| /* Copyright (c) 2014, Intel Corporation. |
| * |
| * Permission to use, copy, modify, and/or distribute this software for any |
| * purpose with or without fee is hereby granted, provided that the above |
| * copyright notice and this permission notice appear in all copies. |
| * |
| * THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES |
| * WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF |
| * MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY |
| * SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES |
| * WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN ACTION |
| * OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF OR IN |
| * CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE. */ |
| |
| /* Developers and authors: |
| * Shay Gueron (1, 2), and Vlad Krasnov (1) |
| * (1) Intel Corporation, Israel Development Center |
| * (2) University of Haifa |
| * Reference: |
| * S.Gueron and V.Krasnov, "Fast Prime Field Elliptic Curve Cryptography with |
| * 256 Bit Primes" */ |
| |
| #include <openssl/ec.h> |
| |
| #include <stdint.h> |
| #include <string.h> |
| |
| #include <openssl/bn.h> |
| #include <openssl/crypto.h> |
| #include <openssl/err.h> |
| |
| #include "../bn/internal.h" |
| #include "../ec/internal.h" |
| #include "../internal.h" |
| |
| |
| #if !defined(OPENSSL_NO_ASM) && defined(OPENSSL_X86_64) && \ |
| !defined(OPENSSL_SMALL) |
| |
| #if BN_BITS2 != 64 |
| #define TOBN(hi, lo) lo, hi |
| #else |
| #define TOBN(hi, lo) ((BN_ULONG)hi << 32 | lo) |
| #endif |
| |
| #if defined(__GNUC__) |
| #define ALIGN32 __attribute((aligned(32))) |
| #elif defined(_MSC_VER) |
| #define ALIGN32 __declspec(align(32)) |
| #else |
| #define ALIGN32 |
| #endif |
| |
| #define ALIGNPTR(p, N) ((uint8_t *)p + N - (size_t)p % N) |
| #define P256_LIMBS (256 / BN_BITS2) |
| |
| typedef struct { |
| BN_ULONG X[P256_LIMBS]; |
| BN_ULONG Y[P256_LIMBS]; |
| BN_ULONG Z[P256_LIMBS]; |
| } P256_POINT; |
| |
| typedef struct { |
| BN_ULONG X[P256_LIMBS]; |
| BN_ULONG Y[P256_LIMBS]; |
| } P256_POINT_AFFINE; |
| |
| typedef P256_POINT_AFFINE PRECOMP256_ROW[64]; |
| |
| /* Functions implemented in assembly */ |
| |
| /* Modular mul by 2: res = 2*a mod P */ |
| void ecp_nistz256_mul_by_2(BN_ULONG res[P256_LIMBS], |
| const BN_ULONG a[P256_LIMBS]); |
| /* Modular div by 2: res = a/2 mod P */ |
| void ecp_nistz256_div_by_2(BN_ULONG res[P256_LIMBS], |
| const BN_ULONG a[P256_LIMBS]); |
| /* Modular mul by 3: res = 3*a mod P */ |
| void ecp_nistz256_mul_by_3(BN_ULONG res[P256_LIMBS], |
| const BN_ULONG a[P256_LIMBS]); |
| /* Modular add: res = a+b mod P */ |
| void ecp_nistz256_add(BN_ULONG res[P256_LIMBS], const BN_ULONG a[P256_LIMBS], |
