 113, 1024 }, { 5, 114, 1024 }, { 6, 115, 1024 }, { 5, 116, 1024 }, { 6, 117, 1024 }, { 6, 118, 1024 }, { 7, 119, 1024 },
+ { 5, 120, 1024 }, { 6, 121, 1024 }, { 6, 122, 1024 }, { 7, 123, 1024 }, { 6, 124, 1024 }, { 7, 125, 1024 }, { 7, 126, 1024 }, { 8, 127, 1024 },
+ { 2, 128, 1024 }, { 3, 129, 1024 }, { 3, 130, 1024 }, { 4, 131, 1024 }, { 3, 132, 1024 }, { 4, 133, 1024 }, { 4, 134, 1024 }, { 5, 135, 1024 },
+ { 3, 136, 1024 }, { 4, 137, 1024 }, { 4, 138, 1024 }, { 5, 139, 1024 }, { 4, 140, 1024 }, { 5, 141, 1024 }, { 5, 142, 1024 }, { 6, 143, 1024 },
+ { 3, 144, 1024 }, { 4, 145, 1024 }, { 4, 146, 1024 }, { 5, 147, 1024 }, { 4, 148, 1024 }, { 5, 149, 1024 }, { 5, 150, 1024 }, { 6, 151, 1024 },
+ { 4, 152, 1024 }, { 5, 153, 1024 }, { 5, 154, 1024 }, { 6, 155, 1024 }, { 5, 156, 1024 }, { 6, 157, 1024 }, { 6, 158, 1024 }, { 7, 159, 1024 },
+ { 3, 160, 1024 }, { 4, 161, 1024 }, { 4, 162, 1024 }, { 5, 163, 1024 }, { 4, 164, 1024 }, { 5, 165, 1024 }, { 5, 166, 1024 }, { 6, 167, 1024 },
+ { 4, 168, 1024 }, { 5, 169, 1024 }, { 5, 170, 1024 }, { 6, 171, 1024 }, { 5, 172, 1024 }, { 6, 173, 1024 }, { 6, 174, 1024 }, { 7, 175, 1024 },
+ { 4, 176, 1024 }, { 5, 177, 1024 }, { 5, 178, 1024 }, { 6, 179, 1024 }, { 5, 180, 1024 }, { 6, 181, 1024 }, { 6, 182, 1024 }, { 7, 183, 1024 },
+ { 5, 184, 1024 }, { 6, 185, 1024 }, { 6, 186, 1024 }, { 7, 187, 1024 }, { 6, 188, 1024 }, { 7, 189, 1024 }, { 7, 190, 1024 }, { 8, 191, 1024 },
+ { 3, 192, 1024 }, { 4, 193, 1024 }, { 4, 194, 1024 }, { 5, 195, 1024 }, { 4, 196, 1024 }, { 5, 197, 1024 }, { 5, 198, 1024 }, { 6, 199, 1024 },
+ { 4, 200, 1024 }, { 5, 201, 1024 }, { 5, 202, 1024 }, { 6, 203, 1024 }, { 5, 204, 1024 }, { 6, 205, 1024 }, { 6, 206, 1024 }, { 7, 207, 1024 },
+ { 4, 208, 1024 }, { 5, 209, 1024 }, { 5, 210, 1024 }, { 6, 211, 1024 }, { 5, 212, 1024 }, { 6, 213, 1024 }, { 6, 214, 1024 }, { 7, 215, 1024 },
+ { 5, 216, 1024 }, { 6, 217, 1024 }, { 6, 218, 1024 }, { 7, 219, 1024 }, { 6, 220, 1024 }, { 7, 221, 1024 }, { 7, 222, 1024 }, { 8, 223, 1024 },
+ { 4, 224, 1024 }, { 5, 225, 1024 }, { 5, 226, 1024 }, { 6, 227, 1024 }, { 5, 228, 1024 }, { 6, 229, 1024 }, { 6, 230, 1024 }, { 7, 231, 1024 },
+ { 5, 232, 1024 }, { 6, 233, 1024 }, { 6, 234, 1024 }, { 7, 235, 1024 }, { 6, 236, 1024 }, { 7, 237, 1024 }, { 7, 238, 1024 }, { 8, 239, 1024 },
+ { 5, 240, 1024 }, { 6, 241, 1024 }, { 6, 242, 1024 }, { 7, 243, 1024 }, { 6, 244, 1024 }, { 7, 245, 1024 }, { 7, 246, 1024 }, { 8, 247, 1024 },
+ { 6, 248, 1024 }, { 7, 249, 1024 }, { 7, 250, 1024 }, { 8, 251, 1024 }, { 7, 252, 1024 }, { 8, 253, 1024 }, { 8, 254, 1024 }, { 9, 255, 1024 },
+ { 2, 256, 1024 }, { 3, 257, 1024 }, { 3, 258, 1024 }, { 4, 259, 1024 }, { 3, 260, 1024 }, { 4, 261, 1024 }, { 4, 262, 1024 }, { 5, 263, 1024 },
+ { 3, 264, 1024 }, { 4, 265, 1024 }, { 4, 266, 1024 }, { 5, 267, 1024 }, { 4, 268, 1024 }, { 5, 269, 1024 }, { 5, 270, 1024 }, { 6, 271, 1024 },
+ { 3, 272, 1024 }, { 4, 273, 1024 }, { 4, 274, 1024 }, { 5, 275, 1024 }, { 4, 276, 1024 }, { 5, 277, 1024 }, { 5, 278, 1024 }, { 6, 279, 1024 },
+ { 4, 280, 1024 }, { 5, 281, 1024 }, { 5, 282, 1024 }, { 6, 283, 1024 }, { 5, 284, 1024 }, { 6, 285, 1024 }, { 6, 286, 1024 }, { 7, 287, 1024 },
+ { 3, 288, 1024 }, { 4, 289, 1024 }, { 4, 290, 1024 }, { 5, 291, 1024 }, { 4, 292, 1024 }, { 5, 293, 1024 }, { 5, 294, 1024 }, { 6, 295, 1024 },
+ { 4, 296, 1024 }, { 5, 297, 1024 }, { 5, 298, 1024 }, { 6, 299, 1024 }, { 5, 300, 1024 }, { 6, 301, 1024 }, { 6, 302, 1024 }, { 7, 303, 1024 },
+ { 4, 304, 1024 }, { 5, 305, 1024 }, { 5, 306, 1024 }, { 6, 307, 1024 }, { 5, 308, 1024 }, { 6, 309, 1024 }, { 6, 310, 1024 }, { 7, 311, 1024 },
+ { 5, 312, 1024 }, { 6, 313, 1024 }, { 6, 314, 1024 }, { 7, 315, 1024 }, { 6, 316, 1024 }, { 7, 317, 1024 }, { 7, 318, 1024 }, { 8, 319, 1024 },
+ { 3, 320, 1024 }, { 4, 321, 1024 }, { 4, 322, 1024 }, { 5, 323, 1024 }, { 4, 324, 1024 }, { 5, 325, 1024 }, { 5, 326, 1024 }, { 6, 327, 1024 },
+ { 4, 328, 1024 }, { 5, 329, 1024 }, { 5, 330, 1024 }, { 6, 331, 1024 }, { 5, 332, 1024 }, { 6, 333, 1024 }, { 6, 334, 1024 }, { 7, 335, 1024 },
+ { 4, 336, 1024 }, { 5, 337, 1024 }, { 5, 338, 1024 }, { 6, 339, 1024 }, { 5, 340, 1024 }, { 6, 341, 1024 }, { 6, 342, 1024 }, { 7, 343, 1024 },
+ { 5, 344, 1024 }, { 6, 345, 1024 }, { 6, 346, 1024 }, { 7, 347, 1024 }, { 6, 348, 1024 }, { 7, 349, 1024 }, { 7, 350, 1024 }, { 8, 351, 1024 },
+ { 4, 352, 1024 }, { 5, 353, 1024 }, { 5, 354, 1024 }, { 6, 355, 1024 }, { 5, 356, 1024 }, { 6, 357, 1024 }, { 6, 358, 1024 }, { 7, 359, 1024 },
+ { 5, 360, 1024 }, { 6, 361, 1024 }, { 6, 362, 1024 }, { 7, 363, 1024 }, { 6, 364, 1024 }, { 7, 365, 1024 }, { 7, 366, 1024 }, { 8, 367, 1024 },
+ { 5, 368, 1024 }, { 6, 369, 1024 }, { 6, 370, 1024 }, { 7, 371, 1024 }, { 6, 372, 1024 }, { 7, 373, 1024 }, { 7, 374, 1024 }, { 8, 375, 1024 },
+ { 6, 376, 1024 }, { 7, 377, 1024 }, { 7, 378, 1024 }, { 8, 379, 1024 }, { 7, 380, 1024 }, { 8, 381, 1024 }, { 8, 382, 1024 }, { 9, 383, 1024 },
+ { 3, 384, 1024 }, { 4, 385, 1024 }, { 4, 386, 1024 }, { 5, 387, 1024 }, { 4, 388, 1024 }, { 5, 389, 1024 }, { 5, 390, 1024 }, { 6, 391, 1024 },
+ { 4, 392, 1024 }, { 5, 393, 1024 }, { 5, 394, 1024 }, { 6, 395, 1024 }, { 5, 396, 1024 }, { 6, 397, 1024 }, { 6, 398, 1024 }, { 7, 399, 1024 },
+ { 4, 400, 1024 }, { 5, 401, 1024 }, { 5, 402, 1024 }, { 6, 403, 1024 }, { 5, 404, 1024 }, { 6, 405, 1024 }, { 6, 406, 1024 }, { 7, 407, 1024 },
+ { 5, 408, 1024 }, { 6, 409, 1024 }, { 6, 410, 1024 }, { 7, 411, 1024 }, { 6, 412, 1024 }, { 7, 413, 1024 }, { 7, 414, 1024 }, { 8, 415, 1024 },
+ { 4, 416, 1024 }, { 5, 417, 1024 }, { 5, 418, 1024 }, { 6, 419, 1024 }, { 5, 420, 1024 }, { 6, 421, 1024 }, { 6, 422, 1024 }, { 7, 423, 1024 },
+ { 5, 424, 1024 }, { 6, 425, 1024 }, { 6, 426, 1024 }, { 7, 427, 1024 }, { 6, 428, 1024 }, { 7, 429, 1024 }, { 7, 430, 1024 }, { 8, 431, 1024 },
+ { 5, 432, 1024 }, { 6, 433, 1024 }, { 6, 434, 1024 }, { 7, 435, 1024 }, { 6, 436, 1024 }, { 7, 437, 1024 }, { 7, 438, 1024 }, { 8, 439, 1024 },
+ { 6, 440, 1024 }, { 7, 441, 1024 }, { 7, 442, 1024 }, { 8, 443, 1024 }, { 7, 444, 1024 }, { 8, 445, 1024 }, { 8, 446, 1024 }, { 9, 447, 1024 },
+ { 4, 448, 1024 }, { 5, 449, 1024 }, { 5, 450, 1024 }, { 6, 451, 1024 }, { 5, 452, 1024 }, { 6, 453, 1024 }, { 6, 454, 1024 }, { 7, 455, 1024 },
+ { 5, 456, 1024 }, { 6, 457, 1024 }, { 6, 458, 1024 }, { 7, 459, 1024 }, { 6, 460, 1024 }, { 7, 461, 1024 }, { 7, 462, 1024 }, { 8, 463, 1024 },
+ { 5, 464, 1024 }, { 6, 465, 1024 }, { 6, 466, 1024 }, { 7, 467, 1024 }, { 6, 468, 1024 }, { 7, 469, 1024 }, { 7, 470, 1024 }, { 8, 471, 1024 },
+ { 6, 472, 1024 }, { 7, 473, 1024 }, { 7, 474, 1024 }, { 8, 475, 1024 }, { 7, 476, 1024 }, { 8, 477, 1024 }, { 8, 478, 1024 }, { 9, 479, 1024 },
+ { 5, 480, 1024 }, { 6, 481, 1024 }, { 6, 482, 1024 }, { 7, 483, 1024 }, { 6, 484, 1024 }, { 7, 485, 1024 }, { 7, 486, 1024 }, { 8, 487, 1024 },
+ { 6, 488, 1024 }, { 7, 489, 1024 }, { 7, 490, 1024 }, { 8, 491, 1024 }, { 7, 492, 1024 }, { 8, 493, 1024 }, { 8, 494, 1024 }, { 9, 495, 1024 },
+ { 6, 496, 1024 }, { 7, 497, 1024 }, { 7, 498, 1024 }, { 8, 499, 1024 }, { 7, 500, 1024 }, { 8, 501, 1024 }, { 8, 502, 1024 }, { 9, 503, 1024 },
+ { 7, 504, 1024 }, { 8, 505, 1024 }, { 8, 506, 1024 }, { 9, 507, 1024 }, { 8, 508, 1024 }, { 9, 509, 1024 }, { 9, 510, 1024 }, { 10, 511, 1024 },
+ { 2, 512, 1024 }, { 3, 513, 1024 }, { 3, 514, 1024 }, { 4, 515, 1024 }, { 3, 516, 1024 }, { 4, 517, 1024 }, { 4, 518, 1024 }, { 5, 519, 1024 },
+ { 3, 520, 1024 }, { 4, 521, 1024 }, { 4, 522, 1024 }, { 5, 523, 1024 }, { 4, 524, 1024 }, { 5, 525, 1024 }, { 5, 526, 1024 }, { 6, 527, 1024 },
+ { 3, 528, 1024 }, { 4, 529, 1024 }, { 4, 530, 1024 }, { 5, 531, 1024 }, { 4, 532, 1024 }, { 5, 533, 1024 }, { 5, 534, 1024 }, { 6, 535, 1024 },
+ { 4, 536, 1024 }, { 5, 537, 1024 }, { 5, 538, 1024 }, { 6, 539, 1024 }, { 5, 540, 1024 }, { 6, 541, 1024 }, { 6, 542, 1024 }, { 7, 543, 1024 },
+ { 3, 544, 1024 }, { 4, 545, 1024 }, { 4, 546, 1024 }, { 5, 547, 1024 }, { 4, 548, 1024 }, { 5, 549, 1024 }, { 5, 550, 1024 }, { 6, 551, 1024 },
+ { 4, 552, 1024 }, { 5, 553, 1024 }, { 5, 554, 1024 }, { 6, 555, 1024 }, { 5, 556, 1024 }, { 6, 557, 1024 }, { 6, 558, 1024 }, { 7, 559, 1024 },
+ { 4, 560, 1024 }, { 5, 561, 1024 }, { 5, 562, 1024 }, { 6, 563, 1024 }, { 5, 564, 1024 }, { 6, 565, 1024 }, { 6, 566, 1024 }, { 7, 567, 1024 },
+ { 5, 568, 1024 }, { 6, 569, 1024 }, { 6, 570, 1024 }, { 7, 571, 1024 }, { 6, 572, 1024 }, { 7, 573, 1024 }, { 7, 574, 1024 }, { 8, 575, 1024 },
+ { 3, 576, 1024 }, { 4, 577, 1024 }, { 4, 578, 1024 }, { 5, 579, 1024 }, { 4, 580, 1024 }, { 5, 581, 1024 }, { 5, 582, 1024 }, { 6, 583, 1024 },
+ { 4, 584, 1024 }, { 5, 585, 1024 }, { 5, 586, 1024 }, { 6, 587, 1024 }, { 5, 588, 1024 }, { 6, 589, 1024 }, { 6, 590, 1024 }, { 7, 591, 1024 },
+ { 4, 592, 1024 }, { 5, 593, 1024 }, { 5, 594, 1024 }, { 6, 595, 1024 }, { 5, 596, 1024 }, { 6, 597, 1024 }, { 6, 598, 1024 }, { 7, 599, 1024 },
+ { 5, 600, 1024 }, { 6, 601, 1024 }, { 6, 602, 1024 }, { 7, 603, 1024 }, { 6, 604, 1024 }, { 7, 605, 1024 }, { 7, 606, 1024 }, { 8, 607, 1024 },
+ { 4, 608, 1024 }, { 5, 609, 1024 }, { 5, 610, 1024 }, { 6, 611, 1024 }, { 5, 612, 1024 }, { 6, 613, 1024 }, { 6, 614, 1024 }, { 7, 615, 1024 },
+ { 5, 616, 1024 }, { 6, 617, 1024 }, { 6, 618, 1024 }, { 7, 619, 1024 }, { 6, 620, 1024 }, { 7, 621, 1024 }, { 7, 622, 1024 }, { 8, 623, 1024 },
