/* * Copyright 2014-2018 The OpenSSL Project Authors. All Rights Reserved. * Copyright (c) 2014, Intel Corporation. All Rights Reserved. * Copyright (c) 2015, CloudFlare, Inc. * * Licensed under the Apache License 2.0 (the "License"). You may not use * this file except in compliance with the License. You can obtain a copy * in the file LICENSE in the source distribution or at * https://www.openssl.org/source/license.html * * Originally written by Shay Gueron (1, 2), and Vlad Krasnov (1, 3) * (1) Intel Corporation, Israel Development Center, Haifa, Israel * (2) University of Haifa, Israel * (3) CloudFlare, Inc. * * Reference: * S.Gueron and V.Krasnov, "Fast Prime Field Elliptic Curve Cryptography with * 256 Bit Primes" */ #include #include "internal/cryptlib.h" #include "crypto/bn.h" #include "ec_local.h" #include "internal/refcount.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 */ struct nistz256_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; CRYPTO_REF_COUNT references; CRYPTO_RWLOCK *lock; }; /* 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_scatter_w5(P256_POINT *val, const P256_POINT *in_t, int idx); void ecp_nistz256_gather_w5(P256_POINT *val, const P256_POINT *in_t, int idx); void ecp_nistz256_scatter_w7(P256_POINT_AFFINE *val, const P256_POINT_AFFINE *in_t, int idx); void ecp_nistz256_gather_w7(P256_POINT_AFFINE *val, const P256_POINT_AFFINE *in_t, int idx); /* 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 NISTZ256_PRE_COMP *ecp_nistz256_pre_comp_new(const EC_GROUP *group); /* Precomputed tables for the default generator */ extern const PRECOMP256_ROW ecp_nistz256_precomputed[37]; /* 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 = 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_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 = bn_get_words(z); if (bn_get_top(z) == (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; } /* * For reference, this macro is used only when new ecp_nistz256 assembly * module is being developed. For example, configure with * -DECP_NISTZ256_REFERENCE_IMPLEMENTATION and implement only functions * performing simplest arithmetic operations on 256-bit vectors. Then * work on implementation of higher-level functions performing point * operations. Then remove ECP_NISTZ256_REFERENCE_IMPLEMENTATION * and never define it again. (The correct macro denoting presence of * ecp_nistz256 module is ECP_NISTZ256_ASM.) */ #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 */ /* * The formulae are incorrect if the points are equal so we check for * this and do doubling if this happens. * * Points here are in Jacobian projective coordinates (Xi, Yi, Zi) * that are bound to the affine coordinates (xi, yi) by the following * equations: * - xi = Xi / (Zi)^2 * - y1 = Yi / (Zi)^3 * * For the sake of optimization, the algorithm operates over * intermediate variables U1, U2 and S1, S2 that are derived from * the projective coordinates: * - U1 = X1 * (Z2)^2 ; U2 = X2 * (Z1)^2 * - S1 = Y1 * (Z2)^3 ; S2 = Y2 * (Z1)^3 * * It is easy to prove that is_equal(U1, U2) implies that the affine * x-coordinates are equal, or either point is at infinity. * Likewise is_equal(S1, S2) implies that the affine y-coordinates are * equal, or either