| const BN_ULONG b[P256_LIMBS]); |
| /* Modular sub: res = a-b mod P */ |
| void ecp_nistz256_sub(BN_ULONG res[P256_LIMBS], const BN_ULONG a[P256_LIMBS], |
| const BN_ULONG b[P256_LIMBS]); |
| /* Modular neg: res = -a mod P */ |
| void ecp_nistz256_neg(BN_ULONG res[P256_LIMBS], const BN_ULONG a[P256_LIMBS]); |
| /* Montgomery mul: res = a*b*2^-256 mod P */ |
| void ecp_nistz256_mul_mont(BN_ULONG res[P256_LIMBS], |
| const BN_ULONG a[P256_LIMBS], |
| const BN_ULONG b[P256_LIMBS]); |
| /* Montgomery sqr: res = a*a*2^-256 mod P */ |
| void ecp_nistz256_sqr_mont(BN_ULONG res[P256_LIMBS], |
| const BN_ULONG a[P256_LIMBS]); |
| /* Convert a number from Montgomery domain, by multiplying with 1 */ |
| void ecp_nistz256_from_mont(BN_ULONG res[P256_LIMBS], |
| const BN_ULONG in[P256_LIMBS]); |
| /* Convert a number to Montgomery domain, by multiplying with 2^512 mod P*/ |
| void ecp_nistz256_to_mont(BN_ULONG res[P256_LIMBS], |
| const BN_ULONG in[P256_LIMBS]); |
| /* Functions that perform constant time access to the precomputed tables */ |
| void ecp_nistz256_select_w5(P256_POINT *val, const P256_POINT *in_t, int index); |
| void ecp_nistz256_select_w7(P256_POINT_AFFINE *val, |
| const P256_POINT_AFFINE *in_t, int index); |
| |
| /* One converted into the Montgomery domain */ |
| static const BN_ULONG ONE[P256_LIMBS] = { |
| TOBN(0x00000000, 0x00000001), TOBN(0xffffffff, 0x00000000), |
| TOBN(0xffffffff, 0xffffffff), TOBN(0x00000000, 0xfffffffe), |
| }; |
| |
| /* Precomputed tables for the default generator */ |
| #include "p256-x86_64-table.h" |
| |
| /* Recode window to a signed digit, see ecp_nistputil.c for details */ |
| static unsigned booth_recode_w5(unsigned in) { |
| unsigned s, d; |
| |
| s = ~((in >> 5) - 1); |
| d = (1 << 6) - in - 1; |
| d = (d & s) | (in & ~s); |
| d = (d >> 1) + (d & 1); |
| |
| return (d << 1) + (s & 1); |
| } |
| |
| static unsigned booth_recode_w7(unsigned in) { |
| unsigned s, d; |
| |
| s = ~((in >> 7) - 1); |
| d = (1 << 8) - in - 1; |
| d = (d & s) | (in & ~s); |
| d = (d >> 1) + (d & 1); |
| |
| return (d << 1) + (s & 1); |
| } |
| |
| static void copy_conditional(BN_ULONG dst[P256_LIMBS], |
| const BN_ULONG src[P256_LIMBS], BN_ULONG move) { |
| BN_ULONG mask1 = ((BN_ULONG)0) - move; |
| BN_ULONG mask2 = ~mask1; |
| |
| dst[0] = (src[0] & mask1) ^ (dst[0] & mask2); |
| dst[1] = (src[1] & mask1) ^ (dst[1] & mask2); |
| dst[2] = (src[2] & mask1) ^ (dst[2] & mask2); |
| dst[3] = (src[3] & mask1) ^ (dst[3] & mask2); |
| if (P256_LIMBS == 8) { |
| dst[4] = (src[4] & mask1) ^ (dst[4] & mask2); |
| dst[5] = (src[5] & mask1) ^ (dst[5] & mask2); |
| dst[6] = (src[6] & mask1) ^ (dst[6] & mask2); |