+ { 5, 624, 1024 }, { 6, 625, 1024 }, { 6, 626, 1024 }, { 7, 627, 1024 }, { 6, 628, 1024 }, { 7, 629, 1024 }, { 7, 630, 1024 }, { 8, 631, 1024 },
+ { 6, 632, 1024 }, { 7, 633, 1024 }, { 7, 634, 1024 }, { 8, 635, 1024 }, { 7, 636, 1024 }, { 8, 637, 1024 }, { 8, 638, 1024 }, { 9, 639, 1024 },
+ { 3, 640, 1024 }, { 4, 641, 1024 }, { 4, 642, 1024 }, { 5, 643, 1024 }, { 4, 644, 1024 }, { 5, 645, 1024 }, { 5, 646, 1024 }, { 6, 647, 1024 },
+ { 4, 648, 1024 }, { 5, 649, 1024 }, { 5, 650, 1024 }, { 6, 651, 1024 }, { 5, 652, 1024 }, { 6, 653, 1024 }, { 6, 654, 1024 }, { 7, 655, 1024 },
+ { 4, 656, 1024 }, { 5, 657, 1024 }, { 5, 658, 1024 }, { 6, 659, 1024 }, { 5, 660, 1024 }, { 6, 661, 1024 }, { 6, 662, 1024 }, { 7, 663, 1024 },
+ { 5, 664, 1024 }, { 6, 665, 1024 }, { 6, 666, 1024 }, { 7, 667, 1024 }, { 6, 668, 1024 }, { 7, 669, 1024 }, { 7, 670, 1024 }, { 8, 671, 1024 },
+ { 4, 672, 1024 }, { 5, 673, 1024 }, { 5, 674, 1024 }, { 6, 675, 1024 }, { 5, 676, 1024 }, { 6, 677, 1024 }, { 6, 678, 1024 }, { 7, 679, 1024 },
+ { 5, 680, 1024 }, { 6, 681, 1024 }, { 6, 682, 1024 }, { 7, 683, 1024 }, { 6, 684, 1024 }, { 7, 685, 1024 }, { 7, 686, 1024 }, { 8, 687, 1024 },
+ { 5, 688, 1024 }, { 6, 689, 1024 }, { 6, 690, 1024 }, { 7, 691, 1024 }, { 6, 692, 1024 }, { 7, 693, 1024 }, { 7, 694, 1024 }, { 8, 695, 1024 },
+ { 6, 696, 1024 }, { 7, 697, 1024 }, { 7, 698, 1024 }, { 8, 699, 1024 }, { 7, 700, 1024 }, { 8, 701, 1024 }, { 8, 702, 1024 }, { 9, 703, 1024 },
+ { 4, 704, 1024 }, { 5, 705, 1024 }, { 5, 706, 1024 }, { 6, 707, 1024 }, { 5, 708, 1024 }, { 6, 709, 1024 }, { 6, 710, 1024 }, { 7, 711, 1024 },
+ { 5, 712, 1024 }, { 6, 713, 1024 }, { 6, 714, 1024 }, { 7, 715, 1024 }, { 6, 716, 1024 }, { 7, 717, 1024 }, { 7, 718, 1024 }, { 8, 719, 1024 },
+ { 5, 720, 1024 }, { 6, 721, 1024 }, { 6, 722, 1024 }, { 7, 723, 1024 }, { 6, 724, 1024 }, { 7, 725, 1024 }, { 7, 726, 1024 }, { 8, 727, 1024 },
+ { 6, 728, 1024 }, { 7, 729, 1024 }, { 7, 730, 1024 }, { 8, 731, 1024 }, { 7, 732, 1024 }, { 8, 733, 1024 }, { 8, 734, 1024 }, { 9, 735, 1024 },
+ { 5, 736, 1024 }, { 6, 737, 1024 }, { 6, 738, 1024 }, { 7, 739, 1024 }, { 6, 740, 1024 }, { 7, 741, 1024 }, { 7, 742, 1024 }, { 8, 743, 1024 },
+ { 6, 744, 1024 }, { 7, 745, 1024 }, { 7, 746, 1024 }, { 8, 747, 1024 }, { 7, 748, 1024 }, { 8, 749, 1024 }, { 8, 750, 1024 }, { 9, 751, 1024 },
+ { 6, 752, 1024 }, { 7, 753, 1024 }, { 7, 754, 1024 }, { 8, 755, 1024 }, { 7, 756, 1024 }, { 8, 757, 1024 }, { 8, 758, 1024 }, { 9, 759, 1024 },
+ { 7, 760, 1024 }, { 8, 761, 1024 }, { 8, 762, 1024 }, { 9, 763, 1024 }, { 8, 764, 1024 }, { 9, 765, 1024 }, { 9, 766, 1024 }, { 10, 767, 1024 },
+ { 3, 768, 1024 }, { 4, 769, 1024 }, { 4, 770, 1024 }, { 5, 771, 1024 }, { 4, 772, 1024 }, { 5, 773, 1024 }, { 5, 774, 1024 }, { 6, 775, 1024 },
+ { 4, 776, 1024 }, { 5, 777, 1024 }, { 5, 778, 1024 }, { 6, 779, 1024 }, { 5, 780, 1024 }, { 6, 781, 1024 }, { 6, 782, 1024 }, { 7, 783, 1024 },
+ { 4, 784, 1024 }, { 5, 785, 1024 }, { 5, 786, 1024 }, { 6, 787, 1024 }, { 5, 788, 1024 }, { 6, 789, 1024 }, { 6, 790, 1024 }, { 7, 791, 1024 },
+ { 5, 792, 1024 }, { 6, 793, 1024 }, { 6, 794, 1024 }, { 7, 795, 1024 }, { 6, 796, 1024 }, { 7, 797, 1024 }, { 7, 798, 1024 }, { 8, 799, 1024 },
+ { 4, 800, 1024 }, { 5, 801, 1024 }, { 5, 802, 1024 }, { 6, 803, 1024 }, { 5, 804, 1024 }, { 6, 805, 1024 }, { 6, 806, 1024 }, { 7, 807, 1024 },
+ { 5, 808, 1024 }, { 6, 809, 1024 }, { 6, 810, 1024 }, { 7, 811, 1024 }, { 6, 812, 1024 }, { 7, 813, 1024 }, { 7, 814, 1024 }, { 8, 815, 1024 },
+ { 5, 816, 1024 }, { 6, 817, 1024 }, { 6, 818, 1024 }, { 7, 819, 1024 }, { 6, 820, 1024 }, { 7, 821, 1024 }, { 7, 822, 1024 }, { 8, 823, 1024 },
+ { 6, 824, 1024 }, { 7, 825, 1024 }, { 7, 826, 1024 }, { 8, 827, 1024 }, { 7, 828, 1024 }, { 8, 829, 1024 }, { 8, 830, 1024 }, { 9, 831, 1024 },
+ { 4, 832, 1024 }, { 5, 833, 1024 }, { 5, 834, 1024 }, { 6, 835, 1024 }, { 5, 836, 1024 }, { 6, 837, 1024 }, { 6, 838, 1024 }, { 7, 839, 1024 },
+ { 5, 840, 1024 }, { 6, 841, 1024 }, { 6, 842, 1024 }, { 7, 843, 1024 }, { 6, 844, 1024 }, { 7, 845, 1024 }, { 7, 846, 1024 }, { 8, 847, 1024 },
+ { 5, 848, 1024 }, { 6, 849, 1024 }, { 6, 850, 1024 }, { 7, 851, 1024 }, { 6, 852, 1024 }, { 7, 853, 1024 }, { 7, 854, 1024 }, { 8, 855, 1024 },
+ { 6, 856, 1024 }, { 7, 857, 1024 }, { 7, 858, 1024 }, { 8, 859, 1024 }, { 7, 860, 1024 }, { 8, 861, 1024 }, { 8, 862, 1024 }, { 9, 863, 1024 },
+ { 5, 864, 1024 }, { 6, 865, 1024 }, { 6, 866, 1024 }, { 7, 867, 1024 }, { 6, 868, 1024 }, { 7, 869, 1024 }, { 7, 870, 1024 }, { 8, 871, 1024 },
+ { 6, 872, 1024 }, { 7, 873, 1024 }, { 7, 874, 1024 }, { 8, 875, 1024 }, { 7, 876, 1024 }, { 8, 877, 1024 }, { 8, 878, 1024 }, { 9, 879, 1024 },
+ { 6, 880, 1024 }, { 7, 881, 1024 }, { 7, 882, 1024 }, { 8, 883, 1024 }, { 7, 884, 1024 }, { 8, 885, 1024 }, { 8, 886, 1024 }, { 9, 887, 1024 },
+ { 7, 888, 1024 }, { 8, 889, 1024 }, { 8, 890, 1024 }, { 9, 891, 1024 }, { 8, 892, 1024 }, { 9, 893, 1024 }, { 9, 894, 1024 }, { 10, 895, 1024 },
+ { 4, 896, 1024 }, { 5, 897, 1024 }, { 5, 898, 1024 }, { 6, 899, 1024 }, { 5, 900, 1024 }, { 6, 901, 1024 }, { 6, 902, 1024 }, { 7, 903, 1024 },
+ { 5, 904, 1024 }, { 6, 905, 1024 }, { 6, 906, 1024 }, { 7, 907, 1024 }, { 6, 908, 1024 }, { 7, 909, 1024 }, { 7, 910, 1024 }, { 8, 911, 1024 },
+ { 5, 912, 1024 }, { 6, 913, 1024 }, { 6, 914, 1024 }, { 7, 915, 1024 }, { 6, 916, 1024 }, { 7, 917, 1024 }, { 7, 918, 1024 }, { 8, 919, 1024 },
+ { 6, 920, 1024 }, { 7, 921, 1024 }, { 7, 922, 1024 }, { 8, 923, 1024 }, { 7, 924, 1024 }, { 8, 925, 1024 }, { 8, 926, 1024 }, { 9, 927, 1024 },
+ { 5, 928, 1024 }, { 6, 929, 1024 }, { 6, 930, 1024 }, { 7, 931, 1024 }, { 6, 932, 1024 }, { 7, 933, 1024 }, { 7, 934, 1024 }, { 8, 935, 1024 },
+ { 6, 936, 1024 }, { 7, 937, 1024 }, { 7, 938, 1024 }, { 8, 939, 1024 }, { 7, 940, 1024 }, { 8, 941, 1024 }, { 8, 942, 1024 }, { 9, 943, 1024 },
+ { 6, 944, 1024 }, { 7, 945, 1024 }, { 7, 946, 1024 }, { 8, 947, 1024 }, { 7, 948, 1024 }, { 8, 949, 1024 }, { 8, 950, 1024 }, { 9, 951, 1024 },
+ { 7, 952, 1024 }, { 8, 953, 1024 }, { 8, 954, 1024 }, { 9, 955, 1024 }, { 8, 956, 1024 }, { 9, 957, 1024 }, { 9, 958, 1024 }, { 10, 959, 1024 },
+ { 5, 960, 1024 }, { 6, 961, 1024 }, { 6, 962, 1024 }, { 7, 963, 1024 }, { 6, 964, 1024 }, { 7, 965, 1024 }, { 7, 966, 1024 }, { 8, 967, 1024 },
+ { 6, 968, 1024 }, { 7, 969, 1024 }, { 7, 970, 1024 }, { 8, 971, 1024 }, { 7, 972, 1024 }, { 8, 973, 1024 }, { 8, 974, 1024 }, { 9, 975, 1024 },
+ { 6, 976, 1024 }, { 7, 977, 1024 }, { 7, 978, 1024 }, { 8, 979, 1024 }, { 7, 980, 1024 }, { 8, 981, 1024 }, { 8, 982, 1024 }, { 9, 983, 1024 },
+ { 7, 984, 1024 }, { 8, 985, 1024 }, { 8, 986, 1024 }, { 9, 987, 1024 }, { 8, 988, 1024 }, { 9, 989, 1024 }, { 9, 990, 1024 }, { 10, 991, 1024 },
+ { 6, 992, 1024 }, { 7, 993, 1024 }, { 7, 994, 1024 }, { 8, 995, 1024 }, { 7, 996, 1024 }, { 8, 997, 1024 }, { 8, 998, 1024 }, { 9, 999, 1024 },
+ { 7, 1000, 1024 }, { 8, 1001, 1024 }, { 8, 1002, 1024 }, { 9, 1003, 1024 }, { 8, 1004, 1024 }, { 9, 1005, 1024 }, { 9, 1006, 1024 }, { 10, 1007, 1024 },
+ { 7, 1008, 1024 }, { 8, 1009, 1024 }, { 8, 1010, 1024 }, { 9, 1011, 1024 }, { 8, 1012, 1024 }, { 9, 1013, 1024 }, { 9, 1014, 1024 }, { 10, 1015, 1024 },
+ { 8, 1016, 1024 }, { 9, 1017, 1024 }, { 9, 1018, 1024 }, { 10, 1019, 1024 }, { 9, 1020, 1024 }, { 10, 1021, 1024 }, { 10, 1022, 1024 }, { 11, 1023, 1024 },
+#if FP_LUT > 11
+ { 1, 0, 0 }, { 2, 1, 2048 }, { 2, 2, 2048 }, { 3, 3, 2048 }, { 2, 4, 2048 }, { 3, 5, 2048 }, { 3, 6, 2048 }, { 4, 7, 2048 },
+ { 2, 8, 2048 }, { 3, 9, 2048 }, { 3, 10, 2048 }, { 4, 11, 2048 }, { 3, 12, 2048 }, { 4, 13, 2048 }, { 4, 14, 2048 }, { 5, 15, 2048 },
+ { 2, 16, 2048 }, { 3, 17, 2048 }, { 3, 18, 2048 }, { 4, 19, 2048 }, { 3, 20, 2048 }, { 4, 21, 2048 }, { 4, 22, 2048 }, { 5, 23, 2048 },
+ { 3, 24, 2048 }, { 4, 25, 2048 }, { 4, 26, 2048 }, { 5, 27, 2048 }, { 4, 28, 2048 }, { 5, 29, 2048 }, { 5, 30, 2048 }, { 6, 31, 2048 },
+ { 2, 32, 2048 }, { 3, 33, 2048 }, { 3, 34, 2048 }, { 4, 35, 2048 }, { 3, 36, 2048 }, { 4, 37, 2048 }, { 4, 38, 2048 }, { 5, 39, 2048 },
+ { 3, 40, 2048 }, { 4, 41, 2048 }, { 4, 42, 2048 }, { 5, 43, 2048 }, { 4, 44, 2048 }, { 5, 45, 2048 }, { 5, 46, 2048 }, { 6, 47, 2048 },
+ { 3, 48, 2048 }, { 4, 49, 2048 }, { 4, 50, 2048 }, { 5, 51, 2048 }, { 4, 52, 2048 }, { 5, 53, 2048 }, { 5, 54, 2048 }, { 6, 55, 2048 },
+ { 4, 56, 2048 }, { 5, 57, 2048 }, { 5, 58, 2048 }, { 6, 59, 2048 }, { 5, 60, 2048 }, { 6, 61, 2048 }, { 6, 62, 2048 }, { 7, 63, 2048 },
+ { 2, 64, 2048 }, { 3, 65, 2048 }, { 3, 66, 2048 }, { 4, 67, 2048 }, { 3, 68, 2048 }, { 4, 69, 2048 }, { 4, 70, 2048 }, { 5, 71, 2048 },
+ { 3, 72, 2048 }, { 4, 73, 2048 }, { 4, 74, 2048 }, { 5, 75, 2048 }, { 4, 76, 2048 }, { 5, 77, 2048 }, { 5, 78, 2048 }, { 6, 79, 2048 },
+ { 3, 80, 2048 }, { 4, 81, 2048 }, { 4, 82, 2048 }, { 5, 83, 2048 }, { 4, 84, 2048 }, { 5, 85, 2048 }, { 5, 86, 2048 }, { 6, 87, 2048 },
+ { 4, 88, 2048 }, { 5, 89, 2048 }, { 5, 90, 2048 }, { 6, 91, 2048 }, { 5, 92, 2048 }, { 6, 93, 2048 }, { 6, 94, 2048 }, { 7, 95, 2048 },
+ { 3, 96, 2048 }, { 4, 97, 2048 }, { 4, 98, 2048 }, { 5, 99, 2048 }, { 4, 100, 2048 }, { 5, 101, 2048 }, { 5, 102, 2048 }, { 6, 103, 2048 },
+ { 4, 104, 2048 }, { 5, 105, 2048 }, { 5, 106, 2048 }, { 6, 107, 2048 }, { 5, 108, 2048 }, { 6, 109, 2048 }, { 6, 110, 2048 }, { 7, 111, 2048 },
