X-Git-Url: https://git.openssl.org/gitweb/?p=openssl.git;a=blobdiff_plain;f=crypto%2Fec%2Fecp_nistz256.c;h=50b6d43b7c55d1c7467b5347dc2e5233732f182e;hp=579a3ad622b7efd1cf1dc82f68ff3ef552156ab7;hb=c2f2db9b6fb75ca2d672bb50f4f1f5a23991a6c3;hpb=2c52ac9bfefa813bfef864ff35e3d2afb8dbdae9 diff --git a/crypto/ec/ecp_nistz256.c b/crypto/ec/ecp_nistz256.c index 579a3ad622..50b6d43b7c 100644 --- a/crypto/ec/ecp_nistz256.c +++ b/crypto/ec/ecp_nistz256.c @@ -1,36 +1,35 @@ -/****************************************************************************** - * * - * 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" * - * * - ******************************************************************************/ +/* + * Copyright 2014-2020 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" + */ + +/* + * ECDSA low level APIs are deprecated for public use, but still ok for + * internal use. + */ +#include "internal/deprecated.h" #include #include "internal/cryptlib.h" -#include "internal/bn_int.h" -#include "ec_lcl.h" +#include "crypto/bn.h" +#include "ec_local.h" +#include "internal/refcount.h" #if BN_BITS2 != 64 # define TOBN(hi,lo) lo,hi @@ -75,23 +74,41 @@ struct nistz256_pre_comp_st { */ PRECOMP256_ROW *precomp; void *precomp_storage; - int references; + 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 div by 2: res = a/2 mod P */ -void ecp_nistz256_div_by_2(BN_ULONG res[P256_LIMBS], - const BN_ULONG a[P256_LIMBS]); /* Modular mul by 3: res = 3*a mod P */ void ecp_nistz256_mul_by_3(BN_ULONG res[P256_LIMBS], const BN_ULONG a[P256_LIMBS]); -/* Modular add: res = a+b mod P */ -void ecp_nistz256_add(BN_ULONG res[P256_LIMBS], - const BN_ULONG a[P256_LIMBS], - const BN_ULONG b[P256_LIMBS]); + +/* Modular 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], @@ -179,7 +196,6 @@ static BN_ULONG is_zero(BN_ULONG in) { in |= (0 - in); in = ~in; - in &= BN_MASK2; in >>= BN_BITS2 - 1; return in; } @@ -203,23 +219,41 @@ static BN_ULONG is_equal(const BN_ULONG a[P256_LIMBS], return is_zero(res); } -static BN_ULONG is_one(const BN_ULONG a[P256_LIMBS]) +static BN_ULONG is_one(const BIGNUM *z) { - BN_ULONG res; - - res = a[0] ^ ONE[0]; - res |= a[1] ^ ONE[1]; - res |= a[2] ^ ONE[2]; - res |= a[3] ^ ONE[3]; - if (P256_LIMBS == 8) { - res |= a[4] ^ ONE[4]; - res |= a[5] ^ ONE[5]; - res |= a[6] ^ ONE[6]; + 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 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, @@ -301,19 +335,16 @@ static void ecp_nistz256_point_add(P256_POINT *r, const BN_ULONG *in2_y = b->Y; const BN_ULONG *in2_z = b->Z; - /* We encode infinity as (0,0), which is not on the curve, - * so it is OK. */ - in1infty = (in1_x[0] | in1_x[1] | in1_x[2] | in1_x[3] | - in1_y[0] | in1_y[1] | in1_y[2] | in1_y[3]); + /* + * Infinity in encoded as (,,0) + */ + in1infty = (in1_z[0] | in1_z[1] | in1_z[2] | in1_z[3]); if (P256_LIMBS == 8) - in1infty |= (in1_x[4] | in1_x[5] | in1_x[6] | in1_x[7] | - in1_y[4] | in1_y[5] | in1_y[6] | in1_y[7]); + in1infty |= (in1_z[4] | in1_z[5] | in1_z[6] | in1_z[7]); - 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]); + in2infty = (in2_z[0] | in2_z[1] | in2_z[2] | in2_z[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]); + in2infty |= (in2_z[4] | in2_z[5] | in2_z[6] | in2_z[7]); in1infty = is_zero(in1infty); in2infty = is_zero(in2infty); @@ -333,16 +364,47 @@ static void ecp_nistz256_point_add(P256_POINT *r, ecp_nistz256_sub(H, U2, U1); /* H = U2 - U1 */ /* - * This should not happen during sign/ecdh, so no constant time violation + * 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) { - if (is_equal(S1, S2)) { - ecp_nistz256_point_double(r, a); - return; - } else { - memset(r, 0, sizeof(*r)); - return; - } + 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 */ @@ -402,15 +464,16 @@ static void ecp_nistz256_point_add_affine(P256_POINT *r, const BN_ULONG *in2_y = b->Y; /* - * In affine representation we encode infty as (0,0), which is not on the - * curve, so it is OK + * Infinity in encoded as (,,0) */ - in1infty = (in1_x[0] | in1_x[1] | in1_x[2] | in1_x[3] | - in1_y[0] | in1_y[1] | in1_y[2] | in1_y[3]); + in1infty = (in1_z[0] | in1_z[1] | in1_z[2] | in1_z[3]); if (P256_LIMBS == 8) - in1infty |= (in1_x[4] | in1_x[5] | in1_x[6] | in1_x[7] | - in1_y[4] | in1_y[5] | in1_y[6] | in1_y[7]); + 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) @@ -625,9 +688,9 @@ __owur static int ecp_nistz256_windowed_mul(const EC_GROUP *group, } /* - * 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. + * 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); @@ -725,12 +788,12 @@ __owur static int ecp_nistz256_windowed_mul(const EC_GROUP *group, } /* Coordinates of G, for which we have precomputed tables */ -const static BN_ULONG def_xG[P256_LIMBS] = { +static const 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] = { +static const BN_ULONG def_yG[P256_LIMBS] = { TOBN(0xddf25357, 0xce95560a), TOBN(0x8b4ab8e4, 0xba19e45c), TOBN(0xd2e88688, 0xdd21f325), TOBN(0x8571ff18, 0x25885d85) }; @@ -743,10 +806,9 @@ 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) && - (bn_get_top(generator->Z) == (P256_LIMBS - P256_LIMBS / 8)) && is_equal(bn_get_words(generator->X), def_xG) && is_equal(bn_get_words(generator->Y), def_yG) && - is_one(bn_get_words(generator->Z)); + is_one(generator->Z); } __owur static int ecp_nistz256_mult_precompute(EC_GROUP *group, BN_CTX *ctx) @@ -757,7 +819,7 @@ __owur static int ecp_nistz256_mult_precompute(EC_GROUP *group, BN_CTX *ctx) * implicit value of infinity at index zero. We use window of size 7, and * therefore require ceil(256/7) = 37 tables. */ - BIGNUM *order; + const BIGNUM *order; EC_POINT *P = NULL, *T = NULL; const EC_POINT *generator; NISTZ256_PRE_COMP *pre_comp; @@ -788,20 +850,17 @@ __owur static int ecp_nistz256_mult_precompute(EC_GROUP *group, BN_CTX *ctx) return 0; if (ctx == NULL) { - ctx = new_ctx = BN_CTX_new(); + ctx = new_ctx = BN_CTX_new_ex(group->libctx); if (ctx == NULL) goto err; } BN_CTX_start(ctx); - order = BN_CTX_get(ctx); + order = EC_GROUP_get0_order(group); 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; @@ -838,7 +897,8 @@ __owur static int ecp_nistz256_mult_precompute(EC_GROUP *group, BN_CTX *ctx) * 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)) + if (group->meth->make_affine == NULL + || !group->meth->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)) { @@ -866,8 +926,7 @@ __owur static int ecp_nistz256_mult_precompute(EC_GROUP *group, BN_CTX *ctx) ret = 1; err: - if (ctx != NULL) - BN_CTX_end(ctx); + BN_CTX_end(ctx); BN_CTX_free(new_ctx); EC_nistz256_pre_comp_free(pre_comp); @@ -888,7 +947,7 @@ __owur static int ecp_nistz256_mult_precompute(EC_GROUP *group, BN_CTX *ctx) */ #if defined(ECP_NISTZ256_AVX2) # if !