| dst[7] = (src[7] & mask1) ^ (dst[7] & mask2); |
| } |
| } |
| |
| static BN_ULONG is_zero(BN_ULONG in) { |
| in |= (0 - in); |
| in = ~in; |
| in &= BN_MASK2; |
| in >>= BN_BITS2 - 1; |
| return in; |
| } |
| |
| static BN_ULONG is_equal(const BN_ULONG a[P256_LIMBS], |
| const BN_ULONG b[P256_LIMBS]) { |
| BN_ULONG res; |
| |
| res = a[0] ^ b[0]; |
| res |= a[1] ^ b[1]; |
| res |= a[2] ^ b[2]; |
| res |= a[3] ^ b[3]; |
| if (P256_LIMBS == 8) { |
| res |= a[4] ^ b[4]; |
| res |= a[5] ^ b[5]; |
| res |= a[6] ^ b[6]; |
| res |= a[7] ^ b[7]; |
| } |
| |
| return is_zero(res); |
| } |
| |
| static BN_ULONG is_one(const BN_ULONG a[P256_LIMBS]) { |
| BN_ULONG res; |
| |
| res = a[0] ^ ONE[0]; |
| res |= a[1] ^ ONE[1]; |
| res |= a[2] ^ ONE[2]; |
| res |= a[3] ^ ONE[3]; |
| if (P256_LIMBS == 8) { |
| res |= a[4] ^ ONE[4]; |
| res |= a[5] ^ ONE[5]; |
| res |= a[6] ^ ONE[6]; |
| } |
| |
| return is_zero(res); |
| } |
| |
| void ecp_nistz256_point_double(P256_POINT *r, const P256_POINT *a); |
| void ecp_nistz256_point_add(P256_POINT *r, const P256_POINT *a, |
| const P256_POINT *b); |
| void ecp_nistz256_point_add_affine(P256_POINT *r, const P256_POINT *a, |
| const P256_POINT_AFFINE *b); |
| |
| /* r = in^-1 mod p */ |
| static void ecp_nistz256_mod_inverse(BN_ULONG r[P256_LIMBS], |
| const BN_ULONG in[P256_LIMBS]) { |
| /* The poly is ffffffff 00000001 00000000 00000000 00000000 ffffffff ffffffff |
| ffffffff |
| We use FLT and used poly-2 as exponent */ |
| BN_ULONG p2[P256_LIMBS]; |
| BN_ULONG p4[P256_LIMBS]; |
| BN_ULONG p8[P256_LIMBS]; |
| BN_ULONG p16[P256_LIMBS]; |
| BN_ULONG p32[P256_LIMBS]; |
| BN_ULONG res[P256_LIMBS]; |
| int i; |
| |
| ecp_nistz256_sqr_mont(res, in); |
| ecp_nistz256_mul_mont(p2, res, in); /* 3*p */ |
| |
| ecp_nistz256_sqr_mont(res, p2); |
| ecp_nistz256_sqr_mont(res, res); |
| ecp_nistz256_mul_mont(p4, res, p2); /* f*p */ |
| |
| ecp_nistz256_sqr_mont(res, p4); |
| ecp_nistz256_sqr_mont(res, res); |
| ecp_nistz256_sqr_mont(res, res); |
| ecp_nistz256_sqr_mont(res, res); |
| ecp_nistz256_mul_mont(p8, res, p4); /* ff*p */ |
| |
| ecp_nistz256_sqr_mont(res, p8); |
| for (i = 0; i < 7; i++) { |
| ecp_nistz256_sqr_mont(res, res); |
| } |
| ecp_nistz256_mul_mont(p16, res, p8); /* ffff*p */ |
| |
| ecp_nistz256_sqr_mont(res, p16); |
| for (i = 0; i < 15; i++) { |
| ecp_nistz256_sqr_mont(res, res); |
| } |
| ecp_nistz256_mul_mont(p32, res, p16); /* ffffffff*p */ |
| |
| ecp_nistz256_sqr_mont(res, p32); |
| for (i = 0; i < 31; i++) { |
| ecp_nistz256_sqr_mont(res, res); |
| } |
| ecp_nistz256_mul_mont(res, res, in); |
| |
| for (i = 0; i < 32 * 4; i++) { |
| ecp_nistz256_sqr_mont(res, res); |
