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ecp_nistz256.c
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ecp_nistz256.c
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/*
* Copyright 2014-2016 The OpenSSL Project Authors. All Rights Reserved.
*
* Licensed under the OpenSSL license (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
*/
/******************************************************************************
* *
* Copyright 2014 Intel Corporation *
* *
* Licensed under the Apache License, Version 2.0 (the "License"); *
* you may not use this file except in compliance with the License. *
* You may obtain a copy of the License at *
* *
* http://www.apache.org/licenses/LICENSE-2.0 *
* *
* Unless required by applicable law or agreed to in writing, software *
* distributed under the License is distributed on an "AS IS" BASIS, *
* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. *
* See the License for the specific language governing permissions and *
* limitations under the License. *
* *
******************************************************************************
* *
* Developers and authors: *
* Shay Gueron (1, 2), and Vlad Krasnov (1) *
* (1) Intel Corporation, Israel Development Center *
* (2) University of Haifa *
* Reference: *
* S.Gueron and V.Krasnov, "Fast Prime Field Elliptic Curve Cryptography with *
* 256 Bit Primes" *
* *
******************************************************************************/
#include <string.h>
#include "internal/cryptlib.h"
#include "internal/bn_int.h"
#include "ec_lcl.h"
#if BN_BITS2 != 64
# define TOBN(hi,lo) lo,hi
#else
# define TOBN(hi,lo) ((BN_ULONG)hi<<32|lo)
#endif
#if defined(__GNUC__)
# define ALIGN32 __attribute((aligned(32)))
#elif defined(_MSC_VER)
# define ALIGN32 __declspec(align(32))
#else
# define ALIGN32
#endif
#define ALIGNPTR(p,N) ((unsigned char *)p+N-(size_t)p%N)
#define P256_LIMBS (256/BN_BITS2)
typedef unsigned short u16;
typedef struct {
BN_ULONG X[P256_LIMBS];
BN_ULONG Y[P256_LIMBS];
BN_ULONG Z[P256_LIMBS];
} P256_POINT;
typedef struct {
BN_ULONG X[P256_LIMBS];
BN_ULONG Y[P256_LIMBS];
} P256_POINT_AFFINE;
typedef P256_POINT_AFFINE PRECOMP256_ROW[64];
/* structure for precomputed multiples of the generator */
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;
int references;
CRYPTO_RWLOCK *lock;
};
/* Functions implemented in assembly */
/* 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 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 BN_ULONG a[P256_LIMBS])
{
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];
}
return is_zero(res);
}
#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;
/* 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]);
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]);
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(Z2sqr, in2_z); /* Z2^2 */
ecp_nistz256_sqr_mont(Z1sqr, in1_z); /* Z1^2 */
ecp_nistz256_mul_mont(S1, Z2sqr, in2_z); /* S1 = Z2^3 */
ecp_nistz256_mul_mont(S2, Z1sqr, in1_z); /* S2 = Z1^3 */
ecp_nistz256_mul_mont(S1, S1, in1_y); /* S1 = Y1*Z2^3 */
ecp_nistz256_mul_mont(S2, S2, in2_y); /* S2 = Y2*Z1^3 */
ecp_nistz256_sub(R, S2, S1); /* R = S2 - S1 */
ecp_nistz256_mul_mont(U1, in1_x, Z2sqr); /* U1 = X1*Z2^2 */
ecp_nistz256_mul_mont(U2, in2_x, Z1sqr); /* U2 = X2*Z1^2 */
ecp_nistz256_sub(H, U2, U1); /* H = U2 - U1 */
/*
* This should not happen during sign/ecdh, so no constant time violation
*/
if (is_equal(U1, U2) && !in1infty && !in2infty) {
if (is_equal(S1, S2)) {
ecp_nistz256_point_double(r, a);
return;
} else {
memset(r, 0, sizeof(*r));
return;
}
}
ecp_nistz256_sqr_mont(Rsqr, R); /* R^2 */
ecp_nistz256_mul_mont(res_z, H, in1_z); /* Z3 = H*Z1*Z2 */
ecp_nistz256_sqr_mont(Hsqr, H); /* H^2 */
ecp_nistz256_mul_mont(res_z, res_z, in2_z); /* Z3 = H*Z1*Z2 */
ecp_nistz256_mul_mont(Hcub, Hsqr, H); /* H^3 */
ecp_nistz256_mul_mont(U2, U1, Hsqr); /* U1*H^2 */
ecp_nistz256_mul_by_2(Hsqr, U2); /* 2*U1*H^2 */
ecp_nistz256_sub(res_x, Rsqr, Hsqr);
ecp_nistz256_sub(res_x, res_x, Hcub);
ecp_nistz256_sub(res_y, U2, res_x);
ecp_nistz256_mul_mont(S2, S1, Hcub);
ecp_nistz256_mul_mont(res_y, R, res_y);
ecp_nistz256_sub(res_y, res_y, S2);
copy_conditional(res_x, in2_x, in1infty);
copy_conditional(res_y, in2_y, in1infty);
copy_conditional(res_z, in2_z, in1infty);
copy_conditional(res_x, in1_x, in2infty);
copy_conditional(res_y, in1_y, in2infty);
copy_conditional(res_z, in1_z, in2infty);
memcpy(r->X, res_x, sizeof(res_x));
memcpy(r->Y, res_y, sizeof(res_y));
memcpy(r->Z, res_z, sizeof(res_z));
}
/* Point addition when b is known to be affine: r = a+b */
static void ecp_nistz256_point_add_affine(P256_POINT *r,
const P256_POINT *a,
const P256_POINT_AFFINE *b)
{
BN_ULONG U2[P256_LIMBS], S2[P256_LIMBS];
BN_ULONG Z1sqr[P256_LIMBS];
BN_ULONG H[P256_LIMBS], R[P256_LIMBS];
BN_ULONG Hsqr[P256_LIMBS];
BN_ULONG Rsqr[P256_LIMBS];
BN_ULONG Hcub[P256_LIMBS];
BN_ULONG res_x[P256_LIMBS];
BN_ULONG res_y[P256_LIMBS];
BN_ULONG res_z[P256_LIMBS];
BN_ULONG in1infty, in2infty;
const BN_ULONG *in1_x = a->X;
const BN_ULONG *in1_y = a->Y;
const BN_ULONG *in1_z = a->Z;
const BN_ULONG *in2_x = b->X;
const BN_ULONG *in2_y = b->Y;
/*
* In affine representation we encode infty 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]);
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]);
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 */
const static BN_ULONG def_xG[P256_LIMBS] = {
TOBN(0x79e730d4, 0x18a9143c), TOBN(0x75ba95fc, 0x5fedb601),
TOBN(0x79fb732b, 0x77622510), TOBN(0x18905f76, 0xa53755c6)
};
const static BN_ULONG def_yG[P256_LIMBS] = {
TOBN(0xddf25357, 0xce95560a), TOBN(0x8b4ab8e4, 0xba19e45c),
TOBN(0xd2e88688, 0xdd21f325), TOBN(0x8571ff18, 0x25885d85)
};
/*
* ecp_nistz256_is_affine_G returns one if |generator| is the standard, P-256
* generator.
*/
static int ecp_nistz256_is_affine_G(const EC_POINT *generator)
{
return (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));
}
__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();
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:
if (ctx != NULL)
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(_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;