+ { 4, 112, 2048 }, { 5, 113, 2048 }, { 5, 114, 2048 }, { 6, 115, 2048 }, { 5, 116, 2048 }, { 6, 117, 2048 }, { 6, 118, 2048 }, { 7, 119, 2048 },
+ { 5, 120, 2048 }, { 6, 121, 2048 }, { 6, 122, 2048 }, { 7, 123, 2048 }, { 6, 124, 2048 }, { 7, 125, 2048 }, { 7, 126, 2048 }, { 8, 127, 2048 },
+ { 2, 128, 2048 }, { 3, 129, 2048 }, { 3, 130, 2048 }, { 4, 131, 2048 }, { 3, 132, 2048 }, { 4, 133, 2048 }, { 4, 134, 2048 }, { 5, 135, 2048 },
+ { 3, 136, 2048 }, { 4, 137, 2048 }, { 4, 138, 2048 }, { 5, 139, 2048 }, { 4, 140, 2048 }, { 5, 141, 2048 }, { 5, 142, 2048 }, { 6, 143, 2048 },
+ { 3, 144, 2048 }, { 4, 145, 2048 }, { 4, 146, 2048 }, { 5, 147, 2048 }, { 4, 148, 2048 }, { 5, 149, 2048 }, { 5, 150, 2048 }, { 6, 151, 2048 },
+ { 4, 152, 2048 }, { 5, 153, 2048 }, { 5, 154, 2048 }, { 6, 155, 2048 }, { 5, 156, 2048 }, { 6, 157, 2048 }, { 6, 158, 2048 }, { 7, 159, 2048 },
+ { 3, 160, 2048 }, { 4, 161, 2048 }, { 4, 162, 2048 }, { 5, 163, 2048 }, { 4, 164, 2048 }, { 5, 165, 2048 }, { 5, 166, 2048 }, { 6, 167, 2048 },
+ { 4, 168, 2048 }, { 5, 169, 2048 }, { 5, 170, 2048 }, { 6, 171, 2048 }, { 5, 172, 2048 }, { 6, 173, 2048 }, { 6, 174, 2048 }, { 7, 175, 2048 },
+ { 4, 176, 2048 }, { 5, 177, 2048 }, { 5, 178, 2048 }, { 6, 179, 2048 }, { 5, 180, 2048 }, { 6, 181, 2048 }, { 6, 182, 2048 }, { 7, 183, 2048 },
+ { 5, 184, 2048 }, { 6, 185, 2048 }, { 6, 186, 2048 }, { 7, 187, 2048 }, { 6, 188, 2048 }, { 7, 189, 2048 }, { 7, 190, 2048 }, { 8, 191, 2048 },
+ { 3, 192, 2048 }, { 4, 193, 2048 }, { 4, 194, 2048 }, { 5, 195, 2048 }, { 4, 196, 2048 }, { 5, 197, 2048 }, { 5, 198, 2048 }, { 6, 199, 2048 },
+ { 4, 200, 2048 }, { 5, 201, 2048 }, { 5, 202, 2048 }, { 6, 203, 2048 }, { 5, 204, 2048 }, { 6, 205, 2048 }, { 6, 206, 2048 }, { 7, 207, 2048 },
+ { 4, 208, 2048 }, { 5, 209, 2048 }, { 5, 210, 2048 }, { 6, 211, 2048 }, { 5, 212, 2048 }, { 6, 213, 2048 }, { 6, 214, 2048 }, { 7, 215, 2048 },
+ { 5, 216, 2048 }, { 6, 217, 2048 }, { 6, 218, 2048 }, { 7, 219, 2048 }, { 6, 220, 2048 }, { 7, 221, 2048 }, { 7, 222, 2048 }, { 8, 223, 2048 },
+ { 4, 224, 2048 }, { 5, 225, 2048 }, { 5, 226, 2048 }, { 6, 227, 2048 }, { 5, 228, 2048 }, { 6, 229, 2048 }, { 6, 230, 2048 }, { 7, 231, 2048 },
+ { 5, 232, 2048 }, { 6, 233, 2048 }, { 6, 234, 2048 }, { 7, 235, 2048 }, { 6, 236, 2048 }, { 7, 237, 2048 }, { 7, 238, 2048 }, { 8, 239, 2048 },
+ { 5, 240, 2048 }, { 6, 241, 2048 }, { 6, 242, 2048 }, { 7, 243, 2048 }, { 6, 244, 2048 }, { 7, 245, 2048 }, { 7, 246, 2048 }, { 8, 247, 2048 },
+ { 6, 248, 2048 }, { 7, 249, 2048 }, { 7, 250, 2048 }, { 8, 251, 2048 }, { 7, 252, 2048 }, { 8, 253, 2048 }, { 8, 254, 2048 }, { 9, 255, 2048 },
+ { 2, 256, 2048 }, { 3, 257, 2048 }, { 3, 258, 2048 }, { 4, 259, 2048 }, { 3, 260, 2048 }, { 4, 261, 2048 }, { 4, 262, 2048 }, { 5, 263, 2048 },
+ { 3, 264, 2048 }, { 4, 265, 2048 }, { 4, 266, 2048 }, { 5, 267, 2048 }, { 4, 268, 2048 }, { 5, 269, 2048 }, { 5, 270, 2048 }, { 6, 271, 2048 },
+ { 3, 272, 2048 }, { 4, 273, 2048 }, { 4, 274, 2048 }, { 5, 275, 2048 }, { 4, 276, 2048 }, { 5, 277, 2048 }, { 5, 278, 2048 }, { 6, 279, 2048 },
+ { 4, 280, 2048 }, { 5, 281, 2048 }, { 5, 282, 2048 }, { 6, 283, 2048 }, { 5, 284, 2048 }, { 6, 285, 2048 }, { 6, 286, 2048 }, { 7, 287, 2048 },
+ { 3, 288, 2048 }, { 4, 289, 2048 }, { 4, 290, 2048 }, { 5, 291, 2048 }, { 4, 292, 2048 }, { 5, 293, 2048 }, { 5, 294, 2048 }, { 6, 295, 2048 },
+ { 4, 296, 2048 }, { 5, 297, 2048 }, { 5, 298, 2048 }, { 6, 299, 2048 }, { 5, 300, 2048 }, { 6, 301, 2048 }, { 6, 302, 2048 }, { 7, 303, 2048 },
+ { 4, 304, 2048 }, { 5, 305, 2048 }, { 5, 306, 2048 }, { 6, 307, 2048 }, { 5, 308, 2048 }, { 6, 309, 2048 }, { 6, 310, 2048 }, { 7, 311, 2048 },
+ { 5, 312, 2048 }, { 6, 313, 2048 }, { 6, 314, 2048 }, { 7, 315, 2048 }, { 6, 316, 2048 }, { 7, 317, 2048 }, { 7, 318, 2048 }, { 8, 319, 2048 },
+ { 3, 320, 2048 }, { 4, 321, 2048 }, { 4, 322, 2048 }, { 5, 323, 2048 }, { 4, 324, 2048 }, { 5, 325, 2048 }, { 5, 326, 2048 }, { 6, 327, 2048 },
+ { 4, 328, 2048 }, { 5, 329, 2048 }, { 5, 330, 2048 }, { 6, 331, 2048 }, { 5, 332, 2048 }, { 6, 333, 2048 }, { 6, 334, 2048 }, { 7, 335, 2048 },
+ { 4, 336, 2048 }, { 5, 337, 2048 }, { 5, 338, 2048 }, { 6, 339, 2048 }, { 5, 340, 2048 }, { 6, 341, 2048 }, { 6, 342, 2048 }, { 7, 343, 2048 },
+ { 5, 344, 2048 }, { 6, 345, 2048 }, { 6, 346, 2048 }, { 7, 347, 2048 }, { 6, 348, 2048 }, { 7, 349, 2048 }, { 7, 350, 2048 }, { 8, 351, 2048 },
+ { 4, 352, 2048 }, { 5, 353, 2048 }, { 5, 354, 2048 }, { 6, 355, 2048 }, { 5, 356, 2048 }, { 6, 357, 2048 }, { 6, 358, 2048 }, { 7, 359, 2048 },
+ { 5, 360, 2048 }, { 6, 361, 2048 }, { 6, 362, 2048 }, { 7, 363, 2048 }, { 6, 364, 2048 }, { 7, 365, 2048 }, { 7, 366, 2048 }, { 8, 367, 2048 },
+ { 5, 368, 2048 }, { 6, 369, 2048 }, { 6, 370, 2048 }, { 7, 371, 2048 }, { 6, 372, 2048 }, { 7, 373, 2048 }, { 7, 374, 2048 }, { 8, 375, 2048 },
+ { 6, 376, 2048 }, { 7, 377, 2048 }, { 7, 378, 2048 }, { 8, 379, 2048 }, { 7, 380, 2048 }, { 8, 381, 2048 }, { 8, 382, 2048 }, { 9, 383, 2048 },
+ { 3, 384, 2048 }, { 4, 385, 2048 }, { 4, 386, 2048 }, { 5, 387, 2048 }, { 4, 388, 2048 }, { 5, 389, 2048 }, { 5, 390, 2048 }, { 6, 391, 2048 },
+ { 4, 392, 2048 }, { 5, 393, 2048 }, { 5, 394, 2048 }, { 6, 395, 2048 }, { 5, 396, 2048 }, { 6, 397, 2048 }, { 6, 398, 2048 }, { 7, 399, 2048 },
+ { 4, 400, 2048 }, { 5, 401, 2048 }, { 5, 402, 2048 }, { 6, 403, 2048 }, { 5, 404, 2048 }, { 6, 405, 2048 }, { 6, 406, 2048 }, { 7, 407, 2048 },
+ { 5, 408, 2048 }, { 6, 409, 2048 }, { 6, 410, 2048 }, { 7, 411, 2048 }, { 6, 412, 2048 }, { 7, 413, 2048 }, { 7, 414, 2048 }, { 8, 415, 2048 },
+ { 4, 416, 2048 }, { 5, 417, 2048 }, { 5, 418, 2048 }, { 6, 419, 2048 }, { 5, 420, 2048 }, { 6, 421, 2048 }, { 6, 422, 2048 }, { 7, 423, 2048 },
+ { 5, 424, 2048 }, { 6, 425, 2048 }, { 6, 426, 2048 }, { 7, 427, 2048 }, { 6, 428, 2048 }, { 7, 429, 2048 }, { 7, 430, 2048 }, { 8, 431, 2048 },
+ { 5, 432, 2048 }, { 6, 433, 2048 }, { 6, 434, 2048 }, { 7, 435, 2048 }, { 6, 436, 2048 }, { 7, 437, 2048 }, { 7, 438, 2048 }, { 8, 439, 2048 },
+ { 6, 440, 2048 }, { 7, 441, 2048 }, { 7, 442, 2048 }, { 8, 443, 2048 }, { 7, 444, 2048 }, { 8, 445, 2048 }, { 8, 446, 2048 }, { 9, 447, 2048 },
+ { 4, 448, 2048 }, { 5, 449, 2048 }, { 5, 450, 2048 }, { 6, 451, 2048 }, { 5, 452, 2048 }, { 6, 453, 2048 }, { 6, 454, 2048 }, { 7, 455, 2048 },
+ { 5, 456, 2048 }, { 6, 457, 2048 }, { 6, 458, 2048 }, { 7, 459, 2048 }, { 6, 460, 2048 }, { 7, 461, 2048 }, { 7, 462, 2048 }, { 8, 463, 2048 },
+ { 5, 464, 2048 }, { 6, 465, 2048 }, { 6, 466, 2048 }, { 7, 467, 2048 }, { 6, 468, 2048 }, { 7, 469, 2048 }, { 7, 470, 2048 }, { 8, 471, 2048 },
+ { 6, 472, 2048 }, { 7, 473, 2048 }, { 7, 474, 2048 }, { 8, 475, 2048 }, { 7, 476, 2048 }, { 8, 477, 2048 }, { 8, 478, 2048 }, { 9, 479, 2048 },
+ { 5, 480, 2048 }, { 6, 481, 2048 }, { 6, 482, 2048 }, { 7, 483, 2048 }, { 6, 484, 2048 }, { 7, 485, 2048 }, { 7, 486, 2048 }, { 8, 487, 2048 },
+ { 6, 488, 2048 }, { 7, 489, 2048 }, { 7, 490, 2048 }, { 8, 491, 2048 }, { 7, 492, 2048 }, { 8, 493, 2048 }, { 8, 494, 2048 }, { 9, 495, 2048 },
+ { 6, 496, 2048 }, { 7, 497, 2048 }, { 7, 498, 2048 }, { 8, 499, 2048 }, { 7, 500, 2048 }, { 8, 501, 2048 }, { 8, 502, 2048 }, { 9, 503, 2048 },
+ { 7, 504, 2048 }, { 8, 505, 2048 }, { 8, 506, 2048 }, { 9, 507, 2048 }, { 8, 508, 2048 }, { 9, 509, 2048 }, { 9, 510, 2048 }, { 10, 511, 2048 },
+ { 2, 512, 2048 }, { 3, 513, 2048 }, { 3, 514, 2048 }, { 4, 515, 2048 }, { 3, 516, 2048 }, { 4, 517, 2048 }, { 4, 518, 2048 }, { 5, 519, 2048 },
+ { 3, 520, 2048 }, { 4, 521, 2048 }, { 4, 522, 2048 }, { 5, 523, 2048 }, { 4, 524, 2048 }, { 5, 525, 2048 }, { 5, 526, 2048 }, { 6, 527, 2048 },
+ { 3, 528, 2048 }, { 4, 529, 2048 }, { 4, 530, 2048 }, { 5, 531, 2048 }, { 4, 532, 2048 }, { 5, 533, 2048 }, { 5, 534, 2048 }, { 6, 535, 2048 },
+ { 4, 536, 2048 }, { 5, 537, 2048 }, { 5, 538, 2048 }, { 6, 539, 2048 }, { 5, 540, 2048 }, { 6, 541, 2048 }, { 6, 542, 2048 }, { 7, 543, 2048 },
+ { 3, 544, 2048 }, { 4, 545, 2048 }, { 4, 546, 2048 }, { 5, 547, 2048 }, { 4, 548, 2048 }, { 5, 549, 2048 }, { 5, 550, 2048 }, { 6, 551, 2048 },
+ { 4, 552, 2048 }, { 5, 553, 2048 }, { 5, 554, 2048 }, { 6, 555, 2048 }, { 5, 556, 2048 }, { 6, 557, 2048 }, { 6, 558, 2048 }, { 7, 559, 2048 },
+ { 4, 560, 2048 }, { 5, 561, 2048 }, { 5, 562, 2048 }, { 6, 563, 2048 }, { 5, 564, 2048 }, { 6, 565, 2048 }, { 6, 566, 2048 }, { 7, 567, 2048 },
+ { 5, 568, 2048 }, { 6, 569, 2048 }, { 6, 570, 2048 }, { 7, 571, 2048 }, { 6, 572, 2048 }, { 7, 573, 2048 }, { 7, 574, 2048 }, { 8, 575, 2048 },
+ { 3, 576, 2048 }, { 4, 577, 2048 }, { 4, 578, 2048 }, { 5, 579, 2048 }, { 4, 580, 2048 }, { 5, 581, 2048 }, { 5, 582, 2048 }, { 6, 583, 2048 },
+ { 4, 584, 2048 }, { 5, 585, 2048 }, { 5, 586, 2048 }, { 6, 587, 2048 }, { 5, 588, 2048 }, { 6, 589, 2048 }, { 6, 590, 2048 }, { 7, 591, 2048 },
+ { 4, 592, 2048 }, { 5, 593, 2048 }, { 5, 594, 2048 }, { 6, 595, 2048 }, { 5, 596, 2048 }, { 6, 597, 2048 }, { 6, 598, 2048 }, { 7, 599, 2048 },
+ { 5, 600, 2048 }, { 6, 601, 2048 }, { 6, 602, 2048 }, { 7, 603, 2048 }, { 6, 604, 2048 }, { 7, 605, 2048 }, { 7, 606, 2048 }, { 8, 607, 2048 },
+ { 4, 608, 2048 }, { 5, 609, 2048 }, { 5, 610, 2048 }, { 6, 611, 2048 }, { 5, 612, 2048 }, { 6, 613, 2048 }, { 6, 614, 2048 }, { 7, 615, 2048 },
+ { 5, 616, 2048 }, { 6, 617, 2048 }, { 6, 618, 2048 }, { 7, 619, 2048 }, { 6, 620, 2048 }, { 7, 621, 2048 }, { 7, 622, 2048 }, { 8, 623, 2048 },