| } |
| ecp_nistz256_mul_mont(res, res, p32); |
| |
| for (i = 0; i < 32; i++) { |
| ecp_nistz256_sqr_mont(res, res); |
| } |
| ecp_nistz256_mul_mont(res, res, p32); |
| |
| for (i = 0; i < 16; i++) { |
| ecp_nistz256_sqr_mont(res, res); |
| } |
| ecp_nistz256_mul_mont(res, res, p16); |
| |
| for (i = 0; i < 8; i++) { |
| ecp_nistz256_sqr_mont(res, res); |
| } |
| ecp_nistz256_mul_mont(res, res, p8); |
| |
| ecp_nistz256_sqr_mont(res, res); |
| ecp_nistz256_sqr_mont(res, res); |
| ecp_nistz256_sqr_mont(res, res); |
| ecp_nistz256_sqr_mont(res, res); |
| ecp_nistz256_mul_mont(res, res, p4); |
| |
| ecp_nistz256_sqr_mont(res, res); |
| ecp_nistz256_sqr_mont(res, res); |
| ecp_nistz256_mul_mont(res, res, p2); |
| |
| ecp_nistz256_sqr_mont(res, res); |
| ecp_nistz256_sqr_mont(res, res); |
| ecp_nistz256_mul_mont(res, res, in); |
| |
| memcpy(r, res, sizeof(res)); |
| } |
| |
| /* ecp_nistz256_bignum_to_field_elem copies the contents of |in| to |out| and |
| * returns one if it fits. Otherwise it returns zero. */ |
| static int ecp_nistz256_bignum_to_field_elem(BN_ULONG out[P256_LIMBS], |
| const BIGNUM *in) { |
| if (in->top > P256_LIMBS) { |
| return 0; |
| } |
| |
| memset(out, 0, sizeof(BN_ULONG) * P256_LIMBS); |
| memcpy(out, in->d, sizeof(BN_ULONG) * in->top); |
| return 1; |
| } |
| |
| /* r = sum(scalar[i]*point[i]) */ |
| static void ecp_nistz256_windowed_mul(const EC_GROUP *group, P256_POINT *r, |
| const BIGNUM **scalar, |
| const EC_POINT **point, int num, |
| BN_CTX *ctx) { |
| static const unsigned kWindowSize = 5; |
| static const unsigned kMask = (1 << (5 /* kWindowSize */ + 1)) - 1; |
| |
| void *table_storage = OPENSSL_malloc(num * 16 * sizeof(P256_POINT) + 64); |
| uint8_t(*p_str)[33] = OPENSSL_malloc(num * 33 * sizeof(uint8_t)); |
| const BIGNUM **scalars = OPENSSL_malloc(num * sizeof(BIGNUM *)); |
| |
| if (table_storage == NULL || |
| p_str == NULL || |
| scalars == NULL) { |
| OPENSSL_PUT_ERROR(EC, ERR_R_MALLOC_FAILURE); |
| goto err; |
| } |
| |
| P256_POINT(*table)[16] = (void *)ALIGNPTR(table_storage, 64); |
| |
| int i; |
| for (i = 0; i < num; i++) { |
| P256_POINT *row = table[i]; |
| |
| if (BN_num_bits(scalar[i]) > 256 || BN_is_negative(scalar[i])) { |
| BIGNUM *mod = BN_CTX_get(ctx); |
| if (mod == NULL) { |
| goto err; |
| } |
| |
| if (!BN_nnmod(mod, scalar[i], &group->order, ctx)) { |
| OPENSSL_PUT_ERROR(EC, ERR_R_BN_LIB); |
| goto err; |
| } |
| scalars[i] = mod; |
| } else { |
| scalars[i] = scalar[i]; |
| } |
| |
| int j; |
| for (j = 0; j < scalars[i]->top * BN_BYTES; j += BN_BYTES) { |
| BN_ULONG d = scalars[i]->d[j / BN_BYTES]; |
| |
| p_str[i][j + 0] = d & 0xff; |
| p_str[i][j + 1] = (d >> 8) & 0xff; |
