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wolfssl/ctaocrypt/src/ecc.c

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/* ecc.c
*
* Copyright (C) 2006-2014 wolfSSL Inc.
*
* This file is part of CyaSSL.
*
* CyaSSL 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.
*
* CyaSSL 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 <cyassl/ctaocrypt/settings.h>
#ifdef HAVE_ECC
#include <cyassl/ctaocrypt/ecc.h>
#include <cyassl/ctaocrypt/asn.h>
#include <cyassl/ctaocrypt/error-crypt.h>
#ifdef HAVE_ECC_ENCRYPT
#include <cyassl/ctaocrypt/hmac.h>
#include <cyassl/ctaocrypt/aes.h>
#endif
/* map
ptmul -> mulmod
*/
#define ECC112
#define ECC128
#define ECC160
#define ECC192
#define ECC224
#define ECC256
#define ECC384
#define ECC521
/* 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);
#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 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 unsigned long 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;
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;
unsigned long 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;
unsigned long 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 < 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;
bitcpy = bitbuf = 0;
first = 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 */
/**
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_BIGINT);
if (p == NULL) {
return NULL;
}
XMEMSET(p, 0, sizeof(ecc_point));
if (mp_init_multi(&p->x, &p->y, &p->z, NULL, NULL, NULL) != MP_OKAY) {
XFREE(p, 0, DYNAMIC_TYPE_BIGINT);
return NULL;
}
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_BIGINT);
}
}
/** 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 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;
}
int 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 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 = ecc_make_key_ex(rng, key, &ecc_sets[x]);
key->idx = x;
return err;
}
int 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 CYASSL_SMALL_STACK
byte* buf;
#else
byte buf[ECC_MAXSIZE];
#endif
int keysize;
if (key == NULL || rng == NULL || dp == NULL)
return ECC_BAD_ARG_E;
#ifdef CYASSL_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 = RNG_GenerateBlock(rng, buf, keysize);
if (err == 0)
buf[0] |= 0x0c;
/* setup the key variables */
if (err == 0) {
err = mp_init_multi(&key->pubkey.x, &key->pubkey.y, &key->pubkey.z,
&key->k, &prime, &order);
if (err != MP_OKAY)
err = MEMORY_E;
}
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);
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);
mp_clear(&prime);
mp_clear(&order);
#ifdef ECC_CLEAN_STACK
XMEMSET(buf, 0, ECC_MAXSIZE);
#endif
#ifdef CYASSL_SMALL_STACK
XFREE(buf, NULL, DYNAMIC_TYPE_TMP_BUFFER);
#endif
return err;
}
/* Setup dynamic pointers is using normal math for proper freeing */
void 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
}
/**
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 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 ( (CYASSL_BIT_SIZE * inlen) > orderBits)
inlen = (orderBits + CYASSL_BIT_SIZE - 1)/CYASSL_BIT_SIZE;
err = mp_read_unsigned_bin(&e, (byte*)in, inlen);
/* may still need bit truncation too */
if (err == MP_OKAY && (CYASSL_BIT_SIZE * inlen) > orderBits)
mp_rshb(&e, CYASSL_BIT_SIZE - (orderBits & 0x7));
}
/* make up a key and export the public copy */
if (err == MP_OKAY) {
ecc_key pubkey;
ecc_init(&pubkey);
for (;;) {
err = 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)
ecc_free(&pubkey);
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;
ecc_free(&pubkey);
if (mp_iszero(&s) == MP_NO)
break;
}
}
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 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 = XMALLOC(ECC_BUFSIZE, NULL, DYNAMIC_TYPE_TMP_BUFFER);
if (tA == NULL) {
return GEN_MEM_ERR;
}
tB = 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]);
}
}
#ifdef ECC_CLEAN_STACK
XMEMSET(tA, 0, ECC_BUFSIZE);
XMEMSET(tB, 0, ECC_BUFSIZE);
#endif
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 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 ( (CYASSL_BIT_SIZE * hashlen) > orderBits)
hashlen = (orderBits + CYASSL_BIT_SIZE - 1)/CYASSL_BIT_SIZE;
err = mp_read_unsigned_bin(&e, hash, hashlen);
/* may still need bit truncation too */
if (err == MP_OKAY && (CYASSL_BIT_SIZE * hashlen) > orderBits)
mp_rshb(&e, CYASSL_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 ecc_export_x963(ecc_key* key, byte* out, word32* outLen)
{
#ifdef CYASSL_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 CYASSL_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 CYASSL_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 ecc_export_x963_ex(ecc_key* key, byte* out, word32* outLen, int compressed)
{
if (compressed == 0)
return ecc_export_x963(key, out, outLen);
#ifdef HAVE_COMP_KEY
else
return ecc_export_x963_compressed(key, out, outLen);
#endif
return NOT_COMPILED_IN;
}
/* import public ECC key in ANSI X9.63 format */