+ { 5, 624, 2048 }, { 6, 625, 2048 }, { 6, 626, 2048 }, { 7, 627, 2048 }, { 6, 628, 2048 }, { 7, 629, 2048 }, { 7, 630, 2048 }, { 8, 631, 2048 },
+ { 6, 632, 2048 }, { 7, 633, 2048 }, { 7, 634, 2048 }, { 8, 635, 2048 }, { 7, 636, 2048 }, { 8, 637, 2048 }, { 8, 638, 2048 }, { 9, 639, 2048 },
+ { 3, 640, 2048 }, { 4, 641, 2048 }, { 4, 642, 2048 }, { 5, 643, 2048 }, { 4, 644, 2048 }, { 5, 645, 2048 }, { 5, 646, 2048 }, { 6, 647, 2048 },
+ { 4, 648, 2048 }, { 5, 649, 2048 }, { 5, 650, 2048 }, { 6, 651, 2048 }, { 5, 652, 2048 }, { 6, 653, 2048 }, { 6, 654, 2048 }, { 7, 655, 2048 },
+ { 4, 656, 2048 }, { 5, 657, 2048 }, { 5, 658, 2048 }, { 6, 659, 2048 }, { 5, 660, 2048 }, { 6, 661, 2048 }, { 6, 662, 2048 }, { 7, 663, 2048 },
+ { 5, 664, 2048 }, { 6, 665, 2048 }, { 6, 666, 2048 }, { 7, 667, 2048 }, { 6, 668, 2048 }, { 7, 669, 2048 }, { 7, 670, 2048 }, { 8, 671, 2048 },
+ { 4, 672, 2048 }, { 5, 673, 2048 }, { 5, 674, 2048 }, { 6, 675, 2048 }, { 5, 676, 2048 }, { 6, 677, 2048 }, { 6, 678, 2048 }, { 7, 679, 2048 },
+ { 5, 680, 2048 }, { 6, 681, 2048 }, { 6, 682, 2048 }, { 7, 683, 2048 }, { 6, 684, 2048 }, { 7, 685, 2048 }, { 7, 686, 2048 }, { 8, 687, 2048 },
+ { 5, 688, 2048 }, { 6, 689, 2048 }, { 6, 690, 2048 }, { 7, 691, 2048 }, { 6, 692, 2048 }, { 7, 693, 2048 }, { 7, 694, 2048 }, { 8, 695, 2048 },
+ { 6, 696, 2048 }, { 7, 697, 2048 }, { 7, 698, 2048 }, { 8, 699, 2048 }, { 7, 700, 2048 }, { 8, 701, 2048 }, { 8, 702, 2048 }, { 9, 703, 2048 },
+ { 4, 704, 2048 }, { 5, 705, 2048 }, { 5, 706, 2048 }, { 6, 707, 2048 }, { 5, 708, 2048 }, { 6, 709, 2048 }, { 6, 710, 2048 }, { 7, 711, 2048 },
+ { 5, 712, 2048 }, { 6, 713, 2048 }, { 6, 714, 2048 }, { 7, 715, 2048 }, { 6, 716, 2048 }, { 7, 717, 2048 }, { 7, 718, 2048 }, { 8, 719, 2048 },
+ { 5, 720, 2048 }, { 6, 721, 2048 }, { 6, 722, 2048 }, { 7, 723, 2048 }, { 6, 724, 2048 }, { 7, 725, 2048 }, { 7, 726, 2048 }, { 8, 727, 2048 },
+ { 6, 728, 2048 }, { 7, 729, 2048 }, { 7, 730, 2048 }, { 8, 731, 2048 }, { 7, 732, 2048 }, { 8, 733, 2048 }, { 8, 734, 2048 }, { 9, 735, 2048 },
+ { 5, 736, 2048 }, { 6, 737, 2048 }, { 6, 738, 2048 }, { 7, 739, 2048 }, { 6, 740, 2048 }, { 7, 741, 2048 }, { 7, 742, 2048 }, { 8, 743, 2048 },
+ { 6, 744, 2048 }, { 7, 745, 2048 }, { 7, 746, 2048 }, { 8, 747, 2048 }, { 7, 748, 2048 }, { 8, 749, 2048 }, { 8, 750, 2048 }, { 9, 751, 2048 },
+ { 6, 752, 2048 }, { 7, 753, 2048 }, { 7, 754, 2048 }, { 8, 755, 2048 }, { 7, 756, 2048 }, { 8, 757, 2048 }, { 8, 758, 2048 }, { 9, 759, 2048 },
+ { 7, 760, 2048 }, { 8, 761, 2048 }, { 8, 762, 2048 }, { 9, 763, 2048 }, { 8, 764, 2048 }, { 9, 765, 2048 }, { 9, 766, 2048 }, { 10, 767, 2048 },
+ { 3, 768, 2048 }, { 4, 769, 2048 }, { 4, 770, 2048 }, { 5, 771, 2048 }, { 4, 772, 2048 }, { 5, 773, 2048 }, { 5, 774, 2048 }, { 6, 775, 2048 },
+ { 4, 776, 2048 }, { 5, 777, 2048 }, { 5, 778, 2048 }, { 6, 779, 2048 }, { 5, 780, 2048 }, { 6, 781, 2048 }, { 6, 782, 2048 }, { 7, 783, 2048 },
+ { 4, 784, 2048 }, { 5, 785, 2048 }, { 5, 786, 2048 }, { 6, 787, 2048 }, { 5, 788, 2048 }, { 6, 789, 2048 }, { 6, 790, 2048 }, { 7, 791, 2048 },
+ { 5, 792, 2048 }, { 6, 793, 2048 }, { 6, 794, 2048 }, { 7, 795, 2048 }, { 6, 796, 2048 }, { 7, 797, 2048 }, { 7, 798, 2048 }, { 8, 799, 2048 },
+ { 4, 800, 2048 }, { 5, 801, 2048 }, { 5, 802, 2048 }, { 6, 803, 2048 }, { 5, 804, 2048 }, { 6, 805, 2048 }, { 6, 806, 2048 }, { 7, 807, 2048 },
+ { 5, 808, 2048 }, { 6, 809, 2048 }, { 6, 810, 2048 }, { 7, 811, 2048 }, { 6, 812, 2048 }, { 7, 813, 2048 }, { 7, 814, 2048 }, { 8, 815, 2048 },
+ { 5, 816, 2048 }, { 6, 817, 2048 }, { 6, 818, 2048 }, { 7, 819, 2048 }, { 6, 820, 2048 }, { 7, 821, 2048 }, { 7, 822, 2048 }, { 8, 823, 2048 },
+ { 6, 824, 2048 }, { 7, 825, 2048 }, { 7, 826, 2048 }, { 8, 827, 2048 }, { 7, 828, 2048 }, { 8, 829, 2048 }, { 8, 830, 2048 }, { 9, 831, 2048 },
+ { 4, 832, 2048 }, { 5, 833, 2048 }, { 5, 834, 2048 }, { 6, 835, 2048 }, { 5, 836, 2048 }, { 6, 837, 2048 }, { 6, 838, 2048 }, { 7, 839, 2048 },
+ { 5, 840, 2048 }, { 6, 841, 2048 }, { 6, 842, 2048 }, { 7, 843, 2048 }, { 6, 844, 2048 }, { 7, 845, 2048 }, { 7, 846, 2048 }, { 8, 847, 2048 },
+ { 5, 848, 2048 }, { 6, 849, 2048 }, { 6, 850, 2048 }, { 7, 851, 2048 }, { 6, 852, 2048 }, { 7, 853, 2048 }, { 7, 854, 2048 }, { 8, 855, 2048 },
+ { 6, 856, 2048 }, { 7, 857, 2048 }, { 7, 858, 2048 }, { 8, 859, 2048 }, { 7, 860, 2048 }, { 8, 861, 2048 }, { 8, 862, 2048 }, { 9, 863, 2048 },
+ { 5, 864, 2048 }, { 6, 865, 2048 }, { 6, 866, 2048 }, { 7, 867, 2048 }, { 6, 868, 2048 }, { 7, 869, 2048 }, { 7, 870, 2048 }, { 8, 871, 2048 },
+ { 6, 872, 2048 }, { 7, 873, 2048 }, { 7, 874, 2048 }, { 8, 875, 2048 }, { 7, 876, 2048 }, { 8, 877, 2048 }, { 8, 878, 2048 }, { 9, 879, 2048 },
+ { 6, 880, 2048 }, { 7, 881, 2048 }, { 7, 882, 2048 }, { 8, 883, 2048 }, { 7, 884, 2048 }, { 8, 885, 2048 }, { 8, 886, 2048 }, { 9, 887, 2048 },
+ { 7, 888, 2048 }, { 8, 889, 2048 }, { 8, 890, 2048 }, { 9, 891, 2048 }, { 8, 892, 2048 }, { 9, 893, 2048 }, { 9, 894, 2048 }, { 10, 895, 2048 },
+ { 4, 896, 2048 }, { 5, 897, 2048 }, { 5, 898, 2048 }, { 6, 899, 2048 }, { 5, 900, 2048 }, { 6, 901, 2048 }, { 6, 902, 2048 }, { 7, 903, 2048 },
+ { 5, 904, 2048 }, { 6, 905, 2048 }, { 6, 906, 2048 }, { 7, 907, 2048 }, { 6, 908, 2048 }, { 7, 909, 2048 }, { 7, 910, 2048 }, { 8, 911, 2048 },
+ { 5, 912, 2048 }, { 6, 913, 2048 }, { 6, 914, 2048 }, { 7, 915, 2048 }, { 6, 916, 2048 }, { 7, 917, 2048 }, { 7, 918, 2048 }, { 8, 919, 2048 },
+ { 6, 920, 2048 }, { 7, 921, 2048 }, { 7, 922, 2048 }, { 8, 923, 2048 }, { 7, 924, 2048 }, { 8, 925, 2048 }, { 8, 926, 2048 }, { 9, 927, 2048 },
+ { 5, 928, 2048 }, { 6, 929, 2048 }, { 6, 930, 2048 }, { 7, 931, 2048 }, { 6, 932, 2048 }, { 7, 933, 2048 }, { 7, 934, 2048 }, { 8, 935, 2048 },
+ { 6, 936, 2048 }, { 7, 937, 2048 }, { 7, 938, 2048 }, { 8, 939, 2048 }, { 7, 940, 2048 }, { 8, 941, 2048 }, { 8, 942, 2048 }, { 9, 943, 2048 },
+ { 6, 944, 2048 }, { 7, 945, 2048 }, { 7, 946, 2048 }, { 8, 947, 2048 }, { 7, 948, 2048 }, { 8, 949, 2048 }, { 8, 950, 2048 }, { 9, 951, 2048 },
+ { 7, 952, 2048 }, { 8, 953, 2048 }, { 8, 954, 2048 }, { 9, 955, 2048 }, { 8, 956, 2048 }, { 9, 957, 2048 }, { 9, 958, 2048 }, { 10, 959, 2048 },
+ { 5, 960, 2048 }, { 6, 961, 2048 }, { 6, 962, 2048 }, { 7, 963, 2048 }, { 6, 964, 2048 }, { 7, 965, 2048 }, { 7, 966, 2048 }, { 8, 967, 2048 },
+ { 6, 968, 2048 }, { 7, 969, 2048 }, { 7, 970, 2048 }, { 8, 971, 2048 }, { 7, 972, 2048 }, { 8, 973, 2048 }, { 8, 974, 2048 }, { 9, 975, 2048 },
+ { 6, 976, 2048 }, { 7, 977, 2048 }, { 7, 978, 2048 }, { 8, 979, 2048 }, { 7, 980, 2048 }, { 8, 981, 2048 }, { 8, 982, 2048 }, { 9, 983, 2048 },
+ { 7, 984, 2048 }, { 8, 985, 2048 }, { 8, 986, 2048 }, { 9, 987, 2048 }, { 8, 988, 2048 }, { 9, 989, 2048 }, { 9, 990, 2048 }, { 10, 991, 2048 },
+ { 6, 992, 2048 }, { 7, 993, 2048 }, { 7, 994, 2048 }, { 8, 995, 2048 }, { 7, 996, 2048 }, { 8, 997, 2048 }, { 8, 998, 2048 }, { 9, 999, 2048 },
+ { 7, 1000, 2048 }, { 8, 1001, 2048 }, { 8, 1002, 2048 }, { 9, 1003, 2048 }, { 8, 1004, 2048 }, { 9, 1005, 2048 }, { 9, 1006, 2048 }, { 10, 1007, 2048 },
+ { 7, 1008, 2048 }, { 8, 1009, 2048 }, { 8, 1010, 2048 }, { 9, 1011, 2048 }, { 8, 1012, 2048 }, { 9, 1013, 2048 }, { 9, 1014, 2048 }, { 10, 1015, 2048 },
+ { 8, 1016, 2048 }, { 9, 1017, 2048 }, { 9, 1018, 2048 }, { 10, 1019, 2048 }, { 9, 1020, 2048 }, { 10, 1021, 2048 }, { 10, 1022, 2048 }, { 11, 1023, 2048 },
+ { 2, 1024, 2048 }, { 3, 1025, 2048 }, { 3, 1026, 2048 }, { 4, 1027, 2048 }, { 3, 1028, 2048 }, { 4, 1029, 2048 }, { 4, 1030, 2048 }, { 5, 1031, 2048 },
+ { 3, 1032, 2048 }, { 4, 1033, 2048 }, { 4, 1034, 2048 }, { 5, 1035, 2048 }, { 4, 1036, 2048 }, { 5, 1037, 2048 }, { 5, 1038, 2048 }, { 6, 1039, 2048 },
+ { 3, 1040, 2048 }, { 4, 1041, 2048 }, { 4, 1042, 2048 }, { 5, 1043, 2048 }, { 4, 1044, 2048 }, { 5, 1045, 2048 }, { 5, 1046, 2048 }, { 6, 1047, 2048 },
+ { 4, 1048, 2048 }, { 5, 1049, 2048 }, { 5, 1050, 2048 }, { 6, 1051, 2048 }, { 5, 1052, 2048 }, { 6, 1053, 2048 }, { 6, 1054, 2048 }, { 7, 1055, 2048 },
+ { 3, 1056, 2048 }, { 4, 1057, 2048 }, { 4, 1058, 2048 }, { 5, 1059, 2048 }, { 4, 1060, 2048 }, { 5, 1061, 2048 }, { 5, 1062, 2048 }, { 6, 1063, 2048 },
+ { 4, 1064, 2048 }, { 5, 1065, 2048 }, { 5, 1066, 2048 }, { 6, 1067, 2048 }, { 5, 1068, 2048 }, { 6, 1069, 2048 }, { 6, 1070, 2048 }, { 7, 1071, 2048 },
+ { 4, 1072, 2048 }, { 5, 1073, 2048 }, { 5, 1074, 2048 }, { 6, 1075, 2048 }, { 5, 1076, 2048 }, { 6, 1077, 2048 }, { 6, 1078, 2048 }, { 7, 1079, 2048 },
+ { 5, 1080, 2048 }, { 6, 1081, 2048 }, { 6, 1082, 2048 }, { 7, 1083, 2048 }, { 6, 1084, 2048 }, { 7, 1085, 2048 }, { 7, 1086, 2048 }, { 8, 1087, 2048 },
+ { 3, 1088, 2048 }, { 4, 1089, 2048 }, { 4, 1090, 2048 }, { 5, 1091, 2048 }, { 4, 1092, 2048 }, { 5, 1093, 2048 }, { 5, 1094, 2048 }, { 6, 1095, 2048 },
+ { 4, 1096, 2048 }, { 5, 1097, 2048 }, { 5, 1098, 2048 }, { 6, 1099, 2048 }, { 5, 1100, 2048 }, { 6, 1101, 2048 }, { 6, 1102, 2048 }, { 7, 1103, 2048 },
+ { 4, 1104, 2048 }, { 5, 1105, 2048 }, { 5, 1106, 2048 }, { 6, 1107, 2048 }, { 5, 1108, 2048 }, { 6, 1109, 2048 }, { 6, 1110, 2048 }, { 7, 1111, 2048 },
+ { 5, 1112, 2048 }, { 6, 1113, 2048 }, { 6, 1114, 2048 }, { 7, 1115, 2048 }, { 6, 1116, 2048 }, { 7, 1117, 2048 }, { 7, 1118, 2048 }, { 8, 1119, 2048 },