point is at infinity. * * The special case of either point being the point at infinity (Z1 or Z2 * is zero), is handled separately later on in this function, so we avoid * jumping to point_double here in those special cases. * * When both points are inverse of each other, we know that the affine * x-coordinates are equal, and the y-coordinates have different sign. * Therefore since U1 = U2, we know H = 0, and therefore Z3 = H*Z1*Z2 * will equal 0, thus the result is infinity, if we simply let this * function continue normally. * * We use bitwise operations to avoid potential side-channels introduced by * the short-circuiting behaviour of boolean operators. */ if (is_equal(U1, U2) & ~in1infty & ~in2infty & is_equal(S1, S2)) { /* * This is obviously not constant-time but it should never happen during * single point multiplication, so there is no timing leak for ECDH or * ECDSA signing. */ ecp_nistz256_point_double(r, a); 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. */ __owur static int ecp_nistz256_bignum_to_field_elem(BN_ULONG out[P256_LIMBS], const BIGNUM *in) { return bn_copy_words(out, in, P256_LIMBS); } /* r = sum(scalar[i]*point[i]) */ __owur static int ecp_nistz256_windowed_mul(const EC_GROUP *group, P256_POINT *r, const BIGNUM **scalar, const EC_POINT **point, size_t num, BN_CTX *ctx) { size_t i; int j, ret = 0; unsigned int idx; unsigned char (*p_str)[33] = NULL; const unsigned int window_size = 5; const unsigned int mask = (1 << (window_size + 1)) - 1; unsigned int wvalue; P256_POINT *temp; /* place for 5 temporary points */ const BIGNUM **scalars = NULL; P256_POINT (*table)[16] = NULL; void *table_storage = NULL; if ((num * 16 + 6) > OPENSSL_MALLOC_MAX_NELEMS(P256_POINT) || (table_storage = OPENSSL_malloc((num * 16 + 5) * 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; } table = (void *)ALIGNPTR(table_storage, 64); temp = (P256_POINT *)(table + num); 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 < bn_get_top(scalars[i]) * BN_BYTES; j += BN_BYTES) { BN_ULONG d = bn_get_words(scalars[i])[j / BN_BYTES]; p_str[i][j + 0] = (unsigned char)d; p_str[i][j + 1] = (unsigned char)(d >> 8); p_str[i][j + 2] = (unsigned char)(d >> 16); p_str[i][j + 3] = (unsigned char)(d >>= 24); if (BN_BYTES == 8) { d >>= 8; p_str[i][j + 4] = (unsigned char)d; p_str[i][j + 5] = (unsigned char)(d >> 8); p_str[i][j + 6] = (unsigned char)(d >> 16); p_str[i][j + 7] = (unsigned char)(d >> 24); } } for (; j < 33; j++) p_str[i][j] = 0; if (!ecp_nistz256_bignum_to_field_elem(temp[0].X, point[i]->X) || !ecp_nistz256_bignum_to_field_elem(temp[0].Y, point[i]->Y) || !ecp_nistz256_bignum_to_field_elem(temp[0].Z, point[i]->Z)) { ECerr(EC_F_ECP_NISTZ256_WINDOWED_MUL, EC_R_COORDINATES_OUT_OF_RANGE); goto err; } /* * row[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. */ ecp_nistz256_scatter_w5 (row, &temp[0], 1); ecp_nistz256_point_double(&temp[1], &temp[0]); /*1+1=2 */ ecp_nistz256_scatter_w5 (row, &temp[1], 2); ecp_nistz256_point_add (&temp[2], &temp[1], &temp[0]); /*2+1=3 */ ecp_nistz256_scatter_w5 (row, &temp[2], 3); ecp_nistz256_point_double(&temp[1], &temp[1]); /*2*2=4 */ ecp_nistz256_scatter_w5 (row, &temp[1], 4); ecp_nistz256_point_double(&temp[2], &temp[2]); /*2*3=6 */ ecp_nistz256_scatter_w5 (row, &temp[2], 6); ecp_nistz256_point_add (&temp[3], &temp[1], &temp[0]); /*4+1=5 */ ecp_nistz256_scatter_w5 (row, &temp[3], 5); ecp_nistz256_point_add (&temp[4], &temp[2], &temp[0]); /*6+1=7 */ ecp_nistz256_scatter_w5 (row, &temp[4], 7); ecp_nistz256_point_double(&temp[1], &temp[1]); /*2*4=8 */ ecp_nistz256_scatter_w5 (row, &temp[1], 8); ecp_nistz256_point_double(&temp[2], &temp[2]); /*2*6=12 */ ecp_nistz256_scatter_w5 (row, &temp[2], 12); ecp_nistz256_point_double(&temp[3], &temp[3]); /*2*5=10 */ ecp_nistz256_scatter_w5 (row, &temp[3], 10); ecp_nistz256_point_double(&temp[4], &temp[4]); /*2*7=14 */ ecp_nistz256_scatter_w5 (row, &temp[4], 14); ecp_nistz256_point_add (&temp[2], &temp[2], &temp[0]); /*12+1=13*/ ecp_nistz256_scatter_w5 (row, &temp[2], 13); ecp_nistz256_point_add (&temp[3], &temp[3], &temp[0]); /*10+1=11*/ ecp_nistz256_scatter_w5 (row, &temp[3], 11); ecp_nistz256_point_add (&temp[4], &temp[4], &temp[0]); /*14+1=15*/ ecp_nistz256_scatter_w5 (row, &temp[4], 15); ecp_nistz256_point_add (&temp[2], &temp[1], &temp[0]); /*8+1=9 */ ecp_nistz256_scatter_w5 (row, &temp[2], 9); ecp_nistz256_point_double(&temp[1], &temp[1]); /*2*8=16 */ ecp_nistz256_scatter_w5 (row, &temp[1], 16); } idx = 255; wvalue = p_str[0][(idx - 1) / 8]; wvalue = (wvalue >> ((idx - 1) % 8)) & mask; /* * We gather to temp[0], because we know it's position relative * to table */ ecp_nistz256_gather_w5(&temp[0], table[0], _booth_recode_w5(wvalue) >> 1); memcpy(r, &temp[0], sizeof(temp[0])); while (idx >= 5) { for (i = (idx == 255 ? 1 : 0); i < num; i++) { unsigned int off = (idx - 1) / 8; wvalue = p_str[i][off] | p_str[i][off + 1] << 8; wvalue = (wvalue >> ((idx - 1) % 8)) & mask; wvalue = _booth_recode_w5(wvalue); ecp_nistz256_gather_w5(&temp[0], table[i], wvalue >> 1); ecp_nistz256_neg(temp[1].Y, temp[0].Y); copy_conditional(temp[0].Y, temp[1].Y, (wvalue & 1)); ecp_nistz256_point_add(r, r, &temp[0]); } idx -= 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_gather_w5(&temp[0], table[i], wvalue >> 1); ecp_nistz256_neg(temp[1].Y, temp[0].Y); copy_conditional(temp[0].Y, temp[1].Y, wvalue & 1); ecp_nistz256_point_add(r, r, &temp[0]); } ret = 1; err: OPENSSL_free(table_storage); OPENSSL_free(p_str); OPENSSL_free(scalars); return ret; } /* Coordinates of G, for which we have precomputed tables */ static const BN_ULONG def_xG[P256_LIMBS] = { TOBN(0x79e730d4, 0x18a9143c), TOBN(0x75ba95fc, 0x5fedb601), TOBN(0x79fb732b, 0x77622510), TOBN(0x18905f76, 0xa53755c6) }; static const 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 (bn_get_top(generator->X) == P256_LIMBS) && (bn_get_top(generator->Y) == P256_LIMBS) && is_equal(bn_get_words(generator->X), def_xG) && is_equal(bn_get_words(generator->Y), def_yG) && is_one(generator->Z); } __owur 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. */ const BIGNUM *order; EC_POINT *P = NULL, *T = NULL; const EC_POINT *generator; NISTZ256_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 NISTZ256_PRE_COMP object, throw it away */ EC_pre_comp_free(group); 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_ex(group->libctx); if (ctx == NULL) goto err; } BN_CTX_start(ctx); order = EC_GROUP_get0_order(group); if (order == NULL) 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; } 