| p_str[i][j + 2] = (d >> 16) & 0xff; |
| p_str[i][j + 3] = (d >>= 24) & 0xff; |
| if (BN_BYTES == 8) { |
| d >>= 8; |
| p_str[i][j + 4] = d & 0xff; |
| p_str[i][j + 5] = (d >> 8) & 0xff; |
| p_str[i][j + 6] = (d >> 16) & 0xff; |
| p_str[i][j + 7] = (d >> 24) & 0xff; |
| } |
| } |
| |
| for (; j < 33; j++) { |
| p_str[i][j] = 0; |
| } |
| |
| /* table[0] is implicitly (0,0,0) (the point at infinity), therefore it is |
| * not stored. All other values are actually stored with an offset of -1 in |
| * table. */ |
| |
| if (!ecp_nistz256_bignum_to_field_elem(row[1 - 1].X, &point[i]->X) || |
| !ecp_nistz256_bignum_to_field_elem(row[1 - 1].Y, &point[i]->Y) || |
| !ecp_nistz256_bignum_to_field_elem(row[1 - 1].Z, &point[i]->Z)) { |
| OPENSSL_PUT_ERROR(EC, EC_R_COORDINATES_OUT_OF_RANGE); |
| goto err; |
| } |
| |
| ecp_nistz256_point_double(&row[2 - 1], &row[1 - 1]); |
| ecp_nistz256_point_add(&row[3 - 1], &row[2 - 1], &row[1 - 1]); |
| ecp_nistz256_point_double(&row[4 - 1], &row[2 - 1]); |
| ecp_nistz256_point_double(&row[6 - 1], &row[3 - 1]); |
| ecp_nistz256_point_double(&row[8 - 1], &row[4 - 1]); |
| ecp_nistz256_point_double(&row[12 - 1], &row[6 - 1]); |
| ecp_nistz256_point_add(&row[5 - 1], &row[4 - 1], &row[1 - 1]); |
| ecp_nistz256_point_add(&row[7 - 1], &row[6 - 1], &row[1 - 1]); |
| ecp_nistz256_point_add(&row[9 - 1], &row[8 - 1], &row[1 - 1]); |
| ecp_nistz256_point_add(&row[13 - 1], &row[12 - 1], &row[1 - 1]); |
| ecp_nistz256_point_double(&row[14 - 1], &row[7 - 1]); |
| ecp_nistz256_point_double(&row[10 - 1], &row[5 - 1]); |
| ecp_nistz256_point_add(&row[15 - 1], &row[14 - 1], &row[1 - 1]); |
| ecp_nistz256_point_add(&row[11 - 1], &row[10 - 1], &row[1 - 1]); |
| ecp_nistz256_point_add(&row[16 - 1], &row[15 - 1], &row[1 - 1]); |
| } |
| |
| BN_ULONG tmp[P256_LIMBS]; |
| ALIGN32 P256_POINT h; |
| unsigned index = 255; |
| unsigned wvalue = p_str[0][(index - 1) / 8]; |
| wvalue = (wvalue >> ((index - 1) % 8)) & kMask; |
| |
| ecp_nistz256_select_w5(r, table[0], booth_recode_w5(wvalue) >> 1); |
| |
| while (index >= 5) { |
| for (i = (index == 255 ? 1 : 0); i < num; i++) { |
| unsigned off = (index - 1) / 8; |
| |
| wvalue = p_str[i][off] | p_str[i][off + 1] << 8; |
| wvalue = (wvalue >> ((index - 1) % 8)) & kMask; |
| |
| wvalue = booth_recode_w5(wvalue); |
| |
| ecp_nistz256_select_w5(&h, table[i], wvalue >> 1); |
| |
| ecp_nistz256_neg(tmp, h.Y); |
| copy_conditional(h.Y, tmp, (wvalue & 1)); |
| |
| ecp_nistz256_point_add(r, r, &h); |
| } |
| |
| index -= kWindowSize; |
| |
| ecp_nistz256_point_double(r, r); |
| ecp_nistz256_point_double(r, r); |
| ecp_nistz256_point_double(r, r); |
| ecp_nistz256_point_double(r, r); |