+ { 4, 1120, 2048 }, { 5, 1121, 2048 }, { 5, 1122, 2048 }, { 6, 1123, 2048 }, { 5, 1124, 2048 }, { 6, 1125, 2048 }, { 6, 1126, 2048 }, { 7, 1127, 2048 },
+ { 5, 1128, 2048 }, { 6, 1129, 2048 }, { 6, 1130, 2048 }, { 7, 1131, 2048 }, { 6, 1132, 2048 }, { 7, 1133, 2048 }, { 7, 1134, 2048 }, { 8, 1135, 2048 },
+ { 5, 1136, 2048 }, { 6, 1137, 2048 }, { 6, 1138, 2048 }, { 7, 1139, 2048 }, { 6, 1140, 2048 }, { 7, 1141, 2048 }, { 7, 1142, 2048 }, { 8, 1143, 2048 },
+ { 6, 1144, 2048 }, { 7, 1145, 2048 }, { 7, 1146, 2048 }, { 8, 1147, 2048 }, { 7, 1148, 2048 }, { 8, 1149, 2048 }, { 8, 1150, 2048 }, { 9, 1151, 2048 },
+ { 3, 1152, 2048 }, { 4, 1153, 2048 }, { 4, 1154, 2048 }, { 5, 1155, 2048 }, { 4, 1156, 2048 }, { 5, 1157, 2048 }, { 5, 1158, 2048 }, { 6, 1159, 2048 },
+ { 4, 1160, 2048 }, { 5, 1161, 2048 }, { 5, 1162, 2048 }, { 6, 1163, 2048 }, { 5, 1164, 2048 }, { 6, 1165, 2048 }, { 6, 1166, 2048 }, { 7, 1167, 2048 },
+ { 4, 1168, 2048 }, { 5, 1169, 2048 }, { 5, 1170, 2048 }, { 6, 1171, 2048 }, { 5, 1172, 2048 }, { 6, 1173, 2048 }, { 6, 1174, 2048 }, { 7, 1175, 2048 },
+ { 5, 1176, 2048 }, { 6, 1177, 2048 }, { 6, 1178, 2048 }, { 7, 1179, 2048 }, { 6, 1180, 2048 }, { 7, 1181, 2048 }, { 7, 1182, 2048 }, { 8, 1183, 2048 },
+ { 4, 1184, 2048 }, { 5, 1185, 2048 }, { 5, 1186, 2048 }, { 6, 1187, 2048 }, { 5, 1188, 2048 }, { 6, 1189, 2048 }, { 6, 1190, 2048 }, { 7, 1191, 2048 },
+ { 5, 1192, 2048 }, { 6, 1193, 2048 }, { 6, 1194, 2048 }, { 7, 1195, 2048 }, { 6, 1196, 2048 }, { 7, 1197, 2048 }, { 7, 1198, 2048 }, { 8, 1199, 2048 },
+ { 5, 1200, 2048 }, { 6, 1201, 2048 }, { 6, 1202, 2048 }, { 7, 1203, 2048 }, { 6, 1204, 2048 }, { 7, 1205, 2048 }, { 7, 1206, 2048 }, { 8, 1207, 2048 },
+ { 6, 1208, 2048 }, { 7, 1209, 2048 }, { 7, 1210, 2048 }, { 8, 1211, 2048 }, { 7, 1212, 2048 }, { 8, 1213, 2048 }, { 8, 1214, 2048 }, { 9, 1215, 2048 },
+ { 4, 1216, 2048 }, { 5, 1217, 2048 }, { 5, 1218, 2048 }, { 6, 1219, 2048 }, { 5, 1220, 2048 }, { 6, 1221, 2048 }, { 6, 1222, 2048 }, { 7, 1223, 2048 },
+ { 5, 1224, 2048 }, { 6, 1225, 2048 }, { 6, 1226, 2048 }, { 7, 1227, 2048 }, { 6, 1228, 2048 }, { 7, 1229, 2048 }, { 7, 1230, 2048 }, { 8, 1231, 2048 },
+ { 5, 1232, 2048 }, { 6, 1233, 2048 }, { 6, 1234, 2048 }, { 7, 1235, 2048 }, { 6, 1236, 2048 }, { 7, 1237, 2048 }, { 7, 1238, 2048 }, { 8, 1239, 2048 },
+ { 6, 1240, 2048 }, { 7, 1241, 2048 }, { 7, 1242, 2048 }, { 8, 1243, 2048 }, { 7, 1244, 2048 }, { 8, 1245, 2048 }, { 8, 1246, 2048 }, { 9, 1247, 2048 },
+ { 5, 1248, 2048 }, { 6, 1249, 2048 }, { 6, 1250, 2048 }, { 7, 1251, 2048 }, { 6, 1252, 2048 }, { 7, 1253, 2048 }, { 7, 1254, 2048 }, { 8, 1255, 2048 },
+ { 6, 1256, 2048 }, { 7, 1257, 2048 }, { 7, 1258, 2048 }, { 8, 1259, 2048 }, { 7, 1260, 2048 }, { 8, 1261, 2048 }, { 8, 1262, 2048 }, { 9, 1263, 2048 },
+ { 6, 1264, 2048 }, { 7, 1265, 2048 }, { 7, 1266, 2048 }, { 8, 1267, 2048 }, { 7, 1268, 2048 }, { 8, 1269, 2048 }, { 8, 1270, 2048 }, { 9, 1271, 2048 },
+ { 7, 1272, 2048 }, { 8, 1273, 2048 }, { 8, 1274, 2048 }, { 9, 1275, 2048 }, { 8, 1276, 2048 }, { 9, 1277, 2048 }, { 9, 1278, 2048 }, { 10, 1279, 2048 },
+ { 3, 1280, 2048 }, { 4, 1281, 2048 }, { 4, 1282, 2048 }, { 5, 1283, 2048 }, { 4, 1284, 2048 }, { 5, 1285, 2048 }, { 5, 1286, 2048 }, { 6, 1287, 2048 },
+ { 4, 1288, 2048 }, { 5, 1289, 2048 }, { 5, 1290, 2048 }, { 6, 1291, 2048 }, { 5, 1292, 2048 }, { 6, 1293, 2048 }, { 6, 1294, 2048 }, { 7, 1295, 2048 },
+ { 4, 1296, 2048 }, { 5, 1297, 2048 }, { 5, 1298, 2048 }, { 6, 1299, 2048 }, { 5, 1300, 2048 }, { 6, 1301, 2048 }, { 6, 1302, 2048 }, { 7, 1303, 2048 },
+ { 5, 1304, 2048 }, { 6, 1305, 2048 }, { 6, 1306, 2048 }, { 7, 1307, 2048 }, { 6, 1308, 2048 }, { 7, 1309, 2048 }, { 7, 1310, 2048 }, { 8, 1311, 2048 },
+ { 4, 1312, 2048 }, { 5, 1313, 2048 }, { 5, 1314, 2048 }, { 6, 1315, 2048 }, { 5, 1316, 2048 }, { 6, 1317, 2048 }, { 6, 1318, 2048 }, { 7, 1319, 2048 },
+ { 5, 1320, 2048 }, { 6, 1321, 2048 }, { 6, 1322, 2048 }, { 7, 1323, 2048 }, { 6, 1324, 2048 }, { 7, 1325, 2048 }, { 7, 1326, 2048 }, { 8, 1327, 2048 },
+ { 5, 1328, 2048 }, { 6, 1329, 2048 }, { 6, 1330, 2048 }, { 7, 1331, 2048 }, { 6, 1332, 2048 }, { 7, 1333, 2048 }, { 7, 1334, 2048 }, { 8, 1335, 2048 },
+ { 6, 1336, 2048 }, { 7, 1337, 2048 }, { 7, 1338, 2048 }, { 8, 1339, 2048 }, { 7, 1340, 2048 }, { 8, 1341, 2048 }, { 8, 1342, 2048 }, { 9, 1343, 2048 },
+ { 4, 1344, 2048 }, { 5, 1345, 2048 }, { 5, 1346, 2048 }, { 6, 1347, 2048 }, { 5, 1348, 2048 }, { 6, 1349, 2048 }, { 6, 1350, 2048 }, { 7, 1351, 2048 },
+ { 5, 1352, 2048 }, { 6, 1353, 2048 }, { 6, 1354, 2048 }, { 7, 1355, 2048 }, { 6, 1356, 2048 }, { 7, 1357, 2048 }, { 7, 1358, 2048 }, { 8, 1359, 2048 },
+ { 5, 1360, 2048 }, { 6, 1361, 2048 }, { 6, 1362, 2048 }, { 7, 1363, 2048 }, { 6, 1364, 2048 }, { 7, 1365, 2048 }, { 7, 1366, 2048 }, { 8, 1367, 2048 },
+ { 6, 1368, 2048 }, { 7, 1369, 2048 }, { 7, 1370, 2048 }, { 8, 1371, 2048 }, { 7, 1372, 2048 }, { 8, 1373, 2048 }, { 8, 1374, 2048 }, { 9, 1375, 2048 },
+ { 5, 1376, 2048 }, { 6, 1377, 2048 }, { 6, 1378, 2048 }, { 7, 1379, 2048 }, { 6, 1380, 2048 }, { 7, 1381, 2048 }, { 7, 1382, 2048 }, { 8, 1383, 2048 },
+ { 6, 1384, 2048 }, { 7, 1385, 2048 }, { 7, 1386, 2048 }, { 8, 1387, 2048 }, { 7, 1388, 2048 }, { 8, 1389, 2048 }, { 8, 1390, 2048 }, { 9, 1391, 2048 },
+ { 6, 1392, 2048 }, { 7, 1393, 2048 }, { 7, 1394, 2048 }, { 8, 1395, 2048 }, { 7, 1396, 2048 }, { 8, 1397, 2048 }, { 8, 1398, 2048 }, { 9, 1399, 2048 },
+ { 7, 1400, 2048 }, { 8, 1401, 2048 }, { 8, 1402, 2048 }, { 9, 1403, 2048 }, { 8, 1404, 2048 }, { 9, 1405, 2048 }, { 9, 1406, 2048 }, { 10, 1407, 2048 },
+ { 4, 1408, 2048 }, { 5, 1409, 2048 }, { 5, 1410, 2048 }, { 6, 1411, 2048 }, { 5, 1412, 2048 }, { 6, 1413, 2048 }, { 6, 1414, 2048 }, { 7, 1415, 2048 },
+ { 5, 1416, 2048 }, { 6, 1417, 2048 }, { 6, 1418, 2048 }, { 7, 1419, 2048 }, { 6, 1420, 2048 }, { 7, 1421, 2048 }, { 7, 1422, 2048 }, { 8, 1423, 2048 },
+ { 5, 1424, 2048 }, { 6, 1425, 2048 }, { 6, 1426, 2048 }, { 7, 1427, 2048 }, { 6, 1428, 2048 }, { 7, 1429, 2048 }, { 7, 1430, 2048 }, { 8, 1431, 2048 },
+ { 6, 1432, 2048 }, { 7, 1433, 2048 }, { 7, 1434, 2048 }, { 8, 1435, 2048 }, { 7, 1436, 2048 }, { 8, 1437, 2048 }, { 8, 1438, 2048 }, { 9, 1439, 2048 },
+ { 5, 1440, 2048 }, { 6, 1441, 2048 }, { 6, 1442, 2048 }, { 7, 1443, 2048 }, { 6, 1444, 2048 }, { 7, 1445, 2048 }, { 7, 1446, 2048 }, { 8, 1447, 2048 },
+ { 6, 1448, 2048 }, { 7, 1449, 2048 }, { 7, 1450, 2048 }, { 8, 1451, 2048 }, { 7, 1452, 2048 }, { 8, 1453, 2048 }, { 8, 1454, 2048 }, { 9, 1455, 2048 },
+ { 6, 1456, 2048 }, { 7, 1457, 2048 }, { 7, 1458, 2048 }, { 8, 1459, 2048 }, { 7, 1460, 2048 }, { 8, 1461, 2048 }, { 8, 1462, 2048 }, { 9, 1463, 2048 },
+ { 7, 1464, 2048 }, { 8, 1465, 2048 }, { 8, 1466, 2048 }, { 9, 1467, 2048 }, { 8, 1468, 2048 }, { 9, 1469, 2048 }, { 9, 1470, 2048 }, { 10, 1471, 2048 },
+ { 5, 1472, 2048 }, { 6, 1473, 2048 }, { 6, 1474, 2048 }, { 7, 1475, 2048 }, { 6, 1476, 2048 }, { 7, 1477, 2048 }, { 7, 1478, 2048 }, { 8, 1479, 2048 },
+ { 6, 1480, 2048 }, { 7, 1481, 2048 }, { 7, 1482, 2048 }, { 8, 1483, 2048 }, { 7, 1484, 2048 }, { 8, 1485, 2048 }, { 8, 1486, 2048 }, { 9, 1487, 2048 },
+ { 6, 1488, 2048 }, { 7, 1489, 2048 }, { 7, 1490, 2048 }, { 8, 1491, 2048 }, { 7, 1492, 2048 }, { 8, 1493, 2048 }, { 8, 1494, 2048 }, { 9, 1495, 2048 },
+ { 7, 1496, 2048 }, { 8, 1497, 2048 }, { 8, 1498, 2048 }, { 9, 1499, 2048 }, { 8, 1500, 2048 }, { 9, 1501, 2048 }, { 9, 1502, 2048 }, { 10, 1503, 2048 },
+ { 6, 1504, 2048 }, { 7, 1505, 2048 }, { 7, 1506, 2048 }, { 8, 1507, 2048 }, { 7, 1508, 2048 }, { 8, 1509, 2048 }, { 8, 1510, 2048 }, { 9, 1511, 2048 },
+ { 7, 1512, 2048 }, { 8, 1513, 2048 }, { 8, 1514, 2048 }, { 9, 1515, 2048 }, { 8, 1516, 2048 }, { 9, 1517, 2048 }, { 9, 1518, 2048 }, { 10, 1519, 2048 },
+ { 7, 1520, 2048 }, { 8, 1521, 2048 }, { 8, 1522, 2048 }, { 9, 1523, 2048 }, { 8, 1524, 2048 }, { 9, 1525, 2048 }, { 9, 1526, 2048 }, { 10, 1527, 2048 },
+ { 8, 1528, 2048 }, { 9, 1529, 2048 }, { 9, 1530, 2048 }, { 10, 1531, 2048 }, { 9, 1532, 2048 }, { 10, 1533, 2048 }, { 10, 1534, 2048 }, { 11, 1535, 2048 },
+ { 3, 1536, 2048 }, { 4, 1537, 2048 }, { 4, 1538, 2048 }, { 5, 1539, 2048 }, { 4, 1540, 2048 }, { 5, 1541, 2048 }, { 5, 1542, 2048 }, { 6, 1543, 2048 },
+ { 4, 1544, 2048 }, { 5, 1545, 2048 }, { 5, 1546, 2048 }, { 6, 1547, 2048 }, { 5, 1548, 2048 }, { 6, 1549, 2048 }, { 6, 1550, 2048 }, { 7, 1551, 2048 },
+ { 4, 1552, 2048 }, { 5, 1553, 2048 }, { 5, 1554, 2048 }, { 6, 1555, 2048 }, { 5, 1556, 2048 }, { 6, 1557, 2048 }, { 6, 1558, 2048 }, { 7, 1559, 2048 },
+ { 5, 1560, 2048 }, { 6, 1561, 2048 }, { 6, 1562, 2048 }, { 7, 1563, 2048 }, { 6, 1564, 2048 }, { 7, 1565, 2048 }, { 7, 1566, 2048 }, { 8, 1567, 2048 },
+ { 4, 1568, 2048 }, { 5, 1569, 2048 }, { 5, 1570, 2048 }, { 6, 1571, 2048 }, { 5, 1572, 2048 }, { 6, 1573, 2048 }, { 6, 1574, 2048 }, { 7, 1575, 2048 },
+ { 5, 1576, 2048 }, { 6, 1577, 2048 }, { 6, 1578, 2048 }, { 7, 1579, 2048 }, { 6, 1580, 2048 }, { 7, 1581, 2048 }, { 7, 1582, 2048 }, { 8, 1583, 2048 },
+ { 5, 1584, 2048 }, { 6, 1585, 2048 }, { 6, 1586, 2048 }, { 7, 1587, 2048 }, { 6, 1588, 2048 }, { 7, 1589, 2048 }, { 7, 1590, 2048 }, { 8, 1591, 2048 },
+ { 6, 1592, 2048 }, { 7, 1593, 2048 }, { 7, 1594, 2048 }, { 8, 1595, 2048 }, { 7, 1596, 2048 }, { 8, 1597, 2048 }, { 8, 1598, 2048 }, { 9, 1599, 2048 },
+ { 4, 1600, 2048 }, { 5, 1601, 2048 }, { 5, 1602, 2048 }, { 6, 1603, 2048 }, { 5, 1604, 2048 }, { 6, 1605, 2048 }, { 6, 1606, 2048 }, { 7, 1607, 2048 },
