/*
- * Copyright 2014-2017 The OpenSSL Project Authors. All Rights Reserved.
+ * 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 OpenSSL license (the "License"). You may not use
+ * 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)
+ * 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 <string.h>
#include "internal/cryptlib.h"
-#include "internal/bn_int.h"
-#include "ec_lcl.h"
-#include "e_os.h"
+#include "crypto/bn.h"
+#include "ec_local.h"
+#include "internal/refcount.h"
#if BN_BITS2 != 64
# define TOBN(hi,lo) lo,hi
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 */
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;
}
* 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)) {
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);
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_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)
{
- 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;
}
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;
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) {
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;
}
}
if (preComputedTable) {
+ BN_ULONG infty;
+
if ((BN_num_bits(scalar) > 256)
|| BN_is_negative(scalar)) {
if ((tmp_scalar = BN_CTX_get(ctx)) == NULL)
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;
- /* First window */
- wvalue = (p_str[0] << 1) & mask;
- idx += window_size;
+ wvalue = _booth_recode_w7(wvalue);
- wvalue = _booth_recode_w7(wvalue);
+ ecp_nistz256_gather_w7(&p.a, preComputedTable[0],
+ wvalue >> 1);
- 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;
- }
+ ecp_nistz256_neg(p.p.Z, p.p.Y);
+ copy_conditional(p.p.Y, p.p.Z, wvalue & 1);
- 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;
+ /*
+ * Since affine infinity is encoded as (0,0) and
+ * Jacobian is (,,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);
+ wvalue = _booth_recode_w7(wvalue);
- ecp_nistz256_gather_w7(&t.a,
- preComputedTable[i], wvalue >> 1);
+ 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_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);
- }
+ ecp_nistz256_point_add_affine(&p.p, &p.p, &t.a);
}
} else {
p_is_infinity = 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;
return;
CRYPTO_DOWN_REF(&pre->references, &i, pre->lock);
- REF_PRINT_COUNT("EC_nistz256", x);
+ REF_PRINT_COUNT("EC_nistz256", pre);
if (i > 0)
return;
REF_ASSERT_ISNT(i < 0);
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_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_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_generate_public_key,
0, /* keycopy */
0, /* keyfinish */
- ecdh_simple_compute_key
+ 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;