#include /****************************************************************************** * * * Copyright 2014 Intel Corporation * * * * Licensed under the Apache License, Version 2.0 (the "License"); * * you may not use this file except in compliance with the License. * * You may obtain a copy of the License at * * * * http://www.apache.org/licenses/LICENSE-2.0 * * * * Unless required by applicable law or agreed to in writing, software * * distributed under the License is distributed on an "AS IS" BASIS, * * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. * * See the License for the specific language governing permissions and * * limitations under the License. * * * ****************************************************************************** * * * 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 #include #include #include #include "cryptlib.h" #include "ec_lcl.h" #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) ((unsigned char *)p+N-(size_t)p%N) #define P256_LIMBS (256/BN_BITS2) typedef unsigned short u16; 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]; /* structure for precomputed multiples of the generator */ typedef struct ec_pre_comp_st { const EC_GROUP *group; /* Parent EC_GROUP object */ size_t w; /* Window size */ /* * Constant time access to the X and Y coordinates of the pre-computed, * generator multiplies, in the Montgomery domain. Pre-calculated * multiplies are stored in affine form. */ PRECOMP256_ROW *precomp; void *precomp_storage; int references; } EC_PRE_COMP; /* Functions implemented in assembly */ /* * Most of below mentioned functions *preserve* the property of inputs * being fully reduced, i.e. being in [0, modulus) range. Simply put if * inputs are fully reduced, then output is too. Note that reverse is * not true, in sense that given partially reduced inputs output can be * either, not unlikely reduced. And "most" in first sentence refers to * the fact that given the calculations flow one can tolerate that * addition, 1st function below, produces partially reduced result *if* * multiplications by 2 and 3, which customarily use addition, fully * reduce it. This effectively gives two options: a) addition produces * fully reduced result [as long as inputs are, just like remaining * functions]; b) addition is allowed to produce partially reduced * result, but multiplications by 2 and 3 perform additional reduction * step. Choice between the two can be platform-specific, but it was a) * in all cases so far... */ /* 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 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 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 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 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) }; static void *ecp_nistz256_pre_comp_dup(void *); static void ecp_nistz256_pre_comp_free(void *); static void ecp_nistz256_pre_comp_clear_free(void *); static EC_PRE_COMP *ecp_nistz256_pre_comp_new(const EC_GROUP *group); /* Precomputed tables for the default generator */ #include "ecp_nistz256_table.c" /* Recode window to a signed digit, see ecp_nistputil.c for details */ static unsigned int _booth_recode_w5(unsigned int in) { unsigned int 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 int _booth_recode_w7(unsigned int in) { unsigned int 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 = -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 BIGNUM *z) { BN_ULONG res = 0; BN_ULONG *a = z->d; if (z->top == (P256_LIMBS - P256_LIMBS / 8)) { 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]; /* * no check for a[7] (being zero) on 32-bit platforms, * because value of "one" takes only 7 limbs. */ } res = is_zero(res); } return res; } static int ecp_nistz256_set_words(BIGNUM *a, BN_ULONG words[P256_LIMBS]) { if (bn_wexpand(a, P256_LIMBS) == NULL) { ECerr(EC_F_ECP_NISTZ256_SET_WORDS, ERR_R_MALLOC_FAILURE); return 0; } memcpy(a->d, words, sizeof(BN_ULONG) * P256_LIMBS); a->top = P256_LIMBS; bn_correct_top(a); return 1; } #ifndef ECP_NISTZ256_REFERENCE_IMPLEMENTATION 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); #else /* Point double: r = 2*a */ static void ecp_nistz256_point_double(P256_POINT *r, const P256_POINT *a) { BN_ULONG S[P256_LIMBS]; BN_ULONG M[P256_LIMBS]; BN_ULONG Zsqr[P256_LIMBS]; BN_ULONG tmp0[P256_LIMBS]; const BN_ULONG *in_x = a->X; const BN_ULONG *in_y = a->Y; const BN_ULONG *in_z = a->Z; BN_ULONG *res_x = r->X; BN_ULONG *res_y = r->Y; BN_ULONG *res_z = r->Z; ecp_nistz256_mul_by_2(S, in_y); ecp_nistz256_sqr_mont(Zsqr, in_z); ecp_nistz256_sqr_mont(S, S); ecp_nistz256_mul_mont(res_z, in_z, in_y); ecp_nistz256_mul_by_2(res_z, res_z); ecp_nistz256_add(M, in_x, Zsqr); ecp_nistz256_sub(Zsqr, in_x, Zsqr); ecp_nistz256_sqr_mont(res_y, S); ecp_nistz256_div_by_2(res_y, res_y); ecp_nistz256_mul_mont(M, M, Zsqr); ecp_nistz256_mul_by_3(M, M); ecp_nistz256_mul_mont(S, S, in_x); ecp_nistz256_mul_by_2(tmp0, S); ecp_nistz256_sqr_mont(res_x, M); ecp_nistz256_sub(res_x, res_x, tmp0); ecp_nistz256_sub(S, S, res_x); ecp_nistz256_mul_mont(S, S, M); ecp_nistz256_sub(res_y, S, res_y); } /* Point addition: r = a+b */ static void ecp_nistz256_point_add(P256_POINT *r, const P256_POINT *a, const P256_POINT *b) { BN_ULONG U2[P256_LIMBS], S2[P256_LIMBS]; BN_ULONG U1[P256_LIMBS], S1[P256_LIMBS]; BN_ULONG Z1sqr[P256_LIMBS]; BN_ULONG Z2sqr[P256_LIMBS]; BN_ULONG H[P256_LIMBS], R[P256_LIMBS]; BN_ULONG Hsqr[P256_LIMBS]; BN_ULONG Rsqr[P256_LIMBS]; BN_ULONG Hcub[P256_LIMBS]; BN_ULONG res_x[P256_LIMBS]; BN_ULONG res_y[P256_LIMBS]; BN_ULONG res_z[P256_LIMBS]; BN_ULONG in1infty, in2infty; const BN_ULONG *in1_x = a->X; const BN_ULONG *in1_y = a->Y; const BN_ULONG *in1_z = a->Z; const BN_ULONG *in2_x = b->X; const BN_ULONG *in2_y = b->Y; const BN_ULONG *in2_z = b->Z; /* * Infinity in encoded as (,,0) */ in1infty = (in1_z[0] | in1_z[1] | in1_z[2] | in1_z[3]); if (P256_LIMBS == 8) in1infty |= (in1_z[4] | in1_z[5] | in1_z[6] | in1_z[7]); in2infty = (in2_z[0] | in2_z[1] | in2_z[2] | in2_z[3]); if (P256_LIMBS == 8) in2infty |= (in2_z[4] | in2_z[5] | in2_z[6] | in2_z[7]); in1infty = is_zero(in1infty); in2infty = is_zero(in2infty); ecp_nistz256_sqr_mont(Z2sqr, in2_z); /* Z2^2 */ ecp_nistz256_sqr_mont(Z1sqr, in1_z); /* Z1^2 */ ecp_nistz256_mul_mont(S1, Z2sqr, in2_z); /* S1 = Z2^3 */ ecp_nistz256_mul_mont(S2, Z1sqr, in1_z); /* S2 = Z1^3 */ ecp_nistz256_mul_mont(S1, S1, in1_y); /* S1 = Y1*Z2^3 */ ecp_nistz256_mul_mont(S2, S2, in2_y); /* S2 = Y2*Z1^3 */ ecp_nistz256_sub(R, S2, S1); /* R = S2 - S1 */ ecp_nistz256_mul_mont(U1, in1_x, Z2sqr); /* U1 = X1*Z2^2 */ ecp_nistz256_mul_mont(U2, in2_x, Z1sqr); /* U2 = X2*Z1^2 */ ecp_nistz256_sub(H, U2, U1); /* H = U2 - U1 */ /* * This should not happen during sign/ecdh, so no constant time violation */ if (is_equal(U1, U2) && !in1infty && !in2infty) { if (is_equal(S1, S2)) { ecp_nistz256_point_double(r, a); return; } else { memset(r, 0, sizeof(*r)); return; } } ecp_nistz256_sqr_mont(Rsqr, R); /* R^2 */ ecp_nistz256_mul_mont(res_z, H, in1_z); /* Z3 = H*Z1*Z2 */ ecp_nistz256_sqr_mont(Hsqr, H); /* H^2 */ ecp_nistz256_mul_mont(res_z, res_z, in2_z); /* Z3 = H*Z1*Z2 */ ecp_nistz256_mul_mont(Hcub, Hsqr, H); /* H^3 */ ecp_nistz256_mul_mont(U2, U1, Hsqr); /* U1*H^2 */ ecp_nistz256_mul_by_2(Hsqr, U2); /* 2*U1*H^2 */ ecp_nistz256_sub(res_x, Rsqr, Hsqr); ecp_nistz256_sub(res_x, res_x, Hcub); ecp_nistz256_sub(res_y, U2, res_x); ecp_nistz256_mul_mont(S2, S1, Hcub); ecp_nistz256_mul_mont(res_y, R, res_y); ecp_nistz256_sub(res_y, res_y, S2); copy_conditional(res_x, in2_x, in1infty); copy_conditional(res_y, in2_y, in1infty); copy_conditional(res_z, in2_z, in1infty); copy_conditional(res_x, in1_x, in2infty); copy_conditional(res_y, in1_y, in2infty); copy_conditional(res_z, in1_z, in2infty); memcpy(r->X, res_x, sizeof(res_x)); memcpy(r->Y, res_y, sizeof(res_y)); memcpy(r->Z, res_z, sizeof(res_z)); } /* Point addition when b is known to be affine: r = a+b */ static void ecp_nistz256_point_add_affine(P256_POINT *r, const P256_POINT *a, const P256_POINT_AFFINE *b) { BN_ULONG U2[P256_LIMBS], S2[P256_LIMBS]; BN_ULONG Z1sqr[P256_LIMBS]; BN_ULONG H[P256_LIMBS], R[P256_LIMBS]; BN_ULONG Hsqr[P256_LIMBS]; BN_ULONG Rsqr[P256_LIMBS]; BN_ULONG Hcub[P256_LIMBS]; BN_ULONG res_x[P256_LIMBS]; BN_ULONG res_y[P256_LIMBS]; BN_ULONG res_z[P256_LIMBS]; BN_ULONG in1infty, in2infty; const BN_ULONG *in1_x = a->X; const BN_ULONG *in1_y = a->Y; const BN_ULONG *in1_z = a->Z; const BN_ULONG *in2_x = b->X; const BN_ULONG *in2_y = b->Y; /* * Infinity in encoded as (,,0) */ in1infty = (in1_z[0] | in1_z[1] | in1_z[2] | in1_z[3]); if (P256_LIMBS == 8) in1infty |= (in1_z[4] | in1_z[5] | in1_z[6] | in1_z[7]); /* * In affine representation we encode infinity as (0,0), which is * not on the curve, so it is OK */ in2infty = (in2_x[0] | in2_x[1] | in2_x[2] | in2_x[3] | in2_y[0] | in2_y[1] | in2_y[2] | in2_y[3]); if (P256_LIMBS == 8) in2infty |= (in2_x[4] | in2_x[5] | in2_x[6] | in2_x[7] | in2_y[4] | in2_y[5] | in2_y[6] | in2_y[7]); in1infty = is_zero(in1infty); in2infty = is_zero(in2infty); ecp_nistz256_sqr_mont(Z1sqr, in1_z); /* Z1^2 */ ecp_nistz256_mul_mont(U2, in2_x, Z1sqr); /* U2 = X2*Z1^2 */ ecp_nistz256_sub(H, U2, in1_x); /* H = U2 - U1 */ ecp_nistz256_mul_mont(S2, Z1sqr, in1_z); /* S2 = Z1^3 */ ecp_nistz256_mul_mont(res_z, H, in1_z); /* Z3 = H*Z1*Z2 */ ecp_nistz256_mul_mont(S2, S2, in2_y); /* S2 = Y2*Z1^3 */ ecp_nistz256_sub(R, S2, in1_y); /* R = S2 - S1 */ ecp_nistz256_sqr_mont(Hsqr, H); /* H^2 */ ecp_nistz256_sqr_mont(Rsqr, R); /* R^2 */ ecp_nistz256_mul_mont(Hcub, Hsqr, H); /* H^3 */ ecp_nistz256_mul_mont(U2, in1_x, Hsqr); /* U1*H^2 */ ecp_nistz256_mul_by_2(Hsqr, U2); /* 2*U1*H^2 */ ecp_nistz256_sub(res_x, Rsqr, Hsqr); ecp_nistz256_sub(res_x, res_x, Hcub); ecp_nistz256_sub(H, U2, res_x); ecp_nistz256_mul_mont(S2, in1_y, Hcub); ecp_nistz256_mul_mont(H, H, R); ecp_nistz256_sub(res_y, H, S2); copy_conditional(res_x, in2_x, in1infty); copy_conditional(res_x, in1_x, in2infty); copy_conditional(res_y, in2_y, in1infty); copy_conditional(res_y, in1_y, in2infty); copy_conditional(res_z, ONE, in1infty); copy_conditional(res_z, in1_z, in2infty); memcpy(r->X, res_x, sizeof(res_x)); memcpy(r->Y, res_y, sizeof(res_y)); memcpy(r->Z, res_z, sizeof(res_z)); } #endif /* 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 int ecp_nistz256_windowed_mul(const EC_GROUP *group, P256_POINT *r, const BIGNUM **scalar, const EC_POINT **point, int num, BN_CTX *ctx) { int i, j, ret = 0; unsigned int index; unsigned char (*p_str)[33] = NULL; const unsigned int window_size = 5; const unsigned int mask = (1 << (window_size + 1)) - 1; unsigned int wvalue; BN_ULONG tmp[P256_LIMBS]; ALIGN32 P256_POINT h; const BIGNUM **scalars = NULL; P256_POINT (*table)[16] = NULL; void *table_storage = NULL; if ((table_storage = OPENSSL_malloc(num * 16 * sizeof(P256_POINT) + 64)) == NULL || (p_str = OPENSSL_malloc(num * 33 * sizeof(unsigned char))) == NULL || (scalars = OPENSSL_malloc(num * sizeof(BIGNUM *))) == NULL) { ECerr(EC_F_ECP_NISTZ256_WINDOWED_MUL, ERR_R_MALLOC_FAILURE); goto err; } else { table = (void *)ALIGNPTR(table_storage, 64); } for (i = 0; i < num; i++) { P256_POINT *row = table[i]; /* This is an unusual input, we don't guarantee constant-timeness. */ if ((BN_num_bits(scalar[i]) > 256) || BN_is_negative(scalar[i])) { BIGNUM *mod; if ((mod = BN_CTX_get(ctx)) == NULL) goto err; if (!BN_nnmod(mod, scalar[i], &group->order, ctx)) { ECerr(EC_F_ECP_NISTZ256_WINDOWED_MUL, ERR_R_BN_LIB); goto err; } scalars[i] = mod; } else scalars[i] = scalar[i]; 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)) { ECerr(EC_F_ECP_NISTZ256_WINDOWED_MUL, 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]); } index = 255; wvalue = p_str[0][(index - 1) / 8]; wvalue = (wvalue >> ((index - 1) % 8)) & mask; 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 int off = (index - 1) / 8; wvalue = p_str[i][off] | p_str[i][off + 1] << 8; wvalue = (wvalue >> ((index - 1) % 8)) & mask; 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 -= window_size; 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) & mask; 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); } ret = 1; err: if (table_storage) OPENSSL_free(table_storage); if (p_str) OPENSSL_free(p_str); if (scalars) OPENSSL_free(scalars); return ret; } /* 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) && is_equal(generator->X.d, def_xG) && is_equal(generator->Y.d, def_yG) && is_one(&generator->Z); } static int ecp_nistz256_mult_precompute(EC_GROUP *group, BN_CTX *ctx) { /* * We precompute a table for a Booth encoded exponent (wNAF) based * computation. Each table holds 64 values for safe access, with an * implicit value of infinity at index zero. We use window of size 7, and * therefore require ceil(256/7) = 37 tables. */ BIGNUM *order; EC_POINT *P = NULL, *T = NULL; const EC_POINT *generator; EC_PRE_COMP *pre_comp; BN_CTX *new_ctx = NULL; int i, j, k, ret = 0; size_t w; PRECOMP256_ROW *preComputedTable = NULL; unsigned char *precomp_storage = NULL; /* if there is an old EC_PRE_COMP object, throw it away */ EC_EX_DATA_free_data(&group->extra_data, ecp_nistz256_pre_comp_dup, ecp_nistz256_pre_comp_free, ecp_nistz256_pre_comp_clear_free); generator = EC_GROUP_get0_generator(group); if (generator == NULL) { ECerr(EC_F_ECP_NISTZ256_MULT_PRECOMPUTE, EC_R_UNDEFINED_GENERATOR); return 0; } if (ecp_nistz256_is_affine_G(generator)) { /* * No need to calculate tables for the standard generator because we * have them statically. */ return 1; } if ((pre_comp = ecp_nistz256_pre_comp_new(group)) == NULL) return 0; if (ctx == NULL) { ctx = new_ctx = BN_CTX_new(); if (ctx == NULL) goto err; } BN_CTX_start(ctx); order = BN_CTX_get(ctx); if (order == NULL) goto err; if (!EC_GROUP_get_order(group, order, ctx)) goto err; if (BN_is_zero(order)) { ECerr(EC_F_ECP_NISTZ256_MULT_PRECOMPUTE, EC_R_UNKNOWN_ORDER); goto err; } w = 7; if ((precomp_storage = OPENSSL_malloc(37 * 64 * sizeof(P256_POINT_AFFINE) + 64)) == NULL) { ECerr(EC_F_ECP_NISTZ256_MULT_PRECOMPUTE, ERR_R_MALLOC_FAILURE); goto err; } else { preComputedTable = (void *)ALIGNPTR(precomp_storage, 64); } P = EC_POINT_new(group); T = EC_POINT_new(group); if (P == NULL || T == NULL) goto err; /* * The zero entry is implicitly infinity, and we skip it, storing other * values with -1 offset. */ if (!EC_POINT_copy(T, generator)) goto err; for (k = 0; k < 64; k++) { if (!EC_POINT_copy(P, T)) goto err; for (j = 0; j < 37; j++) { /* * It would be faster to use EC_POINTs_make_affine and * make multiple points affine at the same time. */ if (!EC_POINT_make_affine(group, P, ctx)) goto err; if (!ecp_nistz256_bignum_to_field_elem(preComputedTable[j][k].X, &P->X) || !ecp_nistz256_bignum_to_field_elem(preComputedTable[j][k].Y, &P->Y)) { ECerr(EC_F_ECP_NISTZ256_MULT_PRECOMPUTE, EC_R_COORDINATES_OUT_OF_RANGE); goto err; } for (i = 0; i < 7; i++) { if (!EC_POINT_dbl(group, P, P, ctx)) goto err; } } if (!EC_POINT_add(group, T, T, generator, ctx)) goto err; } pre_comp->group = group; pre_comp->w = w; pre_comp->precomp = preComputedTable; pre_comp->precomp_storage = precomp_storage; precomp_storage = NULL; if (!EC_EX_DATA_set_data(&group->extra_data, pre_comp, ecp_nistz256_pre_comp_dup, ecp_nistz256_pre_comp_free, ecp_nistz256_pre_comp_clear_free)) { goto err; } pre_comp = NULL; ret = 1; err: if (ctx != NULL) BN_CTX_end(ctx); BN_CTX_free(new_ctx); if (pre_comp) ecp_nistz256_pre_comp_free(pre_comp); if (precomp_storage) OPENSSL_free(precomp_storage); if (P) EC_POINT_free(P); if (T) EC_POINT_free(T); return ret; } /* * Note that by default ECP_NISTZ256_AVX2 is undefined. While it's great * code processing 4 points in parallel, corresponding serial operation * is several times slower, because it uses 29x29=58-bit multiplication * as opposite to 64x64=128-bit in integer-only scalar case. As result * it doesn't provide *significant* performance improvement. Note that * just defining ECP_NISTZ256_AVX2 is not sufficient to make it work, * you'd need to compile even asm/ecp_nistz256-avx.pl module. */ #if defined(ECP_NISTZ256_AVX2) # if !