+ { 5, 1608, 2048 }, { 6, 1609, 2048 }, { 6, 1610, 2048 }, { 7, 1611, 2048 }, { 6, 1612, 2048 }, { 7, 1613, 2048 }, { 7, 1614, 2048 }, { 8, 1615, 2048 },
+ { 5, 1616, 2048 }, { 6, 1617, 2048 }, { 6, 1618, 2048 }, { 7, 1619, 2048 }, { 6, 1620, 2048 }, { 7, 1621, 2048 }, { 7, 1622, 2048 }, { 8, 1623, 2048 },
+ { 6, 1624, 2048 }, { 7, 1625, 2048 }, { 7, 1626, 2048 }, { 8, 1627, 2048 }, { 7, 1628, 2048 }, { 8, 1629, 2048 }, { 8, 1630, 2048 }, { 9, 1631, 2048 },
+ { 5, 1632, 2048 }, { 6, 1633, 2048 }, { 6, 1634, 2048 }, { 7, 1635, 2048 }, { 6, 1636, 2048 }, { 7, 1637, 2048 }, { 7, 1638, 2048 }, { 8, 1639, 2048 },
+ { 6, 1640, 2048 }, { 7, 1641, 2048 }, { 7, 1642, 2048 }, { 8, 1643, 2048 }, { 7, 1644, 2048 }, { 8, 1645, 2048 }, { 8, 1646, 2048 }, { 9, 1647, 2048 },
+ { 6, 1648, 2048 }, { 7, 1649, 2048 }, { 7, 1650, 2048 }, { 8, 1651, 2048 }, { 7, 1652, 2048 }, { 8, 1653, 2048 }, { 8, 1654, 2048 }, { 9, 1655, 2048 },
+ { 7, 1656, 2048 }, { 8, 1657, 2048 }, { 8, 1658, 2048 }, { 9, 1659, 2048 }, { 8, 1660, 2048 }, { 9, 1661, 2048 }, { 9, 1662, 2048 }, { 10, 1663, 2048 },
+ { 4, 1664, 2048 }, { 5, 1665, 2048 }, { 5, 1666, 2048 }, { 6, 1667, 2048 }, { 5, 1668, 2048 }, { 6, 1669, 2048 }, { 6, 1670, 2048 }, { 7, 1671, 2048 },
+ { 5, 1672, 2048 }, { 6, 1673, 2048 }, { 6, 1674, 2048 }, { 7, 1675, 2048 }, { 6, 1676, 2048 }, { 7, 1677, 2048 }, { 7, 1678, 2048 }, { 8, 1679, 2048 },
+ { 5, 1680, 2048 }, { 6, 1681, 2048 }, { 6, 1682, 2048 }, { 7, 1683, 2048 }, { 6, 1684, 2048 }, { 7, 1685, 2048 }, { 7, 1686, 2048 }, { 8, 1687, 2048 },
+ { 6, 1688, 2048 }, { 7, 1689, 2048 }, { 7, 1690, 2048 }, { 8, 1691, 2048 }, { 7, 1692, 2048 }, { 8, 1693, 2048 }, { 8, 1694, 2048 }, { 9, 1695, 2048 },
+ { 5, 1696, 2048 }, { 6, 1697, 2048 }, { 6, 1698, 2048 }, { 7, 1699, 2048 }, { 6, 1700, 2048 }, { 7, 1701, 2048 }, { 7, 1702, 2048 }, { 8, 1703, 2048 },
+ { 6, 1704, 2048 }, { 7, 1705, 2048 }, { 7, 1706, 2048 }, { 8, 1707, 2048 }, { 7, 1708, 2048 }, { 8, 1709, 2048 }, { 8, 1710, 2048 }, { 9, 1711, 2048 },
+ { 6, 1712, 2048 }, { 7, 1713, 2048 }, { 7, 1714, 2048 }, { 8, 1715, 2048 }, { 7, 1716, 2048 }, { 8, 1717, 2048 }, { 8, 1718, 2048 }, { 9, 1719, 2048 },
+ { 7, 1720, 2048 }, { 8, 1721, 2048 }, { 8, 1722, 2048 }, { 9, 1723, 2048 }, { 8, 1724, 2048 }, { 9, 1725, 2048 }, { 9, 1726, 2048 }, { 10, 1727, 2048 },
+ { 5, 1728, 2048 }, { 6, 1729, 2048 }, { 6, 1730, 2048 }, { 7, 1731, 2048 }, { 6, 1732, 2048 }, { 7, 1733, 2048 }, { 7, 1734, 2048 }, { 8, 1735, 2048 },
+ { 6, 1736, 2048 }, { 7, 1737, 2048 }, { 7, 1738, 2048 }, { 8, 1739, 2048 }, { 7, 1740, 2048 }, { 8, 1741, 2048 }, { 8, 1742, 2048 }, { 9, 1743, 2048 },
+ { 6, 1744, 2048 }, { 7, 1745, 2048 }, { 7, 1746, 2048 }, { 8, 1747, 2048 }, { 7, 1748, 2048 }, { 8, 1749, 2048 }, { 8, 1750, 2048 }, { 9, 1751, 2048 },
+ { 7, 1752, 2048 }, { 8, 1753, 2048 }, { 8, 1754, 2048 }, { 9, 1755, 2048 }, { 8, 1756, 2048 }, { 9, 1757, 2048 }, { 9, 1758, 2048 }, { 10, 1759, 2048 },
+ { 6, 1760, 2048 }, { 7, 1761, 2048 }, { 7, 1762, 2048 }, { 8, 1763, 2048 }, { 7, 1764, 2048 }, { 8, 1765, 2048 }, { 8, 1766, 2048 }, { 9, 1767, 2048 },
+ { 7, 1768, 2048 }, { 8, 1769, 2048 }, { 8, 1770, 2048 }, { 9, 1771, 2048 }, { 8, 1772, 2048 }, { 9, 1773, 2048 }, { 9, 1774, 2048 }, { 10, 1775, 2048 },
+ { 7, 1776, 2048 }, { 8, 1777, 2048 }, { 8, 1778, 2048 }, { 9, 1779, 2048 }, { 8, 1780, 2048 }, { 9, 1781, 2048 }, { 9, 1782, 2048 }, { 10, 1783, 2048 },
+ { 8, 1784, 2048 }, { 9, 1785, 2048 }, { 9, 1786, 2048 }, { 10, 1787, 2048 }, { 9, 1788, 2048 }, { 10, 1789, 2048 }, { 10, 1790, 2048 }, { 11, 1791, 2048 },
+ { 4, 1792, 2048 }, { 5, 1793, 2048 }, { 5, 1794, 2048 }, { 6, 1795, 2048 }, { 5, 1796, 2048 }, { 6, 1797, 2048 }, { 6, 1798, 2048 }, { 7, 1799, 2048 },
+ { 5, 1800, 2048 }, { 6, 1801, 2048 }, { 6, 1802, 2048 }, { 7, 1803, 2048 }, { 6, 1804, 2048 }, { 7, 1805, 2048 }, { 7, 1806, 2048 }, { 8, 1807, 2048 },
+ { 5, 1808, 2048 }, { 6, 1809, 2048 }, { 6, 1810, 2048 }, { 7, 1811, 2048 }, { 6, 1812, 2048 }, { 7, 1813, 2048 }, { 7, 1814, 2048 }, { 8, 1815, 2048 },
+ { 6, 1816, 2048 }, { 7, 1817, 2048 }, { 7, 1818, 2048 }, { 8, 1819, 2048 }, { 7, 1820, 2048 }, { 8, 1821, 2048 }, { 8, 1822, 2048 }, { 9, 1823, 2048 },
+ { 5, 1824, 2048 }, { 6, 1825, 2048 }, { 6, 1826, 2048 }, { 7, 1827, 2048 }, { 6, 1828, 2048 }, { 7, 1829, 2048 }, { 7, 1830, 2048 }, { 8, 1831, 2048 },
+ { 6, 1832, 2048 }, { 7, 1833, 2048 }, { 7, 1834, 2048 }, { 8, 1835, 2048 }, { 7, 1836, 2048 }, { 8, 1837, 2048 }, { 8, 1838, 2048 }, { 9, 1839, 2048 },
+ { 6, 1840, 2048 }, { 7, 1841, 2048 }, { 7, 1842, 2048 }, { 8, 1843, 2048 }, { 7, 1844, 2048 }, { 8, 1845, 2048 }, { 8, 1846, 2048 }, { 9, 1847, 2048 },
+ { 7, 1848, 2048 }, { 8, 1849, 2048 }, { 8, 1850, 2048 }, { 9, 1851, 2048 }, { 8, 1852, 2048 }, { 9, 1853, 2048 }, { 9, 1854, 2048 }, { 10, 1855, 2048 },
+ { 5, 1856, 2048 }, { 6, 1857, 2048 }, { 6, 1858, 2048 }, { 7, 1859, 2048 }, { 6, 1860, 2048 }, { 7, 1861, 2048 }, { 7, 1862, 2048 }, { 8, 1863, 2048 },
+ { 6, 1864, 2048 }, { 7, 1865, 2048 }, { 7, 1866, 2048 }, { 8, 1867, 2048 }, { 7, 1868, 2048 }, { 8, 1869, 2048 }, { 8, 1870, 2048 }, { 9, 1871, 2048 },
+ { 6, 1872, 2048 }, { 7, 1873, 2048 }, { 7, 1874, 2048 }, { 8, 1875, 2048 }, { 7, 1876, 2048 }, { 8, 1877, 2048 }, { 8, 1878, 2048 }, { 9, 1879, 2048 },
+ { 7, 1880, 2048 }, { 8, 1881, 2048 }, { 8, 1882, 2048 }, { 9, 1883, 2048 }, { 8, 1884, 2048 }, { 9, 1885, 2048 }, { 9, 1886, 2048 }, { 10, 1887, 2048 },
+ { 6, 1888, 2048 }, { 7, 1889, 2048 }, { 7, 1890, 2048 }, { 8, 1891, 2048 }, { 7, 1892, 2048 }, { 8, 1893, 2048 }, { 8, 1894, 2048 }, { 9, 1895, 2048 },
+ { 7, 1896, 2048 }, { 8, 1897, 2048 }, { 8, 1898, 2048 }, { 9, 1899, 2048 }, { 8, 1900, 2048 }, { 9, 1901, 2048 }, { 9, 1902, 2048 }, { 10, 1903, 2048 },
+ { 7, 1904, 2048 }, { 8, 1905, 2048 }, { 8, 1906, 2048 }, { 9, 1907, 2048 }, { 8, 1908, 2048 }, { 9, 1909, 2048 }, { 9, 1910, 2048 }, { 10, 1911, 2048 },
+ { 8, 1912, 2048 }, { 9, 1913, 2048 }, { 9, 1914, 2048 }, { 10, 1915, 2048 }, { 9, 1916, 2048 }, { 10, 1917, 2048 }, { 10, 1918, 2048 }, { 11, 1919, 2048 },
+ { 5, 1920, 2048 }, { 6, 1921, 2048 }, { 6, 1922, 2048 }, { 7, 1923, 2048 }, { 6, 1924, 2048 }, { 7, 1925, 2048 }, { 7, 1926, 2048 }, { 8, 1927, 2048 },
+ { 6, 1928, 2048 }, { 7, 1929, 2048 }, { 7, 1930, 2048 }, { 8, 1931, 2048 }, { 7, 1932, 2048 }, { 8, 1933, 2048 }, { 8, 1934, 2048 }, { 9, 1935, 2048 },
+ { 6, 1936, 2048 }, { 7, 1937, 2048 }, { 7, 1938, 2048 }, { 8, 1939, 2048 }, { 7, 1940, 2048 }, { 8, 1941, 2048 }, { 8, 1942, 2048 }, { 9, 1943, 2048 },
+ { 7, 1944, 2048 }, { 8, 1945, 2048 }, { 8, 1946, 2048 }, { 9, 1947, 2048 }, { 8, 1948, 2048 }, { 9, 1949, 2048 }, { 9, 1950, 2048 }, { 10, 1951, 2048 },
+ { 6, 1952, 2048 }, { 7, 1953, 2048 }, { 7, 1954, 2048 }, { 8, 1955, 2048 }, { 7, 1956, 2048 }, { 8, 1957, 2048 }, { 8, 1958, 2048 }, { 9, 1959, 2048 },
+ { 7, 1960, 2048 }, { 8, 1961, 2048 }, { 8, 1962, 2048 }, { 9, 1963, 2048 }, { 8, 1964, 2048 }, { 9, 1965, 2048 }, { 9, 1966, 2048 }, { 10, 1967, 2048 },
+ { 7, 1968, 2048 }, { 8, 1969, 2048 }, { 8, 1970, 2048 }, { 9, 1971, 2048 }, { 8, 1972, 2048 }, { 9, 1973, 2048 }, { 9, 1974, 2048 }, { 10, 1975, 2048 },
+ { 8, 1976, 2048 }, { 9, 1977, 2048 }, { 9, 1978, 2048 }, { 10, 1979, 2048 }, { 9, 1980, 2048 }, { 10, 1981, 2048 }, { 10, 1982, 2048 }, { 11, 1983, 2048 },
+ { 6, 1984, 2048 }, { 7, 1985, 2048 }, { 7, 1986, 2048 }, { 8, 1987, 2048 }, { 7, 1988, 2048 }, { 8, 1989, 2048 }, { 8, 1990, 2048 }, { 9, 1991, 2048 },
+ { 7, 1992, 2048 }, { 8, 1993, 2048 }, { 8, 1994, 2048 }, { 9, 1995, 2048 }, { 8, 1996, 2048 }, { 9, 1997, 2048 }, { 9, 1998, 2048 }, { 10, 1999, 2048 },
+ { 7, 2000, 2048 }, { 8, 2001, 2048 }, { 8, 2002, 2048 }, { 9, 2003, 2048 }, { 8, 2004, 2048 }, { 9, 2005, 2048 }, { 9, 2006, 2048 }, { 10, 2007, 2048 },
+ { 8, 2008, 2048 }, { 9, 2009, 2048 }, { 9, 2010, 2048 }, { 10, 2011, 2048 }, { 9, 2012, 2048 }, { 10, 2013, 2048 }, { 10, 2014, 2048 }, { 11, 2015, 2048 },
+ { 7, 2016, 2048 }, { 8, 2017, 2048 }, { 8, 2018, 2048 }, { 9, 2019, 2048 }, { 8, 2020, 2048 }, { 9, 2021, 2048 }, { 9, 2022, 2048 }, { 10, 2023, 2048 },
+ { 8, 2024, 2048 }, { 9, 2025, 2048 }, { 9, 2026, 2048 }, { 10, 2027, 2048 }, { 9, 2028, 2048 }, { 10, 2029, 2048 }, { 10, 2030, 2048 }, { 11, 2031, 2048 },
+ { 8, 2032, 2048 }, { 9, 2033, 2048 }, { 9, 2034, 2048 }, { 10, 2035, 2048 }, { 9, 2036, 2048 }, { 10, 2037, 2048 }, { 10, 2038, 2048 }, { 11, 2039, 2048 },
+ { 9, 2040, 2048 }, { 10, 2041, 2048 }, { 10, 2042, 2048 }, { 11, 2043, 2048 }, { 10, 2044, 2048 }, { 11, 2045, 2048 }, { 11, 2046, 2048 }, { 12, 2047, 2048 },
+#endif
+#endif
+#endif
+#endif
+#endif
+#endif
+};
+
+/* find a hole and free as required, return -1 if no hole found */
+static int find_hole(void)
+{
+ unsigned x;
+ int y, z;
+ for (z = -1, y = INT_MAX, x = 0; x < FP_ENTRIES; x++) {
+ if (fp_cache[x].lru_count < y && fp_cache[x].lock == 0) {
+ z = x;
+ y = fp_cache[x].lru_count;
+ }
+ }
+
+ /* decrease all */
+ for (x = 0; x < FP_ENTRIES; x++) {
+ if (fp_cache[x].lru_count > 3) {
+ --(fp_cache[x].lru_count);
+ }
+ }
+
+ /* free entry z */
+ if (z >= 0 && fp_cache[z].g) {
+ mp_clear(&fp_cache[z].mu);
+ ecc_del_point(fp_cache[z].g);
+ fp_cache[z].g = NULL;
+ for (x = 0; x < (1U<<FP_LUT); x++) {
+ 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 = 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)) {
