| /* 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 <assert.h> |
| #include <stdint.h> |
| #include <string.h> |
| |
| #include <openssl/bn.h> |
| #include <openssl/crypto.h> |
| #include <openssl/err.h> |
| |
| #include "../bn/internal.h" |
| #include "../internal.h" |
| #include "internal.h" |
| #include "p256-x86_64.h" |
| |
| |
| #if !defined(OPENSSL_NO_ASM) && defined(OPENSSL_X86_64) && \ |
| !defined(OPENSSL_SMALL) |
| |
| typedef P256_POINT_AFFINE PRECOMP256_ROW[64]; |
| |
| /* 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 util-64.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); |
| } |
| |
| /* copy_conditional copies |src| to |dst| if |move| is one and leaves it as-is |
| * if |move| is zero. |
| * |
| * WARNING: this breaks the usual convention of constant-time functions |
| * returning masks. */ |
| 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); |
| } |
| } |
| |
| /* is_not_zero returns one iff in != 0 and zero otherwise. |
| * |
| * WARNING: this breaks the usual convention of constant-time functions |
| * returning masks. |
| * |
| * (define-fun is_not_zero ((in (_ BitVec 64))) (_ BitVec 64) |
| * (bvlshr (bvor in (bvsub #x0000000000000000 in)) #x000000000000003f) |
| * ) |
| * |
| * (declare-fun x () (_ BitVec 64)) |
| * |
| * (assert (and (= x #x0000000000000000) (= (is_not_zero x) #x0000000000000001))) |
| * (check-sat) |
| * |
| * (assert (and (not (= x #x0000000000000000)) (= (is_not_zero x) #x0000000000000000))) |
| * (check-sat) |
| * */ |
| static BN_ULONG is_not_zero(BN_ULONG in) { |
| in |= (0 - in); |
| in >>= BN_BITS2 - 1; |
| return in; |
| } |
| |
| /* ecp_nistz256_mod_inverse_mont sets |r| to (|in| * 2^-256)^-1 * 2^256 mod p. |
| * That is, |r| is the modular inverse of |in| for input and output in the |
| * Montgomery domain. */ |
| static void ecp_nistz256_mod_inverse_mont(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(r, res, in); |
| } |
| |
| /* 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 = p * p_scalar */ |
| static int ecp_nistz256_windowed_mul(const EC_GROUP *group, P256_POINT *r, |
| const EC_POINT *p, const BIGNUM *p_scalar, |
| BN_CTX *ctx) { |
| assert(p != NULL); |
| assert(p_scalar != NULL); |
| |
| static const unsigned kWindowSize = 5; |
| static const unsigned kMask = (1 << (5 /* kWindowSize */ + 1)) - 1; |
| |
| /* A |P256_POINT| is (3 * 32) = 96 bytes, and the 64-byte alignment should |
| * add no more than 63 bytes of overhead. Thus, |table| should require |
| * ~1599 ((96 * 16) + 63) bytes of stack space. */ |
| alignas(64) P256_POINT table[16]; |
| uint8_t p_str[33]; |
| |
| |
| int ret = 0; |
| BN_CTX *new_ctx = NULL; |
| int ctx_started = 0; |
| |
| if (BN_num_bits(p_scalar) > 256 || BN_is_negative(p_scalar)) { |
| if (ctx == NULL) { |
| new_ctx = BN_CTX_new(); |
| if (new_ctx == NULL) { |
| OPENSSL_PUT_ERROR(EC, ERR_R_MALLOC_FAILURE); |
| goto err; |
| } |
| ctx = new_ctx; |