| ecp_nistz256_point_double(r, r); |
| } |
| |
| /* Final window */ |
| for (i = 0; i < num; i++) { |
| wvalue = p_str[i][0]; |
| wvalue = (wvalue << 1) & kMask; |
| |
| wvalue = booth_recode_w5(wvalue); |
| |
| ecp_nistz256_select_w5(&h, table[i], wvalue >> 1); |
| |
| ecp_nistz256_neg(tmp, h.Y); |
| copy_conditional(h.Y, tmp, wvalue & 1); |
| |
| ecp_nistz256_point_add(r, r, &h); |
| } |
| |
| err: |
| OPENSSL_free(table_storage); |
| OPENSSL_free(p_str); |
| OPENSSL_free((BIGNUM**) scalars); |
| } |
| |
| /* Coordinates of G, for which we have precomputed tables */ |
| const static BN_ULONG def_xG[P256_LIMBS] = { |
| TOBN(0x79e730d4, 0x18a9143c), TOBN(0x75ba95fc, 0x5fedb601), |
| TOBN(0x79fb732b, 0x77622510), TOBN(0x18905f76, 0xa53755c6), |
| }; |
| |
| const static BN_ULONG def_yG[P256_LIMBS] = { |
| TOBN(0xddf25357, 0xce95560a), TOBN(0x8b4ab8e4, 0xba19e45c), |
| TOBN(0xd2e88688, 0xdd21f325), TOBN(0x8571ff18, 0x25885d85) |
| }; |
| |
| /* ecp_nistz256_is_affine_G returns one if |generator| is the standard, P-256 |
| * generator. */ |
| static int ecp_nistz256_is_affine_G(const EC_POINT *generator) { |
| return (generator->X.top == P256_LIMBS) && (generator->Y.top == P256_LIMBS) && |
| (generator->Z.top == (P256_LIMBS - P256_LIMBS / 8)) && |
| is_equal(generator->X.d, def_xG) && is_equal(generator->Y.d, def_yG) && |
| is_one(generator->Z.d); |
| } |
| |
| /* r = scalar*G + sum(scalars[i]*points[i]) */ |
| static int ecp_nistz256_points_mul( |
| const EC_GROUP *group, EC_POINT *r, const BIGNUM *scalar, size_t num, |
| const EC_POINT *points[], const BIGNUM *scalars[], BN_CTX *ctx) { |
| static const unsigned kWindowSize = 7; |
| static const unsigned kMask = (1 << (7 /* kWindowSize */ + 1)) - 1; |
| |
| int ret = 0, no_precomp_for_generator = 0, p_is_infinity = 0; |
| ALIGN32 union { |
| P256_POINT p; |
| P256_POINT_AFFINE a; |
| } t, p; |
| |
| if (scalar == NULL && num == 0) { |
| return EC_POINT_set_to_infinity(group, r); |
| } |
| |
| /* Need 256 bits for space for all coordinates. */ |
| bn_wexpand(&r->X, P256_LIMBS); |
| bn_wexpand(&r->Y, P256_LIMBS); |
| bn_wexpand(&r->Z, P256_LIMBS); |
| r->X.top = P256_LIMBS; |
| r->Y.top = P256_LIMBS; |
| r->Z.top = P256_LIMBS; |
| |
| const EC_POINT *generator = NULL; |
| if (scalar) { |
| generator = EC_GROUP_get0_generator(group); |
| if (generator == NULL) { |
| OPENSSL_PUT_ERROR(EC, EC_R_UNDEFINED_GENERATOR); |
| goto err; |
| } |
| |
| if (ecp_nistz256_is_affine_G(generator)) { |
| if (BN_num_bits(scalar) > 256 || BN_is_negative(scalar)) { |
| BIGNUM *tmp_scalar = BN_CTX_get(ctx); |
| if (tmp_scalar == NULL) { |
| goto err; |
| } |
| |