int 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 */
if (mp_init_multi(&key->pubkey.x, &key->pubkey.y, &key->pubkey.z, &key->k,
NULL, NULL) != MP_OKAY) {
return MEMORY_E;
}
err = MP_OKAY;
/* 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);
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 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 ecc_import_private_key(const byte* priv, word32 privSz, const byte* pub,
word32 pubSz, ecc_key* key)
{
int ret = ecc_import_x963(pub, pubSz, key);
if (ret != 0)
return ret;
key->type = ECC_PRIVATEKEY;
return mp_read_unsigned_bin(&key->k, priv, privSz);
}
/**
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 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 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 */
if (mp_init_multi(&key->pubkey.x, &key->pubkey.y, &key->pubkey.z, &key->k,
NULL, NULL) != MP_OKAY) {
return MEMORY_E;
}
err = MP_OKAY;
/* 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);
}
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 ecc_size(ecc_key* key)
{
if (key == NULL) return 0;
return key->dp->size;
}
/* worst case estimate, check actual return from ecc_sign_hash for actual value
of signature size in octets */
int ecc_sig_size(ecc_key* key)
{
int sz = 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 CyaSSL_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 },
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{ 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 CYASSL_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 CYASSL_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;
XMEMSET(kb, 0, KB_SIZE);
/* map R back from projective space */
if (map) {
err = ecc_map(R, modulus, mp);
} else {
err = MP_OKAY;
}
}
#ifdef CYASSL_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 CYASSL_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 CYASSL_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 CYASSL_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;
}
}
}
}
XMEMSET(kb[0], 0, KB_SIZE);
XMEMSET(kb[1], 0, KB_SIZE);
#ifdef CYASSL_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 != -1) {
/* 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 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 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 */
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* 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 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 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 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 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* 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 = ecc_ctx_reset(ctx, rng);
if (ret != 0) {
ecc_ctx_free(ctx);
ctx = NULL;
}
return ctx;
}
/* free any resources, clear any keys */
void ecc_ctx_free(ecEncCtx* ctx)
{
if (ctx) {
XMEMSET(ctx, 0, 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 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 CYASSL_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 CYASSL_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 = ecc_shared_secret(privKey, pubKey, sharedSecret, &sharedSz);
if (ret == 0) {
switch (ctx->kdfAlgo) {
case ecHKDF_SHA256 :
ret = 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 = AesSetKey(&aes, encKey, KEY_SIZE_128, encIv,
AES_ENCRYPTION);
if (ret != 0)
break;
ret = AesCbcEncrypt(&aes, out, msg, msgSz);
}
break;
default:
ret = BAD_FUNC_ARG;
break;
}
}
if (ret == 0) {
switch (ctx->macAlgo) {
case ecHMAC_SHA256:
{
Hmac hmac;
ret = HmacSetKey(&hmac, SHA256, macKey, SHA256_DIGEST_SIZE);
if (ret != 0)
break;
ret = HmacUpdate(&hmac, out, msgSz);
if (ret != 0)
break;
ret = HmacUpdate(&hmac, ctx->macSalt, ctx->macSaltSz);
if (ret != 0)
break;
ret = HmacFinal(&hmac, out+msgSz);
}
break;
default:
ret = BAD_FUNC_ARG;
break;
}
}
if (ret == 0)
*outSz = msgSz + digestSz;
#ifdef CYASSL_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 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 CYASSL_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 CYASSL_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 = ecc_shared_secret(privKey, pubKey, sharedSecret, &sharedSz);
if (ret == 0) {
switch (ctx->kdfAlgo) {
case ecHKDF_SHA256 :
ret = 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 = HmacSetKey(&hmac, SHA256, macKey, SHA256_DIGEST_SIZE);
if (ret != 0)
break;
ret = HmacUpdate(&hmac, msg, msgSz-digestSz);
if (ret != 0)
break;
ret = HmacUpdate(&hmac, ctx->macSalt, ctx->macSaltSz);
if (ret != 0)
break;
ret = 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 = AesSetKey(&aes, encKey, KEY_SIZE_128, encIv,
AES_DECRYPTION);
if (ret != 0)
break;
ret = AesCbcDecrypt(&aes, out, msg, msgSz-digestSz);
}
break;
default:
ret = BAD_FUNC_ARG;
break;
}
}
if (ret == 0)
*outSz = msgSz - digestSz;
#ifdef CYASSL_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 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 */
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