+ 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] = ecc_new_point();
+ if (fp_cache[idx].LUT[x] == NULL) {
+ for (y = 0; y < x; y++) {
+ ecc_del_point(fp_cache[idx].LUT[y]);
+ fp_cache[idx].LUT[y] = NULL;
+ }
+ ecc_del_point(fp_cache[idx].g);
+ fp_cache[idx].g = NULL;
+ fp_cache[idx].lru_count = 0;
+ return GEN_MEM_ERR;
+ }
+ }
+
+ fp_cache[idx].lru_count = 0;
+
+ return MP_OKAY;
+}
+
+/* build the LUT by spacing the bits of the input by #modulus/FP_LUT bits apart
+ *
+ * The algorithm builds patterns in increasing bit order by first making all
+ * single bit input patterns, then all two bit input patterns and so on
+ */
+static int build_lut(int idx, mp_int* modulus, mp_digit* mp, mp_int* mu)
+{
+ unsigned x, y, err, 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], 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 (err != MP_OKAY)
+ break;
+ 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], 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++) {
+ ecc_del_point(fp_cache[idx].LUT[y]);
+ fp_cache[idx].LUT[y] = NULL;
+ }
+ ecc_del_point(fp_cache[idx].g);
+ fp_cache[idx].g = NULL;
+ fp_cache[idx].lru_count = 0;
+ mp_clear(&fp_cache[idx].mu);
+ mp_clear(&tmp);
+
+ return err;
+}
+
+/* perform a fixed point ECC mulmod */
+static int accel_fp_mul(int idx, mp_int* k, ecc_point *R, mp_int* modulus,
+ mp_digit* mp, int map)
+{
+#define KB_SIZE 128
+
+#ifdef WOLFSSL_SMALL_STACK
+ unsigned char* kb;
+#else
+ unsigned char kb[128];
+#endif
+ int x;
+ unsigned y, z, err, bitlen, bitpos, lut_gap, first;
+ mp_int tk;
+
+ if (mp_init(&tk) != 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)) {
+ mp_int order;
+ if (mp_init(&order) != MP_OKAY) {
+ mp_clear(&tk);
+ return MP_INIT_E;
+ }
+
+ /* find order */
+ y = mp_unsigned_bin_size(modulus);
+ for (x = 0; ecc_sets[x].size; x++) {
+ if (y <= (unsigned)ecc_sets[x].size) break;
+ }
+
+ /* back off if we are on the 521 bit curve */
+ if (y == 66) --x;
+
+ if ((err = mp_read_radix(&order, ecc_sets[x].order, 16)) != MP_OKAY) {
+ mp_clear(&order);
+ mp_clear(&tk);
+ return err;
+ }
+
+ /* k must be less than modulus */
+ if (mp_cmp(k, &order) != MP_LT) {
+ if ((err = mp_mod(k, &order, &tk)) != MP_OKAY) {
+ mp_clear(&tk);
+ mp_clear(&order);
+ return err;
+ }
+ } else {
+ mp_copy(k, &tk);
+ }
+ mp_clear(&order);
+ } else {
+ mp_copy(k, &tk);
+ }
+
+ /* 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)) {
+ mp_clear(&tk);
+ return BUFFER_E;
+ }
+
+ /* store k */
+#ifdef WOLFSSL_SMALL_STACK
+ kb = (unsigned char*)XMALLOC(KB_SIZE, NULL, DYNAMIC_TYPE_TMP_BUFFER);
+ if (kb == NULL)
+ return MEMORY_E;
+#endif
+
+ XMEMSET(kb, 0, KB_SIZE);
+ if ((err = mp_to_unsigned_bin(&tk, kb)) != MP_OKAY) {
+ mp_clear(&tk);
+ }
+ else {
+ /* let's reverse kb so it's little endian */
+ x = 0;
+ y = mp_unsigned_bin_size(&tk) - 1;
+ mp_clear(&tk);
+
+ while ((unsigned)x < y) {
+ z = kb[x]; kb[x] = kb[y]; kb[y] = z;
+ ++x; --y;
+ }
+
+ /* at this point we can start, yipee */
+ first = 1;
+ for (x = lut_gap-1; x >= 0; x--) {
+ /* extract FP_LUT bits from kb spread out by lut_gap bits and offset
+ by x bits from the start */
+ bitpos = x;
+ for (y = z = 0; y < FP_LUT; y++) {
+ z |= ((kb[bitpos>>3] >> (bitpos&7)) & 1) << y;
+ bitpos += lut_gap; /* it's y*lut_gap + x, but here we can avoid
+ the mult in each loop */
+ }
+
+ /* double if not first */
+ if (!first) {
+ if ((err = ecc_projective_dbl_point(R, R, 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,
+ 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) {
+ z = 0;
+ ForceZero(kb, KB_SIZE);
+ /* map R back from projective space */
+ if (map) {
+ err = ecc_map(R, modulus, mp);
+ } else {
+ err = MP_OKAY;
+ }
+ }
+
+#ifdef WOLFSSL_SMALL_STACK
+ XFREE(kb, NULL, DYNAMIC_TYPE_TMP_BUFFER);
+#endif
+
+#undef KB_SIZE
+
+ return err;
+}
+
+#ifdef ECC_SHAMIR
+/* perform a fixed point ECC mulmod */
+static int accel_fp_mul2add(int idx1, int idx2,
+ mp_int* kA, mp_int* kB,
+ ecc_point *R, mp_int* modulus, mp_digit* mp)
+{
+#define KB_SIZE 128
+
+#ifdef WOLFSSL_SMALL_STACK
+ unsigned char* kb[2];
+#else
+ unsigned char kb[2][128];
+#endif
+ int x;
+ unsigned y, z, err, bitlen, bitpos, lut_gap, first, zA, zB;
+ mp_int tka;
+ mp_int tkb;
+ mp_int order;
+
+ if (mp_init_multi(&tka, &tkb, 0, 0, 0, 0) != 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_init(&order)) != MP_OKAY) {
+ mp_clear(&tkb);
+ mp_clear(&tka);
+ return err;
+ }
+ if ((err = mp_read_radix(&order, ecc_sets[x].order, 16)) != MP_OKAY) {
+ mp_clear(&tkb);
+ mp_clear(&tka);
+ mp_clear(&order);
+ return err;
+ }
+
+ /* kA must be less than modulus */
+ if (mp_cmp(kA, &order) != MP_LT) {
+ if ((err = mp_mod(kA, &order, &tka)) != MP_OKAY) {
+ mp_clear(&tkb);
+ mp_clear(&tka);
+ mp_clear(&order);
+ return err;
+ }
+ } else {
+ mp_copy(kA, &tka);
+ }
+ mp_clear(&order);
+ } else {
+ mp_copy(kA, &tka);
+ }
+
+ /* 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_init(&order)) != MP_OKAY) {
+ mp_clear(&tkb);
+ mp_clear(&tka);
+ return err;
+ }
+ if ((err = mp_read_radix(&order, ecc_sets[x].order, 16)) != MP_OKAY) {
+ mp_clear(&tkb);
+ mp_clear(&tka);
+ mp_clear(&order);
+ return err;
+ }
+
+ /* kB must be less than modulus */
+ if (mp_cmp(kB, &order) != MP_LT) {
+ if ((err = mp_mod(kB, &order, &tkb)) != MP_OKAY) {
+ mp_clear(&tkb);
+ mp_clear(&tka);
+ mp_clear(&order);
+ return err;
+ }
+ } else {
+ mp_copy(kB, &tkb);
+ }
+ mp_clear(&order);
+ } else {
+ mp_copy(kB, &tkb);
+ }
+
+ /* 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)) ) {
+ mp_clear(&tka);
+ mp_clear(&tkb);
+ return BUFFER_E;
+ }
+
+ /* store k */
+#ifdef WOLFSSL_SMALL_STACK
+ kb[0] = (unsigned char*)XMALLOC(KB_SIZE, NULL, DYNAMIC_TYPE_TMP_BUFFER);
+ if (kb[0] == NULL)
+ return MEMORY_E;
+#endif
+
+ XMEMSET(kb[0], 0, KB_SIZE);
+ if ((err = mp_to_unsigned_bin(&tka, kb[0])) != MP_OKAY) {
+ mp_clear(&tka);
+ mp_clear(&tkb);
+ XFREE(kb[0], NULL, DYNAMIC_TYPE_TMP_BUFFER);
+ return err;
+ }
+
+ /* let's reverse kb so it's little endian */
+ x = 0;
+ y = mp_unsigned_bin_size(&tka) - 1;
+ mp_clear(&tka);
+ while ((unsigned)x < y) {
+ z = kb[0][x]; kb[0][x] = kb[0][y]; kb[0][y] = z;
+ ++x; --y;
+ }
+
+ /* store b */
+#ifdef WOLFSSL_SMALL_STACK
+ kb[1] = (unsigned char*)XMALLOC(KB_SIZE, NULL, DYNAMIC_TYPE_TMP_BUFFER);
+ if (kb[1] == NULL) {
+ XFREE(kb[0], NULL, DYNAMIC_TYPE_TMP_BUFFER);
+ return MEMORY_E;
+ }
+#endif
+
+ XMEMSET(kb[1], 0, KB_SIZE);
+ if ((err = mp_to_unsigned_bin(&tkb, kb[1])) != MP_OKAY) {
+ mp_clear(&tkb);
+ }
+ else {
+ x = 0;
+ y = mp_unsigned_bin_size(&tkb) - 1;
+ mp_clear(&tkb);
+ while ((unsigned)x < y) {
+ z = kb[1][x]; kb[1][x] = kb[1][y]; kb[1][y] = z;
+ ++x; --y;
+ }
+
+ /* at this point we can start, yipee */
+ first = 1;
+ for (x = lut_gap-1; x >= 0; x--) {
+ /* extract FP_LUT bits from kb spread out by lut_gap bits and
+ offset by x bits from the start */
+ bitpos = x;
+ for (y = zA = zB = 0; y < FP_LUT; y++) {
+ zA |= ((kb[0][bitpos>>3] >> (bitpos&7)) & 1) << y;
+ zB |= ((kb[1][bitpos>>3] >> (bitpos&7)) & 1) << y;
+ bitpos += lut_gap; /* it's y*lut_gap + x, but here we can avoid
+ the mult in each loop */
+ }
+
+ /* double if not first */
+ if (!first) {
+ if ((err = ecc_projective_dbl_point(R, R, 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, modulus, mp)) != MP_OKAY) {
+ break;
+ }
+ }
+ if (zB) {
+ if ((err = ecc_projective_add_point(R, fp_cache[idx2].LUT[zB],
+ R, 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, 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;
+ }
+ }
+ }
+ }
+
+ ForceZero(kb[0], KB_SIZE);
+ ForceZero(kb[1], KB_SIZE);
+
+#ifdef WOLFSSL_SMALL_STACK
+ XFREE(kb[0], NULL, DYNAMIC_TYPE_TMP_BUFFER);
+ XFREE(kb[1], NULL, DYNAMIC_TYPE_TMP_BUFFER);
+#endif
+
+#undef KB_SIZE
+
+ return ecc_map(R, modulus, mp);
+}
+
+/** ECC Fixed Point mulmod global
+ 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)
+ 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* modulus)
+{
+ 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) {
+ InitMutex(&ecc_fp_lock);
+ initMutex = 1;
+ }
+ if (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, 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, 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, modulus, &mp);
+ } else {
+ err = normal_ecc_mul2add(A, kA, B, kB, C, modulus);
+ }
+ }
+
+#ifndef HAVE_THREAD_LS
+ UnLockMutex(&ecc_fp_lock);
+#endif /* HAVE_THREAD_LS */
+ mp_clear(&mu);
+
+ return err;
+}
+#endif
+
+/** ECC Fixed Point mulmod global
+ k The multiplicand
+ G Base point to multiply
+ R [out] Destination of product
+ 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 ecc_mulmod(mp_int* k, ecc_point *G, ecc_point *R, mp_int* modulus,
+ int map)
+{
+ int idx, err = MP_OKAY;
+ mp_digit mp;
+ mp_int mu;
+ int mpSetup = 0;
+
+ if (mp_init(&mu) != MP_OKAY)
+ return MP_INIT_E;
+
+#ifndef HAVE_THREAD_LS
+ if (initMutex == 0) {
+ InitMutex(&ecc_fp_lock);
+ initMutex = 1;
+ }
+
+ if (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, 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, modulus, &mp, map);
+ } else {
+ err = normal_ecc_mulmod(k, G, R, modulus, map);
+ }
+ }
+
+#ifndef HAVE_THREAD_LS
+ UnLockMutex(&ecc_fp_lock);
+#endif /* HAVE_THREAD_LS */
+ mp_clear(&mu);
+
+ return err;
+}
+
+/* helper function for freeing the cache ...