(defined(__x86_64) || defined(__x86_64__)) || \ defined(_M_AMD64) || defined(_MX64)) || \ !(defined(__GNUC__) || defined(_MSC_VER)) /* this is for ALIGN32 */ # undef ECP_NISTZ256_AVX2 # else /* Constant time access, loading four values, from four consecutive tables */ void ecp_nistz256_avx2_select_w7(P256_POINT_AFFINE * val, const P256_POINT_AFFINE * in_t, int index); void ecp_nistz256_avx2_multi_select_w7(void *result, const void *in, int index0, int index1, int index2, int index3); void ecp_nistz256_avx2_transpose_convert(void *RESULTx4, const void *in); void ecp_nistz256_avx2_convert_transpose_back(void *result, const void *Ax4); void ecp_nistz256_avx2_point_add_affine_x4(void *RESULTx4, const void *Ax4, const void *Bx4); void ecp_nistz256_avx2_point_add_affines_x4(void *RESULTx4, const void *Ax4, const void *Bx4); void ecp_nistz256_avx2_to_mont(void *RESULTx4, const void *Ax4); void ecp_nistz256_avx2_from_mont(void *RESULTx4, const void *Ax4); void ecp_nistz256_avx2_set1(void *RESULTx4); int ecp_nistz_avx2_eligible(void); static void booth_recode_w7(unsigned char *sign, unsigned char *digit, unsigned char in) { unsigned char s, d; s = ~((in >> 7) - 1); d = (1 << 8) - in - 1; d = (d & s) | (in & ~s); d = (d >> 1) + (d & 1); *sign = s & 1; *digit = d; } /* * ecp_nistz256_avx2_mul_g performs multiplication by G, using only the * precomputed table. It does 4 affine point additions in parallel, * significantly speeding up point multiplication for a fixed value. */ static void ecp_nistz256_avx2_mul_g(P256_POINT *r, unsigned char p_str[33], const P256_POINT_AFFINE(*preComputedTable)[64]) { const unsigned int window_size = 7; const unsigned int mask = (1 << (window_size + 1)) - 1; unsigned int wvalue; /* Using 4 windows at a time */ unsigned char sign0, digit0; unsigned char sign1, digit1; unsigned char sign2, digit2; unsigned char sign3, digit3; unsigned int index = 0; BN_ULONG tmp[P256_LIMBS]; int i; ALIGN32 BN_ULONG aX4[4 * 9 * 3] = { 0 }; ALIGN32 BN_ULONG bX4[4 * 9 * 2] = { 0 }; ALIGN32 P256_POINT_AFFINE point_arr[P256_LIMBS]; ALIGN32 P256_POINT res_point_arr[P256_LIMBS]; /* Initial four windows */ wvalue = *((u16 *) & p_str[0]); wvalue = (wvalue << 1) & mask; index += window_size; booth_recode_w7(&sign0, &digit0, wvalue); wvalue = *((u16 *) & p_str[(index - 1) / 8]); wvalue = (wvalue >> ((index - 1) % 8)) & mask; index += window_size; booth_recode_w7(&sign1, &digit1, wvalue); wvalue = *((u16 *) & p_str[(index - 1) / 8]); wvalue = (wvalue >> ((index - 1) % 8)) & mask; index += window_size; booth_recode_w7(&sign2, &digit2, wvalue); wvalue = *((u16 *) & p_str[(index - 1) / 8]); wvalue = (wvalue >> ((index - 1) % 8)) & mask; index += window_size; booth_recode_w7(&sign3, &digit3, wvalue); ecp_nistz256_avx2_multi_select_w7(point_arr, preComputedTable[0], digit0, digit1, digit2, digit3); ecp_nistz256_neg(tmp, point_arr[0].Y); copy_conditional(point_arr[0].Y, tmp, sign0); ecp_nistz256_neg(tmp, point_arr[1].Y); copy_conditional(point_arr[1].Y, tmp, sign1); ecp_nistz256_neg(tmp, point_arr[2].Y); copy_conditional(point_arr[2].Y, tmp, sign2); ecp_nistz256_neg(tmp, point_arr[3].Y); copy_conditional(point_arr[3].Y, tmp, sign3); ecp_nistz256_avx2_transpose_convert(aX4, point_arr); ecp_nistz256_avx2_to_mont(aX4, aX4); ecp_nistz256_avx2_to_mont(&aX4[4 * 9], &aX4[4 * 9]); ecp_nistz256_avx2_set1(&aX4[4 * 9 * 2]); wvalue = *((u16 *) & p_str[(index - 1) / 8]); wvalue = (wvalue >> ((index - 1) % 8)) & mask; index += window_size; booth_recode_w7(&sign0, &digit0, wvalue); wvalue = *((u16 *) & p_str[(index - 1) / 8]); wvalue = (wvalue >> ((index - 1) % 8)) & mask; index += window_size; booth_recode_w7(&sign1, &digit1, wvalue); wvalue = *((u16 *) & p_str[(index - 1) / 8]); wvalue = (wvalue >> ((index - 1) % 8)) & mask; index += window_size; booth_recode_w7(&sign2, &digit2, wvalue); wvalue = *((u16 *) & p_str[(index - 1) / 8]); wvalue = (wvalue >> ((index - 1) % 8)) & mask; index += window_size; booth_recode_w7(&sign3, &digit3, wvalue); ecp_nistz256_avx2_multi_select_w7(point_arr, preComputedTable[4 * 1], digit0, digit1, digit2, digit3); ecp_nistz256_neg(tmp, point_arr[0].Y); copy_conditional(point_arr[0].Y, tmp, sign0); ecp_nistz256_neg(tmp, point_arr[1].Y); copy_conditional(point_arr[1].Y, tmp, sign1); ecp_nistz256_neg(tmp, point_arr[2].Y); copy_conditional(point_arr[2].Y, tmp, sign2); ecp_nistz256_neg(tmp, point_arr[3].Y); copy_conditional(point_arr[3].Y, tmp, sign3); ecp_nistz256_avx2_transpose_convert(bX4, point_arr); ecp_nistz256_avx2_to_mont(bX4, bX4); ecp_nistz256_avx2_to_mont(&bX4[4 * 9], &bX4[4 * 9]); /* Optimized when both inputs are affine */ ecp_nistz256_avx2_point_add_affines_x4(aX4, aX4, bX4); for (i = 2; i < 9; i++) { wvalue = *((u16 *) & p_str[(index - 1) / 8]); wvalue = (wvalue >> ((index - 1) % 8)) & mask; index += window_size; booth_recode_w7(&sign0, &digit0, wvalue); wvalue = *((u16 *) & p_str[(index - 1) / 8]); wvalue = (wvalue >> ((index - 1) % 8)) & mask; index += window_size; booth_recode_w7(&sign1, &digit1, wvalue); wvalue = *((u16 *) & p_str[(index - 1) / 8]); wvalue = (wvalue >> ((index - 1) % 8)) & mask; index += window_size; booth_recode_w7(&sign2, &digit2, wvalue); wvalue = *((u16 *) & p_str[(index - 1) / 8]); wvalue = (wvalue >> ((index - 1) % 8)) & mask; index += window_size; booth_recode_w7(&sign3, &digit3, wvalue); ecp_nistz256_avx2_multi_select_w7(point_arr, preComputedTable[4 * i], digit0, digit1, digit2, digit3); ecp_nistz256_neg(tmp, point_arr[0].Y); copy_conditional(point_arr[0].Y, tmp, sign0); ecp_nistz256_neg(tmp, point_arr[1].Y); copy_conditional(point_arr[1].Y, tmp, sign1); ecp_nistz256_neg(tmp, point_arr[2].Y); copy_conditional(point_arr[2].Y, tmp, sign2); ecp_nistz256_neg(tmp, point_arr[3].Y); copy_conditional(point_arr[3].Y, tmp, sign3); ecp_nistz256_avx2_transpose_convert(bX4, point_arr); ecp_nistz256_avx2_to_mont(bX4, bX4); ecp_nistz256_avx2_to_mont(&bX4[4 * 9], &bX4[4 * 9]); ecp_nistz256_avx2_point_add_affine_x4(aX4, aX4, bX4); } ecp_nistz256_avx2_from_mont(&aX4[4 * 9 * 0], &aX4[4 * 9 * 0]); ecp_nistz256_avx2_from_mont(&aX4[4 * 9 * 1], &aX4[4 * 9 * 1]); ecp_nistz256_avx2_from_mont(&aX4[4 * 9 * 2], &aX4[4 * 9 * 2]); ecp_nistz256_avx2_convert_transpose_back(res_point_arr, aX4); /* Last window is performed serially */ wvalue = *((u16 *) & p_str[(index - 1) / 8]); wvalue = (wvalue >> ((index - 1) % 8)) & mask; booth_recode_w7(&sign0, &digit0, wvalue); ecp_nistz256_avx2_select_w7((P256_POINT_AFFINE *) r, preComputedTable[36], digit0); ecp_nistz256_neg(tmp, r->Y); copy_conditional(r->Y, tmp, sign0); memcpy(r->Z, ONE, sizeof(ONE)); /* Sum the four windows */ ecp_nistz256_point_add(r, r, &res_point_arr[0]); ecp_nistz256_point_add(r, r, &res_point_arr[1]); ecp_nistz256_point_add(r, r, &res_point_arr[2]); ecp_nistz256_point_add(r, r, &res_point_arr[3]); } # endif #endif static int ecp_nistz256_set_from_affine(EC_POINT *out, const EC_GROUP *group, const P256_POINT_AFFINE *in, BN_CTX *ctx) { BIGNUM x, y; BN_ULONG d_x[P256_LIMBS], d_y[P256_LIMBS]; int ret = 0; memcpy(d_x, in->X, sizeof(d_x)); x.d = d_x; x.dmax = x.top = P256_LIMBS; x.neg = 0; x.flags = BN_FLG_STATIC_DATA; memcpy(d_y, in->Y, sizeof(d_y)); y.d = d_y; y.dmax = y.top = P256_LIMBS; y.neg = 0; y.flags = BN_FLG_STATIC_DATA; ret = EC_POINT_set_affine_coordinates_GFp(group, out, &x, &y, ctx); return ret; } /* 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) { int i = 0, ret = 0, no_precomp_for_generator = 0, p_is_infinity = 0; size_t j; unsigned char p_str[33] = { 0 }; const PRECOMP256_ROW *preComputedTable = NULL; const EC_PRE_COMP *pre_comp = NULL; const EC_POINT *generator = NULL; unsigned int index = 0; BN_CTX *new_ctx = NULL; const BIGNUM **new_scalars = NULL; const EC_POINT **new_points = NULL; const unsigned int window_size = 7; const unsigned int mask = (1 << (window_size + 1)) - 1; unsigned int wvalue; ALIGN32 union { P256_POINT p; P256_POINT_AFFINE a; } t, p; BIGNUM *tmp_scalar; if (group->meth != r->meth) { ECerr(EC_F_ECP_NISTZ256_POINTS_MUL, EC_R_INCOMPATIBLE_OBJECTS); return 0; } if ((scalar == NULL) && (num == 0)) return EC_POINT_set_to_infinity(group, r); for (j = 0; j < num; j++) { if (group->meth != points[j]->meth) { ECerr(EC_F_ECP_NISTZ256_POINTS_MUL, EC_R_INCOMPATIBLE_OBJECTS); return 0; } } if (ctx == NULL) { ctx = new_ctx = BN_CTX_new(); if (ctx == NULL) goto err; } BN_CTX_start(ctx); if (scalar) { generator = EC_GROUP_get0_generator(group); if (generator == NULL) { ECerr(EC_F_ECP_NISTZ256_POINTS_MUL, EC_R_UNDEFINED_GENERATOR); goto err; } /* look if we can use precomputed multiples of generator */ pre_comp = EC_EX_DATA_get_data(group->extra_data, ecp_nistz256_pre_comp_dup, ecp_nistz256_pre_comp_free, ecp_nistz256_pre_comp_clear_free); if (pre_comp) { /* * If there is a precomputed table for the generator, check that * it was generated with the same generator. */ EC_POINT *pre_comp_generator = EC_POINT_new(group); if (pre_comp_generator == NULL) goto err; if (!ecp_nistz256_set_from_affine (pre_comp_generator, group, pre_comp->precomp[0], ctx)) { EC_POINT_free(pre_comp_generator); goto err; } if (0 == EC_POINT_cmp(group, generator, pre_comp_generator, ctx)) preComputedTable = (const PRECOMP256_ROW *)pre_comp->precomp; EC_POINT_free(pre_comp_generator); } if (preComputedTable == NULL && ecp_nistz256_is_affine_G(generator)) { /* * If there is no precomputed data, but the generator * is the default, a hardcoded table of precomputed * data is used. This is because applications, such as * Apache, do not use EC_KEY_precompute_mult. */ preComputedTable = (const PRECOMP256_ROW *)ecp_nistz256_precomputed; } if (preComputedTable) { if ((BN_num_bits(scalar) > 256) || BN_is_negative(scalar)) { if ((tmp_scalar = BN_CTX_get(ctx)) == NULL) goto err; if (!BN_nnmod(tmp_scalar, scalar, &group->order, ctx)) { ECerr(EC_F_ECP_NISTZ256_POINTS_MUL, ERR_R_BN_LIB); goto err; } scalar = tmp_scalar; } 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 < 33; i++) p_str[i] = 0; #if defined(ECP_NISTZ256_AVX2) if (ecp_nistz_avx2_eligible()) { ecp_nistz256_avx2_mul_g(&p.p, p_str, preComputedTable); } else #endif { BN_ULONG infty; /* First window */ wvalue = (p_str[0] << 1) & mask; index += window_size; wvalue = _booth_recode_w7(wvalue); ecp_nistz256_select_w7(&p.a, preComputedTable[0], wvalue >> 1); ecp_nistz256_neg(p.p.Z, p.p.Y); copy_conditional(p.p.Y, p.p.Z, wvalue & 1); /* * Since affine infinity is encoded as (0,0) and * Jacobian ias (,,0), we need to harmonize them * by assigning "one" or zero to Z. */ infty = (p.p.X[0] | p.p.X[1] | p.p.X[2] | p.p.X[3] | p.p.Y[0] | p.p.Y[1] | p.p.Y[2] | p.p.Y[3]); if (P256_LIMBS == 8) infty |= (p.p.X[4] | p.p.X[5] | p.p.X[6] | p.p.X[7] | p.p.Y[4] | p.p.Y[5] | p.p.Y[6] | p.p.Y[7]); infty = 0 - is_zero(infty); infty = ~infty; p.p.Z[0] = ONE[0] & infty; p.p.Z[1] = ONE[1] & infty; p.p.Z[2] = ONE[2] & infty; p.p.Z[3] = ONE[3] & infty; if (P256_LIMBS == 8) { p.p.Z[4] = ONE[4] & infty; p.p.Z[5] = ONE[5] & infty; p.p.Z[6] = ONE[6] & infty; p.p.Z[7] = ONE[7] & infty; } for (i = 1; i < 37; i++) { unsigned int off = (index - 1) / 8; wvalue = p_str[off] | p_str[off + 1] << 8; wvalue = (wvalue >> ((index - 1) % 8)) & mask; index += window_size; wvalue = _booth_recode_w7(wvalue); ecp_nistz256_select_w7(&t.a, preComputedTable[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. */ new_scalars = OPENSSL_malloc((num + 1) * sizeof(BIGNUM *)); if (!new_scalars) { ECerr(EC_F_ECP_NISTZ256_POINTS_MUL, ERR_R_MALLOC_FAILURE); goto err; } new_points = OPENSSL_malloc((num + 1) * sizeof(EC_POINT *)); if (!new_points) { ECerr(EC_F_ECP_NISTZ256_POINTS_MUL, ERR_R_MALLOC_FAILURE); goto err; } memcpy(new_scalars, scalars, num * sizeof(BIGNUM *)); new_scalars[num] = scalar; memcpy(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; if (!ecp_nistz256_windowed_mul(group, out, scalars, points, num, 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 (!ecp_nistz256_set_words(&r->X, p.p.X) || !ecp_nistz256_set_words(&r->Y, p.p.Y) || !ecp_nistz256_set_words(&r->Z, p.p.Z)) { goto err; } r->Z_is_one = is_one(&r->Z) & 1; ret = 1; err: if (ctx) BN_CTX_end(ctx); BN_CTX_free(new_ctx); if (new_points) OPENSSL_free(new_points); if (new_scalars) OPENSSL_free(new_scalars); 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]; BN_ULONG x_ret[P256_LIMBS], y_ret[P256_LIMBS]; if (EC_POINT_is_at_infinity(group, point)) { ECerr(EC_F_ECP_NISTZ256_GET_AFFINE, 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)) { ECerr(EC_F_ECP_NISTZ256_GET_AFFINE, 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) { ecp_nistz256_from_mont(x_ret, x_aff); if (!ecp_nistz256_set_words(x, x_ret)) return 0; } if (y != NULL) { 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_ret, y_aff); if (!ecp_nistz256_set_words(y, y_ret)) return 0; } return 1; } static EC_PRE_COMP *ecp_nistz256_pre_comp_new(const EC_GROUP *group) { EC_PRE_COMP *ret = NULL; if (!group) return NULL; ret = (EC_PRE_COMP *)OPENSSL_malloc(sizeof(EC_PRE_COMP)); if (!ret) { ECerr(EC_F_ECP_NISTZ256_PRE_COMP_NEW, ERR_R_MALLOC_FAILURE); return ret; } ret->group = group; ret->w = 6; /* default */ ret->precomp = NULL; ret->precomp_storage = NULL; ret->references = 1; return ret; } static void *ecp_nistz256_pre_comp_dup(void *src_) { EC_PRE_COMP *src = src_; /* no need to actually copy, these objects never change! */ CRYPTO_add(&src->references, 1, CRYPTO_LOCK_EC_PRE_COMP); return src_; } static void ecp_nistz256_pre_comp_free(void *pre_) { int i; EC_PRE_COMP *pre = pre_; if (!pre) return; i = CRYPTO_add(&pre->references, -1, CRYPTO_LOCK_EC_PRE_COMP); if (i > 0) return; if (pre->precomp_storage) OPENSSL_free(pre->precomp_storage); OPENSSL_free(pre); } static void ecp_nistz256_pre_comp_clear_free(void *pre_) { int i; EC_PRE_COMP *pre = pre_; if (!pre) return; i = CRYPTO_add(&pre->references, -1, CRYPTO_LOCK_EC_PRE_COMP); if (i > 0) return; if (pre->precomp_storage) { OPENSSL_cleanse(pre->precomp, 32 * sizeof(unsigned char) * (1 << pre->w) * 2 * 37); OPENSSL_free(pre->precomp_storage); } OPENSSL_cleanse(pre, sizeof(*pre)); OPENSSL_free(pre); } static int ecp_nistz256_window_have_precompute_mult(const EC_GROUP *group) { /* There is a hard-coded table for the default generator. */ const EC_POINT *generator = EC_GROUP_get0_generator(group); if (generator != NULL && ecp_nistz256_is_affine_G(generator)) { /* There is a hard-coded table for the default generator. */ return 1; } return EC_EX_DATA_get_data(group->extra_data, ecp_nistz256_pre_comp_dup, ecp_nistz256_pre_comp_free, ecp_nistz256_pre_comp_clear_free) != NULL; } const EC_METHOD *EC_GFp_nistz256_method(void) { static const EC_METHOD ret = { EC_FLAGS_DEFAULT_OCT, NID_X9_62_prime_field, 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, ec_GFp_simple_group_get_curve, ec_GFp_simple_group_get_degree, ec_GFp_simple_group_check_discriminant, ec_GFp_simple_point_init, ec_GFp_simple_point_finish, ec_GFp_simple_point_clear_finish, ec_GFp_simple_point_copy, ec_GFp_simple_point_set_to_infinity, ec_GFp_simple_set_Jprojective_coordinates_GFp, ec_GFp_simple_get_Jprojective_coordinates_GFp, ec_GFp_simple_point_set_affine_coordinates, ecp_nistz256_get_affine, 0, 0, 0, ec_GFp_simple_add, ec_GFp_simple_dbl, ec_GFp_simple_invert, ec_GFp_simple_is_at_infinity, ec_GFp_simple_is_on_curve, ec_GFp_simple_cmp, ec_GFp_simple_make_affine, ec_GFp_simple_points_make_affine, ecp_nistz256_points_mul, /* mul */ ecp_nistz256_mult_precompute, /* precompute_mult */ ecp_nistz256_window_have_precompute_mult, /* have_precompute_mult */ ec_GFp_mont_field_mul, ec_GFp_mont_field_sqr, 0, /* field_div */ ec_GFp_mont_field_encode, ec_GFp_mont_field_decode, ec_GFp_mont_field_set_to_one }; return &ret; }