| } |
| BN_CTX_start(ctx); |
| ctx_started = 1; |
| BIGNUM *mod = BN_CTX_get(ctx); |
| if (mod == NULL) { |
| OPENSSL_PUT_ERROR(EC, ERR_R_MALLOC_FAILURE); |
| goto err; |
| } |
| if (!BN_nnmod(mod, p_scalar, &group->order, ctx)) { |
| OPENSSL_PUT_ERROR(EC, ERR_R_BN_LIB); |
| goto err; |
| } |
| p_scalar = mod; |
| } |
| |
| int j; |
| for (j = 0; j < p_scalar->top * BN_BYTES; j += BN_BYTES) { |
| BN_ULONG d = p_scalar->d[j / BN_BYTES]; |
| |
| p_str[j + 0] = d & 0xff; |
| p_str[j + 1] = (d >> 8) & 0xff; |
| p_str[j + 2] = (d >> 16) & 0xff; |
| p_str[j + 3] = (d >>= 24) & 0xff; |
| if (BN_BYTES == 8) { |
| d >>= 8; |
| p_str[j + 4] = d & 0xff; |
| p_str[j + 5] = (d >> 8) & 0xff; |
| p_str[j + 6] = (d >> 16) & 0xff; |
| p_str[j + 7] = (d >> 24) & 0xff; |
| } |
| } |
| |
| for (; j < 33; j++) { |
| p_str[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. */ |
| P256_POINT *row = table; |
| |
| if (!ecp_nistz256_bignum_to_field_elem(row[1 - 1].X, &p->X) || |
| !ecp_nistz256_bignum_to_field_elem(row[1 - 1].Y, &p->Y) || |
| !ecp_nistz256_bignum_to_field_elem(row[1 - 1].Z, &p->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_double(&row[16 - 1], &row[8 - 1]); |
| |
| BN_ULONG tmp[P256_LIMBS]; |
| alignas(32) P256_POINT h; |
| unsigned index = 255; |
| unsigned wvalue = p_str[(index - 1) / 8]; |
| wvalue = (wvalue >> ((index - 1) % 8)) & kMask; |
| |
| ecp_nistz256_select_w5(r, table, booth_recode_w5(wvalue) >> 1); |
| |
| while (index >= 5) { |
| if (index != 255) { |
| unsigned off = (index - 1) / 8; |
| |
| wvalue = p_str[off] | p_str[off + 1] << 8; |
| wvalue = (wvalue >> ((index - 1) % 8)) & kMask; |
| |
| wvalue = booth_recode_w5(wvalue); |
| |
| ecp_nistz256_select_w5(&h, table, 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 */ |
| wvalue = p_str[0]; |
| wvalue = (wvalue << 1) & kMask; |
| |
| wvalue = booth_recode_w5(wvalue); |
| |
| ecp_nistz256_select_w5(&h, table, wvalue >> 1); |
| |
| ecp_nistz256_neg(tmp, h.Y); |
| copy_conditional(h.Y, tmp, wvalue & 1); |
| |
| ecp_nistz256_point_add(r, r, &h); |
| |
| ret = 1; |
| |
| err: |
| if (ctx_started) { |
| BN_CTX_end(ctx); |
| } |
| BN_CTX_free(new_ctx); |
| return ret; |
| } |
| |
| static int ecp_nistz256_points_mul( |
| const EC_GROUP *group, EC_POINT *r, const BIGNUM *g_scalar, |
| const EC_POINT *p_, const BIGNUM *p_scalar, BN_CTX *ctx) { |
| assert((p_ != NULL) == (p_scalar != NULL)); |
| |
| static const unsigned kWindowSize = 7; |
| static const unsigned kMask = (1 << (7 /* kWindowSize */ + 1)) - 1; |
| |
| alignas(32) union { |
| P256_POINT p; |
| P256_POINT_AFFINE a; |
| } t, p; |
| |
| int ret = 0; |
| BN_CTX *new_ctx = NULL; |
| int ctx_started = 0; |
| |
| if (g_scalar != NULL) { |
| if (BN_num_bits(g_scalar) > 256 || BN_is_negative(g_scalar)) { |
| if (ctx == NULL) { |
| new_ctx = BN_CTX_new(); |
| if (new_ctx == NULL) { |
| goto err; |
| } |
| ctx = new_ctx; |
| } |
| BN_CTX_start(ctx); |