+ must be called with the cache mutex locked */
+static void wc_ecc_fp_free_cache(void)
+{
+ unsigned x, y;
+ for (x = 0; x < FP_ENTRIES; x++) {
+ if (fp_cache[x].g != NULL) {
+ for (y = 0; y < (1U<<FP_LUT); y++) {
+ ecc_del_point(fp_cache[x].LUT[y]);
+ fp_cache[x].LUT[y] = NULL;
+ }
+ ecc_del_point(fp_cache[x].g);
+ fp_cache[x].g = NULL;
+ mp_clear(&fp_cache[x].mu);
+ fp_cache[x].lru_count = 0;
+ fp_cache[x].lock = 0;
+ }
+ }
+}
+
+/** Free the Fixed Point cache */
+void wc_ecc_fp_free(void)
+{
+#ifndef HAVE_THREAD_LS
+ if (initMutex == 0) {
+ InitMutex(&ecc_fp_lock);
+ initMutex = 1;
+ }
+
+ if (LockMutex(&ecc_fp_lock) == 0) {
+#endif /* HAVE_THREAD_LS */
+
+ wc_ecc_fp_free_cache();
+
+#ifndef HAVE_THREAD_LS
+ UnLockMutex(&ecc_fp_lock);
+ FreeMutex(&ecc_fp_lock);
+ initMutex = 0;
+ }
+#endif /* HAVE_THREAD_LS */
+}
+
+
+#endif /* FP_ECC */
+
+#ifdef HAVE_ECC_ENCRYPT
+
+
+enum ecCliState {
+ ecCLI_INIT = 1,
+ ecCLI_SALT_GET = 2,
+ ecCLI_SALT_SET = 3,
+ ecCLI_SENT_REQ = 4,
+ ecCLI_RECV_RESP = 5,
+ ecCLI_BAD_STATE = 99
+};
+
+enum ecSrvState {
+ ecSRV_INIT = 1,
+ ecSRV_SALT_GET = 2,
+ ecSRV_SALT_SET = 3,
+ ecSRV_RECV_REQ = 4,
+ ecSRV_SENT_RESP = 5,
+ ecSRV_BAD_STATE = 99
+};
+
+
+struct ecEncCtx {
+ const byte* kdfSalt; /* optional salt for kdf */
+ const byte* kdfInfo; /* optional info for kdf */
+ const byte* macSalt; /* optional salt for mac */
+ word32 kdfSaltSz; /* size of kdfSalt */
+ word32 kdfInfoSz; /* size of kdfInfo */
+ word32 macSaltSz; /* size of macSalt */
+ 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_ENC_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_ENC_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, 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 resue */
+int wc_ecc_ctx_reset(ecEncCtx* ctx, 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);
+}
+
+
+/* alloc/init and set defaults, return new Context */
+ecEncCtx* wc_ecc_ctx_new(int flags, RNG* rng)
+{
+ int ret = 0;
+ ecEncCtx* ctx = (ecEncCtx*)XMALLOC(sizeof(ecEncCtx), 0, DYNAMIC_TYPE_ECC);
+
+ if (ctx)
+ ctx->protocol = (byte)flags;
+
+ ret = wc_ecc_ctx_reset(ctx, rng);
+ if (ret != 0) {
+ wc_ecc_ctx_free(ctx);
+ ctx = NULL;
+ }
+
+ return ctx;
+}
+
+
+/* free any resources, clear any keys */
+void wc_ecc_ctx_free(ecEncCtx* ctx)
+{
+ if (ctx) {
+ ForceZero(ctx, sizeof(ecEncCtx));
+ XFREE(ctx, 0, 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_64;
+ *blockSz = AES_BLOCK_SIZE;
+ break;
+ default:
+ return BAD_FUNC_ARG;
+ }
+
+ switch (ctx->macAlgo) {
+ case ecHMAC_SHA256:
+ *digestSz = SHA256_DIGEST_SIZE;
+ break;
+ default:
+ return BAD_FUNC_ARG;
+ }
+ } else
+ return BAD_FUNC_ARG;
+
+ *keysLen = *encKeySz + *ivSz + *digestSz;
+
+ return 0;
+}
+
+
+/* ecc encrypt with shared secret run through kdf
+ ctx holds non default algos and inputs
+ msgSz should be the right size for encAlgo, i.e., already padded
+ return 0 on success */
+int wc_ecc_encrypt(ecc_key* privKey, ecc_key* pubKey, const byte* msg,
+ word32 msgSz, byte* out, word32* outSz, ecEncCtx* ctx)
+{
+ int ret;
+ word32 blockSz;
+ word32 digestSz;
+ ecEncCtx localCtx;
+#ifdef WOLFSSL_SMALL_STACK
+ byte* sharedSecret;
+ byte* keys;
+#else
+ byte sharedSecret[ECC_MAXSIZE]; /* 521 max size */
+ byte keys[ECC_BUFSIZE]; /* max size */
+#endif
+ word32 sharedSz = ECC_MAXSIZE;
+ int keysLen;
+ int encKeySz;
+ int ivSz;
+ int offset = 0; /* keys offset if doing msg exchange */
+ byte* encKey;
+ byte* encIv;
+ byte* macKey;
+
+ if (privKey == NULL || pubKey == NULL || msg == NULL || out == NULL ||
+ outSz == NULL)
+ return BAD_FUNC_ARG;
+
+ if (ctx == NULL) { /* use defaults */
+ ecc_ctx_init(&localCtx, 0);
+ ctx = &localCtx;
+ }
+
+ ret = ecc_get_key_sizes(ctx, &encKeySz, &ivSz, &keysLen, &digestSz,
+ &blockSz);
+ if (ret != 0)
+ return ret;
+
+ if (ctx->protocol == REQ_RESP_SERVER) {
+ offset = keysLen;
+ keysLen *= 2;
+
+ if (ctx->srvSt != ecSRV_RECV_REQ)
+ return BAD_ENC_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_ENC_STATE_E;
+
+ ctx->cliSt = ecCLI_SENT_REQ; /* only do this once */
+ }
+
+ if (keysLen > ECC_BUFSIZE) /* keys size */
+ return BUFFER_E;
+
+ if ( (msgSz%blockSz) != 0)
+ return BAD_PADDING_E;
+
+ if (*outSz < (msgSz + digestSz))
+ return BUFFER_E;
+
+#ifdef WOLFSSL_SMALL_STACK
+ sharedSecret = (byte*)XMALLOC(ECC_MAXSIZE, NULL, DYNAMIC_TYPE_TMP_BUFFER);
+ if (sharedSecret == NULL)
+ return MEMORY_E;
+
+ keys = (byte*)XMALLOC(ECC_BUFSIZE, NULL, DYNAMIC_TYPE_TMP_BUFFER);
+ if (keys == NULL) {
+ XFREE(sharedSecret, NULL, DYNAMIC_TYPE_TMP_BUFFER);
+ return MEMORY_E;
+ }
+#endif
+
+ ret = wc_ecc_shared_secret(privKey, pubKey, sharedSecret, &sharedSz);
+
+ if (ret == 0) {
+ switch (ctx->kdfAlgo) {
+ case ecHKDF_SHA256 :
+ ret = wc_HKDF(SHA256, sharedSecret, sharedSz, ctx->kdfSalt,
+ ctx->kdfSaltSz, ctx->kdfInfo, ctx->kdfInfoSz,
+ keys, keysLen);
+ break;
+
+ default:
+ ret = BAD_FUNC_ARG;
+ break;
+ }
+ }
+
+ if (ret == 0) {
+ encKey = keys + offset;
+ encIv = encKey + encKeySz;
+ macKey = encKey + encKeySz + ivSz;
+
+ switch (ctx->encAlgo) {
+ case ecAES_128_CBC:
+ {
+ Aes aes;
+ ret = wc_AesSetKey(&aes, encKey, KEY_SIZE_128, encIv,
+ AES_ENCRYPTION);
+ if (ret != 0)
+ break;
+ ret = wc_AesCbcEncrypt(&aes, out, msg, msgSz);
+ }
+ break;
+
+ default:
+ ret = BAD_FUNC_ARG;
+ break;
+ }
+ }
+
+ if (ret == 0) {
+ switch (ctx->macAlgo) {
+ case ecHMAC_SHA256:
+ {
+ Hmac hmac;
+ ret = wc_HmacSetKey(&hmac, SHA256, macKey, SHA256_DIGEST_SIZE);
+ if (ret != 0)
+ break;
+ ret = wc_HmacUpdate(&hmac, out, msgSz);
+ if (ret != 0)
+ break;
+ ret = wc_HmacUpdate(&hmac, ctx->macSalt, ctx->macSaltSz);
+ if (ret != 0)
+ break;
+ ret = wc_HmacFinal(&hmac, out+msgSz);
+ }
+ break;
+
+ default:
+ ret = BAD_FUNC_ARG;
+ break;
+ }
+ }
+
+ if (ret == 0)
+ *outSz = msgSz + digestSz;
+
+#ifdef WOLFSSL_SMALL_STACK
+ XFREE(sharedSecret, NULL, DYNAMIC_TYPE_TMP_BUFFER);
+ XFREE(keys, NULL, DYNAMIC_TYPE_TMP_BUFFER);
+#endif
+
+ return ret;
+}
+
+
+/* ecc decrypt with shared secret run through kdf
+ ctx holds non default algos and inputs
+ return 0 on success */
+int wc_ecc_decrypt(ecc_key* privKey, ecc_key* pubKey, const byte* msg,
+ word32 msgSz, byte* out, word32* outSz, ecEncCtx* ctx)
+{
+ int ret;
+ word32 blockSz;
+ word32 digestSz;
+ ecEncCtx localCtx;
+#ifdef WOLFSSL_SMALL_STACK
+ byte* sharedSecret;
+ byte* keys;
+#else
+ byte sharedSecret[ECC_MAXSIZE]; /* 521 max size */
+ byte keys[ECC_BUFSIZE]; /* max size */
+#endif
+ word32 sharedSz = ECC_MAXSIZE;
+ int keysLen;
+ int encKeySz;
+ int ivSz;
+ int offset = 0; /* in case using msg exchange */
+ byte* encKey;
+ byte* encIv;
+ byte* macKey;
+
+ if (privKey == NULL || pubKey == NULL || msg == NULL || out == NULL ||
+ outSz == NULL)
+ return BAD_FUNC_ARG;
+
+ if (ctx == NULL) { /* use defaults */
+ ecc_ctx_init(&localCtx, 0);
+ ctx = &localCtx;
+ }
+
+ ret = ecc_get_key_sizes(ctx, &encKeySz, &ivSz, &keysLen, &digestSz,
+ &blockSz);
+ if (ret != 0)
+ return ret;
+
+ if (ctx->protocol == REQ_RESP_CLIENT) {
+ offset = keysLen;
+ keysLen *= 2;
+
+ if (ctx->cliSt != ecCLI_SENT_REQ)
+ return BAD_ENC_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_ENC_STATE_E;
+
+ ctx->srvSt = ecSRV_RECV_REQ; /* only do this once */
+ }
+
+ if (keysLen > ECC_BUFSIZE) /* keys size */
+ return BUFFER_E;
+
+ if ( ((msgSz-digestSz) % blockSz) != 0)
+ return BAD_PADDING_E;
+
+ if (*outSz < (msgSz - digestSz))
+ return BUFFER_E;
+
+#ifdef WOLFSSL_SMALL_STACK
+ sharedSecret = (byte*)XMALLOC(ECC_MAXSIZE, NULL, DYNAMIC_TYPE_TMP_BUFFER);
+ if (sharedSecret == NULL)
+ return MEMORY_E;
+
+ keys = (byte*)XMALLOC(ECC_BUFSIZE, NULL, DYNAMIC_TYPE_TMP_BUFFER);
+ if (keys == NULL) {
+ XFREE(sharedSecret, NULL, DYNAMIC_TYPE_TMP_BUFFER);
+ return MEMORY_E;
+ }
+#endif
+
+ ret = wc_ecc_shared_secret(privKey, pubKey, sharedSecret, &sharedSz);
+
+ if (ret == 0) {
+ switch (ctx->kdfAlgo) {
+ case ecHKDF_SHA256 :
+ ret = wc_HKDF(SHA256, sharedSecret, sharedSz, ctx->kdfSalt,
+ ctx->kdfSaltSz, ctx->kdfInfo, ctx->kdfInfoSz,
+ keys, keysLen);
+ break;
+
+ default:
+ ret = BAD_FUNC_ARG;
+ break;
+ }
+ }
+
+ if (ret == 0) {
+ encKey = keys + offset;
+ encIv = encKey + encKeySz;
+ macKey = encKey + encKeySz + ivSz;
+
+ switch (ctx->macAlgo) {
+ case ecHMAC_SHA256:
+ {
+ byte verify[SHA256_DIGEST_SIZE];
+ Hmac hmac;
+ ret = wc_HmacSetKey(&hmac, SHA256, macKey, SHA256_DIGEST_SIZE);
+ if (ret != 0)
+ break;
+ ret = wc_HmacUpdate(&hmac, msg, msgSz-digestSz);
+ if (ret != 0)
+ break;
+ ret = wc_HmacUpdate(&hmac, ctx->macSalt, ctx->macSaltSz);
+ if (ret != 0)
+ break;
+ ret = wc_HmacFinal(&hmac, verify);
+ if (ret != 0)
+ break;
+ if (memcmp(verify, msg + msgSz - digestSz, digestSz) != 0)
+ ret = -1;
+ }
+ break;
+
+ default:
+ ret = BAD_FUNC_ARG;
+ break;
+ }
+ }
+
+ if (ret == 0) {
+ switch (ctx->encAlgo) {
+ case ecAES_128_CBC:
+ {
+ Aes aes;
+ ret = wc_AesSetKey(&aes, encKey, KEY_SIZE_128, encIv,
+ AES_DECRYPTION);
+ if (ret != 0)
+ break;
+ ret = wc_AesCbcDecrypt(&aes, out, msg, msgSz-digestSz);
+ }
+ break;
+
+ default:
+ ret = BAD_FUNC_ARG;
+ break;
+ }
+ }
+
+ if (ret == 0)
+ *outSz = msgSz - digestSz;
+
+#ifdef WOLFSSL_SMALL_STACK
+ XFREE(sharedSecret, NULL, DYNAMIC_TYPE_TMP_BUFFER);
+ XFREE(keys, NULL, DYNAMIC_TYPE_TMP_BUFFER);
+#endif
+
+ return ret;
+}
+
+
+#endif /* HAVE_ECC_ENCRYPT */
+
+
+#ifdef HAVE_COMP_KEY
+
+/* computes the jacobi c = (a | n) (or Legendre if n is prime)
+ * HAC pp. 73 Algorithm 2.149
+ */
+int mp_jacobi(mp_int* a, mp_int* p, int* c)
+{
+ mp_int a1, p1;
+ int k, s, r, res;
+ mp_digit residue;
+
+ /* if p <= 0 return MP_VAL */
+ if (mp_cmp_d(p, 0) != MP_GT) {
+ return MP_VAL;
+ }
+
+ /* step 1. if a == 0, return 0 */
+ if (mp_iszero (a) == 1) {
+ *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;
+
+ /* step 3. write a = a1 * 2**k */
+ if ((res = mp_init_copy (&a1, a)) != MP_OKAY) {
+ return res;
+ }
+
+ if ((res = mp_init (&p1)) != MP_OKAY) {
+ mp_clear(&a1);
+ return res;
+ }
+
+ /* divide out larger power of two */
+ k = mp_cnt_lsb(&a1);
+ res = mp_div_2d(&a1, k, &a1, 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 = p->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* a1 == 3 (mod 4) then s = -s */
+ if ( ((p->dp[0] & 3) == 3) && ((a1.dp[0] & 3) == 3)) {
+ s = -s;
+ }
+ }
+
+ if (res == MP_OKAY) {
+ /* if a1 == 1 we're done */
+ if (mp_cmp_d (&a1, 1) == MP_EQ) {
+ *c = s;
+ } else {
+ /* n1 = n mod a1 */
+ res = mp_mod (p, &a1, &p1);
+ if (res == MP_OKAY)
+ res = mp_jacobi (&p1, &a1, &r);
+
+ if (res == MP_OKAY)
+ *c = s * r;
+ }
+ }
+
+ /* done */
+ mp_clear (&p1);
+ mp_clear (&a1);
+
+ return res;
+}
+
+
+int mp_sqrtmod_prime(mp_int* n, mp_int* prime, mp_int* ret)
+{
+ int res, legendre, done = 0;
+ mp_int t1, C, Q, S, Z, M, T, R, two;
+ mp_digit i;
+
+ /* first handle the simple cases */
+ if (mp_cmp_d(n, 0) == MP_EQ) {
+ mp_zero(ret);
+ return MP_OKAY;
+ }
+ if (mp_cmp_d(prime, 2) == MP_EQ) return MP_VAL; /* prime must be odd */
+ /* TAO removed
+ if ((res = mp_jacobi(n, prime, &legendre)) != MP_OKAY) return res;
+ if (legendre == -1) return MP_VAL; */ /* quadratic non-residue mod prime */
+
+ 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 */
+ res = mp_copy(prime, &Q);
+ if (res == MP_OKAY)
+ res = mp_sub_d(&Q, 1, &Q);
+ /* Q = prime - 1 */
+ if (res == MP_OKAY)
+ mp_zero(&S);
+ /* S = 0 */
+ while (res == MP_OKAY && mp_iseven(&Q)) {
+ res = mp_div_2(&Q, &Q);
+ /* Q = Q / 2 */
+ if (res == MP_OKAY)
+ res = mp_add_d(&S, 1, &S);
+ /* S = S + 1 */
+ }
+
+ /* find a Z such that the Legendre symbol (Z|prime) == -1 */
+ if (res == MP_OKAY)
+ res = mp_set_int(&Z, 2);
+ /* Z = 2 */
+ while (res == MP_OKAY) {
+ res = mp_jacobi(&Z, prime, &legendre);
+ if (res == MP_OKAY && legendre == -1)
+ break;
+ if (res == MP_OKAY)
+ res = mp_add_d(&Z, 1, &Z);
+ /* Z = Z + 1 */
+ }
+
+ if (res == MP_OKAY)
+ res = mp_exptmod(&Z, &Q, prime, &C);
+ /* C = Z ^ Q mod prime */
+ if (res == MP_OKAY)
+ res = mp_add_d(&Q, 1, &t1);
+ if (res == MP_OKAY)
+ res = mp_div_2(&t1, &t1);
+ /* t1 = (Q + 1) / 2 */
+ if (res == MP_OKAY)
+ res = mp_exptmod(n, &t1, prime, &R);
+ /* R = n ^ ((Q + 1) / 2) mod prime */
+ if (res == MP_OKAY)
+ res = mp_exptmod(n, &Q, prime, &T);
+ /* T = n ^ Q mod prime */
+ if (res == MP_OKAY)
+ res = mp_copy(&S, &M);
+ /* M = S */
+ if (res == MP_OKAY)
+ res = mp_set_int(&two, 2);
+
+ while (res == MP_OKAY && done == 0) {
+ res = mp_copy(&T, &t1);
+ 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) {
+ mp_copy(&R, ret);
+ res = MP_OKAY;
+ done = 1;
+ }
+
+ if (done == 0) {
+ 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 = 2 ^ (M - i - 1) */
+ if (res == MP_OKAY)
+ res = mp_exptmod(&C, &t1, prime, &t1);
+ /* t1 = C ^ (2 ^ (M - i - 1)) mod prime */
+ if (res == MP_OKAY)
+ res = mp_sqrmod(&t1, prime, &C);
+ /* C = (t1 * t1) mod prime */
+ if (res == MP_OKAY)
+ res = mp_mulmod(&R, &t1, prime, &R);
+ /* R = (R * t1) mod prime */
+ if (res == MP_OKAY)
+ res = mp_mulmod(&T, &C, prime, &T);
+ /* T = (T * C) mod prime */
+ if (res == MP_OKAY)
+ mp_set(&M, i);
+ /* 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;
+}
+
+
+/* export public ECC key in ANSI X9.63 format compressed */
+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 ECC_BAD_ARG_E;
+
+ if (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;
+ }
+
+ /* store first byte */
+ out[0] = mp_isodd(key->pubkey.y) ? 0x03 : 0x02;
+
+ /* pad and store x */
+ XMEMSET(out+1, 0, numlen);
+ ret = mp_to_unsigned_bin(key->pubkey.x,
+ out+1 + (numlen - mp_unsigned_bin_size(key->pubkey.x)));
+ *outLen = 1 + numlen;
+ return ret;
+}
+
+
+/* d = a - b (mod c) */
+int mp_submod(mp_int* a, mp_int* b, mp_int* c, mp_int* d)
+{
+ int res;
+ mp_int t;
+
+ if ((res = mp_init (&t)) != MP_OKAY) {
+ return res;
+ }
+
+ if ((res = mp_sub (a, b, &t)) != MP_OKAY) {
+ mp_clear (&t);
+ return res;
+ }
+ res = mp_mod (&t, c, d);
+ mp_clear (&t);
+
+ return res;
+}
+
+
+#endif /* HAVE_COMP_KEY */
+
+#endif /* HAVE_ECC */
+