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++) { P256_POINT_AFFINE temp; /* * 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(temp.X, P->X) || !ecp_nistz256_bignum_to_field_elem(temp.Y, P->Y)) { ECerr(EC_F_ECP_NISTZ256_MULT_PRECOMPUTE, EC_R_COORDINATES_OUT_OF_RANGE); goto err; } ecp_nistz256_scatter_w7(preComputedTable[j], &temp, k); 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; SETPRECOMP(group, nistz256, pre_comp); pre_comp = NULL; ret = 1; err: BN_CTX_end(ctx); BN_CTX_free(new_ctx); EC_nistz256_pre_comp_free(pre_comp); OPENSSL_free(precomp_storage); EC_POINT_free(P); 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(_M_X64)) || \ !(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_multi_gather_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 idx = 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[4]; ALIGN32 P256_POINT res_point_arr[4]; /* Initial four windows */ wvalue = *((u16 *) & p_str[0]); wvalue = (wvalue << 1) & mask; idx += window_size; booth_recode_w7(&sign0, &digit0, wvalue); wvalue = *((u16 *) & p_str[(idx - 1) / 8]); wvalue = (wvalue >> ((idx - 1) % 8)) & mask; idx += window_size; booth_recode_w7(&sign1, &digit1, wvalue); wvalue = *((u16 *) & p_str[(idx - 1) / 8]); wvalue = (wvalue >> ((idx - 1) % 8)) & mask; idx += window_size; booth_recode_w7(&sign2, &digit2, wvalue); wvalue = *((u16 *) & p_str[(idx - 1) / 8]); wvalue = (wvalue >> ((idx - 1) % 8)) & mask; idx += window_size; booth_recode_w7(&sign3, &digit3, wvalue); ecp_nistz256_avx2_multi_gather_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[(idx - 1) / 8]); wvalue = (wvalue >> ((idx - 1) % 8)) & mask; idx += window_size; booth_recode_w7(&sign0, &digit0, wvalue); wvalue = *((u16 *) & p_str[(idx - 1) / 8]); wvalue = (wvalue >> ((idx - 1) % 8)) & mask; idx += window_size; booth_recode_w7(&sign1, &digit1, wvalue); wvalue = *((u16 *) & p_str[(idx - 1) / 8]); wvalue = (wvalue >> ((idx - 1) % 8)) & mask; idx += window_size; booth_recode_w7(&sign2, &digit2, wvalue); wvalue = *((u16 *) & p_str[(idx - 1) / 8]); wvalue = (wvalue >> ((idx - 1) % 8)) & mask; idx += window_size; booth_recode_w7(&sign3, &digit3, wvalue); ecp_nistz256_avx2_multi_gather_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[(idx - 1) / 8]); wvalue = (wvalue >> ((idx - 1) % 8)) & mask; idx += window_size; booth_recode_w7(&sign0, &digit0, wvalue); wvalue = *((u16 *) & p_str[(idx - 1) / 8]); wvalue = (wvalue >> ((idx - 1) % 8)) & mask; idx += window_size; booth_recode_w7(&sign1, &digit1, wvalue); wvalue = *((u16 *) & p_str[(idx - 1) / 8]); wvalue = (wvalue >> ((idx - 1) % 8)) & mask; idx += window_size; booth_recode_w7(&sign2, &digit2, wvalue); wvalue = *((u16 *) & p_str[(idx - 1) / 8]); wvalue = (wvalue >> ((idx - 1) % 8)) & mask; idx += window_size; booth_recode_w7(&sign3, &digit3, wvalue); ecp_nistz256_avx2_multi_gather_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[(idx - 1) / 8]); wvalue = (wvalue >> ((idx - 1) % 8)) & mask; booth_recode_w7(&sign0, &digit0, wvalue); ecp_nistz256_gather_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 __owur static int ecp_nistz256_set_from_affine(EC_POINT *out, const EC_GROUP *group, const P256_POINT_AFFINE *in, BN_CTX *ctx) { int ret = 0; if ((ret = bn_set_words(out->X, in->X, P256_LIMBS)) && (ret = bn_set_words(out->Y, in->Y, P256_LIMBS)) && (ret = bn_set_words(out->Z, ONE, P256_LIMBS))) out->Z_is_one = 1; return ret; } /* r = scalar*G + sum(scalars[i]*points[i]) */ __owur 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; unsigned char p_str[33] = { 0 }; const PRECOMP256_ROW *preComputedTable = NULL; const NISTZ256_PRE_COMP *pre_comp = NULL; const EC_POINT *generator = NULL; const BIGNUM **new_scalars = NULL; const EC_POINT **new_points = NULL; unsigned int idx = 0; 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 ((num + 1) == 0 || (num + 1) > OPENSSL_MALLOC_MAX_NELEMS(void *)) { ECerr(EC_F_ECP_NISTZ256_POINTS_MUL, ERR_R_MALLOC_FAILURE); return 0; } 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 = group->pre_comp.nistz256; 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; ecp_nistz256_gather_w7(&p.a, pre_comp->precomp[0], 1); if (!ecp_nistz256_set_from_affine(pre_comp_generator, group, &p.a, 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 = 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 < bn_get_top(scalar) * BN_BYTES; i += BN_BYTES) { BN_ULONG d = bn_get_words(scalar)[i / BN_BYTES]; p_str[i + 0] = (unsigned char)d; p_str[i + 1] = (unsigned char)(d >> 8); p_str[i + 2] = (unsigned char)(d >> 16); p_str[i + 3] = (unsigned char)(d >>= 24); if (BN_BYTES == 8) { d >>= 8; p_str[i + 4] = (unsigned char)d; p_str[i + 5] = (unsigned char)(d >> 8); p_str[i + 6] = (unsigned char)(d >> 16); p_str[i + 7] = (unsigned char)(d >> 24); } } 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; idx += window_size; wvalue = _booth_recode_w7(wvalue); ecp_nistz256_gather_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 = (idx - 1) / 8; wvalue = p_str[off] | p_str[off + 1] << 8; wvalue = (wvalue >> ((idx - 1) % 8)) & mask; idx += window_size; wvalue = _booth_recode_w7(wvalue); ecp_nistz256_gather_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 == NULL) { 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 == NULL) { 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 (!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)) { goto err; } r->Z_is_one = is_one(r->Z) & 1; ret = 1; err: BN_CTX_end(ctx); OPENSSL_free(new_points); OPENSSL_free(new_scalars); return ret; } __owur 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 (!bn_set_words(x, x_ret, P256_LIMBS)) 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 (!bn_set_words(y, y_ret, P256_LIMBS)) return 0; } return 1; } static NISTZ256_PRE_COMP *ecp_nistz256_pre_comp_new(const EC_GROUP *group) { NISTZ256_PRE_COMP *ret = NULL; if (!group) return NULL; ret = OPENSSL_zalloc(sizeof(*ret)); if (ret == NULL) { ECerr(EC_F_ECP_NISTZ256_PRE_COMP_NEW, ERR_R_MALLOC_FAILURE); return ret; } ret->group = group; ret->w = 6; /* default */ ret->references = 1; ret->lock = CRYPTO_THREAD_lock_new(); if (ret->lock == NULL) { ECerr(EC_F_ECP_NISTZ256_PRE_COMP_NEW, ERR_R_MALLOC_FAILURE); OPENSSL_free(ret); return NULL; } return ret; } NISTZ256_PRE_COMP *EC_nistz256_pre_comp_dup(NISTZ256_PRE_COMP *p) { int i; if (p != NULL) CRYPTO_UP_REF(&p->references, &i, p->lock); return p; } void EC_nistz256_pre_comp_free(NISTZ256_PRE_COMP *pre) { int i; if (pre == NULL) return; CRYPTO_DOWN_REF(&pre->references, &i, pre->lock); REF_PRINT_COUNT("EC_nistz256", pre); if (i > 0) return; REF_ASSERT_ISNT(i < 0); OPENSSL_free(pre->precomp_storage); CRYPTO_THREAD_lock_free(pre->lock); 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 HAVEPRECOMP(group, nistz256); } #if defined(__x86_64) || defined(__x86_64__) || \ defined(_M_AMD64) || defined(_M_X64) || \ defined(__powerpc64__) || defined(_ARCH_PP64) || \ defined(__aarch64__) /* * Montgomery mul modulo Order(P): res = a*b*2^-256 mod Order(P) */ void ecp_nistz256_ord_mul_mont(BN_ULONG res[P256_LIMBS], const BN_ULONG a[P256_LIMBS], const BN_ULONG b[P256_LIMBS]); void ecp_nistz256_ord_sqr_mont(BN_ULONG res[P256_LIMBS], const BN_ULONG a[P256_LIMBS], BN_ULONG rep); static int ecp_nistz256_inv_mod_ord(const EC_GROUP *group, BIGNUM *r, const BIGNUM *x, BN_CTX *ctx) { /* RR = 2^512 mod ord(p256) */ static const BN_ULONG RR[P256_LIMBS] = { TOBN(0x83244c95,0xbe79eea2), TOBN(0x4699799c,0x49bd6fa6), TOBN(0x2845b239,0x2b6bec59), TOBN(0x66e12d94,0xf3d95620) }; /* The constant 1 (unlike ONE that is one in Montgomery representation) */ static const BN_ULONG one[P256_LIMBS] = { TOBN(0,1), TOBN(0,0), TOBN(0,0), TOBN(0,0) }; /* * We don't use entry 0 in the table, so we omit it and address * with -1 offset. */ BN_ULONG table[15][P256_LIMBS]; BN_ULONG out[P256_LIMBS], t[P256_LIMBS]; int i, ret = 0; enum { i_1 = 0, i_10, i_11, i_101, i_111, i_1010, i_1111, i_10101, i_101010, i_101111, i_x6, i_x8, i_x16, i_x32 }; /* * Catch allocation failure early. */ if (bn_wexpand(r, P256_LIMBS) == NULL) { ECerr(EC_F_ECP_NISTZ256_INV_MOD_ORD, ERR_R_BN_LIB); goto err; } if ((BN_num_bits(x) > 256) || BN_is_negative(x)) { BIGNUM *tmp; if ((tmp = BN_CTX_get(ctx)) == NULL || !BN_nnmod(tmp, x, group->order, ctx)) { ECerr(EC_F_ECP_NISTZ256_INV_MOD_ORD, ERR_R_BN_LIB); goto err; } x = tmp; } if (!ecp_nistz256_bignum_to_field_elem(t, x)) { ECerr(EC_F_ECP_NISTZ256_INV_MOD_ORD, EC_R_COORDINATES_OUT_OF_RANGE); goto err; } ecp_nistz256_ord_mul_mont(table[0], t, RR); #if 0 /* * Original sparse-then-fixed-window algorithm, retained for reference. */ for (i = 2; i < 16; i += 2) { ecp_nistz256_ord_sqr_mont(table[i-1], table[i/2-1], 1); ecp_nistz256_ord_mul_mont(table[i], table[i-1], table[0]); } /* * The top 128bit of the exponent are highly redudndant, so we * perform an optimized flow */ ecp_nistz256_ord_sqr_mont(t, table[15-1], 4); /* f0 */ ecp_nistz256_ord_mul_mont(t, t, table[15-1]); /* ff */ ecp_nistz256_ord_sqr_mont(out, t, 8); /* ff00 */ ecp_nistz256_ord_mul_mont(out, out, t); /* ffff */ ecp_nistz256_ord_sqr_mont(t, out, 16); /* ffff0000 */ ecp_nistz256_ord_mul_mont(t, t, out); /* ffffffff */ ecp_nistz256_ord_sqr_mont(out, t, 64); /* ffffffff0000000000000000 */ ecp_nistz256_ord_mul_mont(out, out, t); /* ffffffff00000000ffffffff */ ecp_nistz256_ord_sqr_mont(out, out, 32); /* ffffffff00000000ffffffff00000000 */ ecp_nistz256_ord_mul_mont(out, out, t); /* ffffffff00000000ffffffffffffffff */ /* * The bottom 128 bit of the exponent are processed with fixed 4-bit window */ for(i = 0; i < 32; i++) { /* expLo - the low 128 bits of the exponent we use (ord(p256) - 2), * split into nibbles */ static const unsigned char expLo[32] = { 0xb,0xc,0xe,0x6,0xf,0xa,0xa,0xd,0xa,0x7,0x1,0x7,0x9,0xe,0x8,0x4, 