| ctx_started = 1; |
| BIGNUM *tmp_scalar = BN_CTX_get(ctx); |
| if (tmp_scalar == NULL) { |
| goto err; |
| } |
| |
| if (!BN_nnmod(tmp_scalar, g_scalar, &group->order, ctx)) { |
| OPENSSL_PUT_ERROR(EC, ERR_R_BN_LIB); |
| goto err; |
| } |
| g_scalar = tmp_scalar; |
| } |
| |
| uint8_t p_str[33] = {0}; |
| int i; |
| for (i = 0; i < g_scalar->top * BN_BYTES; i += BN_BYTES) { |
| BN_ULONG d = g_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); |
| |
| /* Convert |p| from affine to Jacobian coordinates. We set Z to zero if |p| |
| * is infinity and |ONE| otherwise. |p| was computed from the table, so it |
| * is infinity iff |wvalue >> 1| is zero. */ |
| memset(p.p.Z, 0, sizeof(p.p.Z)); |
| copy_conditional(p.p.Z, ONE, is_not_zero(wvalue >> 1)); |
| |
| 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); |
| } |
| } |
| |
| const int p_is_infinity = g_scalar == NULL; |
| if (p_scalar != NULL) { |
| P256_POINT *out = &t.p; |
| if (p_is_infinity) { |
| out = &p.p; |
| } |
| |
| if (!ecp_nistz256_windowed_mul(group, out, p_, p_scalar, ctx)) { |
| goto err; |
| } |
| |
| if (!p_is_infinity) { |
| ecp_nistz256_point_add(&p.p, &p.p, out); |
| } |
| } |
| |
| /* Not constant-time, but we're only operating on the public output. */ |
| if (!bn_set_words(&r->X, p.p.X, P256_LIMBS) || |
| !bn_set_words(&r->Y, p.p.Y, P256_LIMBS) || |
| !bn_set_words(&r->Z, p.p.Z, P256_LIMBS)) { |
| return 0; |
| } |
| |
| ret = 1; |
| |
| err: |
| if (ctx_started) { |
| BN_CTX_end(ctx); |
| } |
| BN_CTX_free(new_ctx); |
| 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 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_mont(z_inv3, point_z); |
| ecp_nistz256_sqr_mont(z_inv2, z_inv3); |
| |
| /* TODO(davidben): The two calls to |ecp_nistz256_from_mont| may be factored |
| * into one call now that other operations also reduce mod P. */ |
| |
| if (x != NULL) { |
| BN_ULONG x_aff[P256_LIMBS]; |
| ecp_nistz256_mul_mont(x_aff, z_inv2, point_x); |
| ecp_nistz256_from_mont(x_aff, x_aff); |
| if (!bn_set_words(x, x_aff, P256_LIMBS)) { |
| OPENSSL_PUT_ERROR(EC, ERR_R_MALLOC_FAILURE); |
| return 0; |
| } |
| } |
| |
| if (y != NULL) { |
| BN_ULONG y_aff[P256_LIMBS]; |
| ecp_nistz256_mul_mont(z_inv3, z_inv3, z_inv2); |
| ecp_nistz256_mul_mont(y_aff, z_inv3, point_y); |
| ecp_nistz256_from_mont(y_aff, y_aff); |
| if (!bn_set_words(y, y_aff, P256_LIMBS)) { |
| OPENSSL_PUT_ERROR(EC, ERR_R_MALLOC_FAILURE); |
| return 0; |
| } |
| } |
| |
| return 1; |
| } |
| |
| |
| const EC_METHOD EC_GFp_nistz256_method = { |
| ec_GFp_mont_group_init, |
| ec_GFp_mont_group_finish, |
| ec_GFp_mont_group_copy, |
| ec_GFp_mont_group_set_curve, |
| ecp_nistz256_get_affine, |
| ecp_nistz256_points_mul, |
| ec_GFp_mont_field_mul, |
| ec_GFp_mont_field_sqr, |
| ec_GFp_mont_field_encode, |
| ec_GFp_mont_field_decode, |
| }; |
| |
| #endif /* !defined(OPENSSL_NO_ASM) && defined(OPENSSL_X86_64) && \ |
| !defined(OPENSSL_SMALL) */ |