| if (!BN_nnmod(tmp_scalar, scalar, &group->order, ctx)) { |
| OPENSSL_PUT_ERROR(EC, ERR_R_BN_LIB); |
| goto err; |
| } |
| scalar = tmp_scalar; |
| } |
| |
| uint8_t p_str[33] = {0}; |
| int i; |
| for (i = 0; i < scalar->top * BN_BYTES; i += BN_BYTES) { |
| BN_ULONG d = scalar->d[i / BN_BYTES]; |
| |
| p_str[i + 0] = d & 0xff; |
| p_str[i + 1] = (d >> 8) & 0xff; |
| p_str[i + 2] = (d >> 16) & 0xff; |
| p_str[i + 3] = (d >>= 24) & 0xff; |
| if (BN_BYTES == 8) { |
| d >>= 8; |
| p_str[i + 4] = d & 0xff; |
| p_str[i + 5] = (d >> 8) & 0xff; |
| p_str[i + 6] = (d >> 16) & 0xff; |
| p_str[i + 7] = (d >> 24) & 0xff; |
| } |
| } |
| |
| for (; i < (int) sizeof(p_str); i++) { |
| p_str[i] = 0; |
| } |
| |
| /* First window */ |
| unsigned wvalue = (p_str[0] << 1) & kMask; |
| unsigned index = kWindowSize; |
| |
| wvalue = booth_recode_w7(wvalue); |
| |
| const PRECOMP256_ROW *const precomputed_table = |
| (const PRECOMP256_ROW *)ecp_nistz256_precomputed; |
| ecp_nistz256_select_w7(&p.a, precomputed_table[0], wvalue >> 1); |
| |
| ecp_nistz256_neg(p.p.Z, p.p.Y); |
| copy_conditional(p.p.Y, p.p.Z, wvalue & 1); |
| |
| memcpy(p.p.Z, ONE, sizeof(ONE)); |
| |
| for (i = 1; i < 37; i++) { |
| unsigned off = (index - 1) / 8; |
| wvalue = p_str[off] | p_str[off + 1] << 8; |
| wvalue = (wvalue >> ((index - 1) % 8)) & kMask; |
| index += kWindowSize; |
| |
| wvalue = booth_recode_w7(wvalue); |
| |
| ecp_nistz256_select_w7(&t.a, precomputed_table[i], wvalue >> 1); |
| |
| ecp_nistz256_neg(t.p.Z, t.a.Y); |
| copy_conditional(t.a.Y, t.p.Z, wvalue & 1); |
| |
| ecp_nistz256_point_add_affine(&p.p, &p.p, &t.a); |
| } |
| } else { |
| p_is_infinity = 1; |
| no_precomp_for_generator = 1; |
| } |
| } else { |
| p_is_infinity = 1; |
| } |
| |
| if (no_precomp_for_generator) { |
| /* Without a precomputed table for the generator, it has to be handled like |
| * a normal point. */ |
| const BIGNUM **new_scalars; |
| const EC_POINT **new_points; |
| |
| /* Bound |num| so that all the possible overflows in the following can be |
| * excluded. */ |
| if (0xffffff < num) { |
| OPENSSL_PUT_ERROR(EC, ERR_R_MALLOC_FAILURE); |
| return 0; |
| } |
| |
| new_scalars = OPENSSL_malloc((num + 1) * sizeof(BIGNUM *)); |
| if (new_scalars == NULL) { |
| OPENSSL_PUT_ERROR(EC, ERR_R_MALLOC_FAILURE); |
| return 0; |
| } |
| |
| new_points = OPENSSL_malloc((num + 1) * sizeof(EC_POINT *)); |
| if (new_points == NULL) { |
| OPENSSL_free((BIGNUM**) new_scalars); |
| OPENSSL_PUT_ERROR(EC, ERR_R_MALLOC_FAILURE); |
| return 0; |
| } |
| |
| memcpy((BIGNUM**) new_scalars, scalars, num * sizeof(BIGNUM *)); |
| new_scalars[num] = scalar; |
| memcpy((EC_POINT**) new_points, points, num * sizeof(EC_POINT *)); |