(defined(__x86_64) || defined(__x86_64__) || \ - defined(_M_AMD64) || defined(_MX64)) || \ + defined(_M_AMD64) || defined(_M_X64)) || \ !(defined(__GNUC__) || defined(_MSC_VER)) /* this is for ALIGN32 */ # undef ECP_NISTZ256_AVX2 # else @@ -1082,28 +1141,12 @@ __owur static int ecp_nistz256_set_from_affine(EC_POINT *out, const EC_GROUP *gr const P256_POINT_AFFINE *in, BN_CTX *ctx) { - BIGNUM *x, *y; - BN_ULONG d_x[P256_LIMBS], d_y[P256_LIMBS]; int ret = 0; - x = BN_new(); - if (x == NULL) - return 0; - y = BN_new(); - if (y == NULL) { - BN_free(x); - return 0; - } - memcpy(d_x, in->X, sizeof(d_x)); - bn_set_static_words(x, d_x, P256_LIMBS); - - memcpy(d_y, in->Y, sizeof(d_y)); - bn_set_static_words(y, d_y, P256_LIMBS); - - ret = EC_POINT_set_affine_coordinates_GFp(group, out, x, y, ctx); - - BN_free(x); - BN_free(y); + 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; } @@ -1117,12 +1160,10 @@ __owur static int ecp_nistz256_points_mul(const EC_GROUP *group, 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 NISTZ256_PRE_COMP *pre_comp = NULL; const EC_POINT *generator = NULL; - BN_CTX *new_ctx = NULL; const BIGNUM **new_scalars = NULL; const EC_POINT **new_points = NULL; unsigned int idx = 0; @@ -1140,27 +1181,6 @@ __owur static int ecp_nistz256_points_mul(const EC_GROUP *group, return 0; } - 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) { @@ -1182,9 +1202,9 @@ __owur static int ecp_nistz256_points_mul(const EC_GROUP *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, pre_comp->precomp[0], - ctx)) { + group, &p.a, ctx)) { EC_POINT_free(pre_comp_generator); goto err; } @@ -1243,6 +1263,8 @@ __owur static int ecp_nistz256_points_mul(const EC_GROUP *group, } else #endif { + BN_ULONG infty; + /* First window */ wvalue = (p_str[0] << 1) & mask; idx += window_size; @@ -1255,7 +1277,30 @@ __owur static int ecp_nistz256_points_mul(const EC_GROUP *group, ecp_nistz256_neg(p.p.Z, p.p.Y); copy_conditional(p.p.Y, p.p.Z, wvalue & 1); - memcpy(p.p.Z, ONE, sizeof(ONE)); + /* + * 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; @@ -1326,14 +1371,12 @@ __owur static int ecp_nistz256_points_mul(const EC_GROUP *group, !bn_set_words(r->Z, p.p.Z, P256_LIMBS)) { goto err; } - r->Z_is_one = is_one(p.p.Z) & 1; + r->Z_is_one = is_one(r->Z) & 1; ret = 1; err: - if (ctx) - BN_CTX_end(ctx); - BN_CTX_free(new_ctx); + BN_CTX_end(ctx); OPENSSL_free(new_points); OPENSSL_free(new_scalars); return ret; @@ -1399,25 +1442,40 @@ static NISTZ256_PRE_COMP *ecp_nistz256_pre_comp_new(const EC_GROUP *group) ret->group = group; ret->w = 6; /* default */ - ret->precomp = NULL; - ret->precomp_storage = NULL; 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_add(&p->references, 1, CRYPTO_LOCK_EC_PRE_COMP); + CRYPTO_UP_REF(&p->references, &i, p->lock); return p; } void EC_nistz256_pre_comp_free(NISTZ256_PRE_COMP *pre) { - if (pre == NULL - || CRYPTO_add(&pre->references, -1, CRYPTO_LOCK_EC_PRE_COMP) > 0) + 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); } @@ -1435,6 +1493,189 @@ static int ecp_nistz256_window_have_precompute_mult(const EC_GROUP *group) 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 = { @@ -1447,14 +1688,13 @@ const EC_METHOD *EC_GFp_nistz256_method(void) 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, @@ -1472,9 +1712,27 @@ const EC_METHOD *EC_GFp_nistz256_method(void) 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_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;