0xf,0x3,0xb,0x9,0xc,0xa,0xc,0x2,0xf,0xc,0x6,0x3,0x2,0x5,0x4,0xf }; ecp_nistz256_ord_sqr_mont(out, out, 4); /* The exponent is public, no need in constant-time access */ ecp_nistz256_ord_mul_mont(out, out, table[expLo[i]-1]); } #else /* * https://briansmith.org/ecc-inversion-addition-chains-01#p256_scalar_inversion * * Even though this code path spares 12 squarings, 4.5%, and 13 * multiplications, 25%, on grand scale sign operation is not that * much faster, not more that 2%... */ /* pre-calculate powers */ ecp_nistz256_ord_sqr_mont(table[i_10], table[i_1], 1); ecp_nistz256_ord_mul_mont(table[i_11], table[i_1], table[i_10]); ecp_nistz256_ord_mul_mont(table[i_101], table[i_11], table[i_10]); ecp_nistz256_ord_mul_mont(table[i_111], table[i_101], table[i_10]); ecp_nistz256_ord_sqr_mont(table[i_1010], table[i_101], 1); ecp_nistz256_ord_mul_mont(table[i_1111], table[i_1010], table[i_101]); ecp_nistz256_ord_sqr_mont(table[i_10101], table[i_1010], 1); ecp_nistz256_ord_mul_mont(table[i_10101], table[i_10101], table[i_1]); ecp_nistz256_ord_sqr_mont(table[i_101010], table[i_10101], 1); ecp_nistz256_ord_mul_mont(table[i_101111], table[i_101010], table[i_101]); ecp_nistz256_ord_mul_mont(table[i_x6], table[i_101010], table[i_10101]); ecp_nistz256_ord_sqr_mont(table[i_x8], table[i_x6], 2); ecp_nistz256_ord_mul_mont(table[i_x8], table[i_x8], table[i_11]); ecp_nistz256_ord_sqr_mont(table[i_x16], table[i_x8], 8); ecp_nistz256_ord_mul_mont(table[i_x16], table[i_x16], table[i_x8]); ecp_nistz256_ord_sqr_mont(table[i_x32], table[i_x16], 16); ecp_nistz256_ord_mul_mont(table[i_x32], table[i_x32], table[i_x16]); /* calculations */ ecp_nistz256_ord_sqr_mont(out, table[i_x32], 64); ecp_nistz256_ord_mul_mont(out, out, table[i_x32]); for (i = 0; i < 27; i++) { static const struct { unsigned char p, i; } chain[27] = { { 32, i_x32 }, { 6, i_101111 }, { 5, i_111 }, { 4, i_11 }, { 5, i_1111 }, { 5, i_10101 }, { 4, i_101 }, { 3, i_101 }, { 3, i_101 }, { 5, i_111 }, { 9, i_101111 }, { 6, i_1111 }, { 2, i_1 }, { 5, i_1 }, { 6, i_1111 }, { 5, i_111 }, { 4, i_111 }, { 5, i_111 }, { 5, i_101 }, { 3, i_11 }, { 10, i_101111 }, { 2, i_11 }, { 5, i_11 }, { 5, i_11 }, { 3, i_1 }, { 7, i_10101 }, { 6, i_1111 } }; ecp_nistz256_ord_sqr_mont(out, out, chain[i].p); ecp_nistz256_ord_mul_mont(out, out, table[chain[i].i]); } #endif ecp_nistz256_ord_mul_mont(out, out, one); /* * Can't fail, but check return code to be consistent anyway. */ if (!bn_set_words(r, out, P256_LIMBS)) goto err; ret = 1; err: return ret; } #else # define ecp_nistz256_inv_mod_ord NULL #endif 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_group_simple_order_bits, 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_inv, ec_GFp_mont_field_encode, ec_GFp_mont_field_decode, ec_GFp_mont_field_set_to_one, ec_key_simple_priv2oct, ec_key_simple_oct2priv, 0, /* set private */ ec_key_simple_generate_key, ec_key_simple_check_key, ec_key_simple_generate_public_key, 0, /* keycopy */ 0, /* keyfinish */ ecdh_simple_compute_key, ecdsa_simple_sign_setup, ecdsa_simple_sign_sig, ecdsa_simple_verify_sig, ecp_nistz256_inv_mod_ord, /* can be #define-d NULL */ 0, /* blind_coordinates */ 0, /* ladder_pre */ 0, /* ladder_step */ 0 /* ladder_post */ }; return &ret; }