| new_points[num] = generator; |
| |
| scalars = new_scalars; |
| points = new_points; |
| num++; |
| } |
| |
| if (num) { |
| P256_POINT *out = &t.p; |
| if (p_is_infinity) { |
| out = &p.p; |
| } |
| |
| ecp_nistz256_windowed_mul(group, out, scalars, points, num, ctx); |
| |
| if (!p_is_infinity) { |
| ecp_nistz256_point_add(&p.p, &p.p, out); |
| } |
| } |
| |
| if (no_precomp_for_generator) { |
| OPENSSL_free((BIGNUM **) scalars); |
| OPENSSL_free((EC_POINT **) points); |
| } |
| |
| memcpy(r->X.d, p.p.X, sizeof(p.p.X)); |
| memcpy(r->Y.d, p.p.Y, sizeof(p.p.Y)); |
| memcpy(r->Z.d, p.p.Z, sizeof(p.p.Z)); |
| bn_correct_top(&r->X); |
| bn_correct_top(&r->Y); |
| bn_correct_top(&r->Z); |
| |
| ret = 1; |
| |
| err: |
| return ret; |
| } |
| |
| static int ecp_nistz256_get_affine(const EC_GROUP *group, const EC_POINT *point, |
| BIGNUM *x, BIGNUM *y, BN_CTX *ctx) { |
| BN_ULONG z_inv2[P256_LIMBS]; |
| BN_ULONG z_inv3[P256_LIMBS]; |
| BN_ULONG x_aff[P256_LIMBS]; |
| BN_ULONG y_aff[P256_LIMBS]; |
| BN_ULONG point_x[P256_LIMBS], point_y[P256_LIMBS], point_z[P256_LIMBS]; |
| |
| if (EC_POINT_is_at_infinity(group, point)) { |
| OPENSSL_PUT_ERROR(EC, EC_R_POINT_AT_INFINITY); |
| return 0; |
| } |
| |
| if (!ecp_nistz256_bignum_to_field_elem(point_x, &point->X) || |
| !ecp_nistz256_bignum_to_field_elem(point_y, &point->Y) || |
| !ecp_nistz256_bignum_to_field_elem(point_z, &point->Z)) { |
| OPENSSL_PUT_ERROR(EC, EC_R_COORDINATES_OUT_OF_RANGE); |
| return 0; |
| } |
| |
| ecp_nistz256_mod_inverse(z_inv3, point_z); |
| ecp_nistz256_sqr_mont(z_inv2, z_inv3); |
| ecp_nistz256_mul_mont(x_aff, z_inv2, point_x); |
| |
| if (x != NULL) { |
| bn_wexpand(x, P256_LIMBS); |
| x->top = P256_LIMBS; |
| ecp_nistz256_from_mont(x->d, x_aff); |
| bn_correct_top(x); |
| } |
| |
| if (y != NULL) { |
| ecp_nistz256_mul_mont(z_inv3, z_inv3, z_inv2); |
| ecp_nistz256_mul_mont(y_aff, z_inv3, point_y); |
| bn_wexpand(y, P256_LIMBS); |
| y->top = P256_LIMBS; |
| ecp_nistz256_from_mont(y->d, y_aff); |
| bn_correct_top(y); |
| } |
| |
| return 1; |
| } |
| |
| const EC_METHOD *EC_GFp_nistz256_method(void) { |
| static const EC_METHOD ret = { |
| ec_GFp_mont_group_init, |
| ec_GFp_mont_group_finish, |
| ec_GFp_mont_group_clear_finish, |
| ec_GFp_mont_group_copy, |
| ec_GFp_mont_group_set_curve, |
| ecp_nistz256_get_affine, |
| ecp_nistz256_points_mul, |
| 0, /* precompute_mult */ |
| ec_GFp_mont_field_mul, |
| ec_GFp_mont_field_sqr, |
| ec_GFp_mont_field_encode, |
| ec_GFp_mont_field_decode, |
| ec_GFp_mont_field_set_to_one, |
| }; |
| |
| return &ret; |
| } |
| |
| #endif /* !defined(OPENSSL_NO_ASM) && defined(OPENSSL_X86_64) && \ |
| !defined(OPENSSL_SMALL) */ |