1569 lines
52 KiB
C
1569 lines
52 KiB
C
/******************************************************************************
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* *
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* Copyright 2014 Intel Corporation *
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* *
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* Licensed under the Apache License, Version 2.0 (the "License"); *
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* you may not use this file except in compliance with the License. *
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* You may obtain a copy of the License at *
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* *
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* http://www.apache.org/licenses/LICENSE-2.0 *
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* *
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* Unless required by applicable law or agreed to in writing, software *
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* distributed under the License is distributed on an "AS IS" BASIS, *
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* WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. *
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* See the License for the specific language governing permissions and *
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* limitations under the License. *
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* *
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******************************************************************************
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* *
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* Developers and authors: *
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* Shay Gueron (1, 2), and Vlad Krasnov (1) *
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* (1) Intel Corporation, Israel Development Center *
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* (2) University of Haifa *
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* Reference: *
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* S.Gueron and V.Krasnov, "Fast Prime Field Elliptic Curve Cryptography with *
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* 256 Bit Primes" *
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* *
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******************************************************************************/
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#include <string.h>
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#include <openssl/bn.h>
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#include <openssl/err.h>
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#include <openssl/ec.h>
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#include "cryptlib.h"
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#include "ec_lcl.h"
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#if BN_BITS2 != 64
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# define TOBN(hi,lo) lo,hi
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#else
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# define TOBN(hi,lo) ((BN_ULONG)hi<<32|lo)
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#endif
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#if defined(__GNUC__)
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# define ALIGN32 __attribute((aligned(32)))
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#elif defined(_MSC_VER)
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# define ALIGN32 __declspec(align(32))
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#else
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# define ALIGN32
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#endif
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#define ALIGNPTR(p,N) ((unsigned char *)p+N-(size_t)p%N)
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#define P256_LIMBS (256/BN_BITS2)
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typedef unsigned short u16;
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typedef struct {
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BN_ULONG X[P256_LIMBS];
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BN_ULONG Y[P256_LIMBS];
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BN_ULONG Z[P256_LIMBS];
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} P256_POINT;
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typedef struct {
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BN_ULONG X[P256_LIMBS];
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BN_ULONG Y[P256_LIMBS];
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} P256_POINT_AFFINE;
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typedef P256_POINT_AFFINE PRECOMP256_ROW[64];
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/* structure for precomputed multiples of the generator */
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typedef struct ec_pre_comp_st {
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const EC_GROUP *group; /* Parent EC_GROUP object */
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size_t w; /* Window size */
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/*
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* Constant time access to the X and Y coordinates of the pre-computed,
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* generator multiplies, in the Montgomery domain. Pre-calculated
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* multiplies are stored in affine form.
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*/
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PRECOMP256_ROW *precomp;
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void *precomp_storage;
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int references;
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} EC_PRE_COMP;
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/* Functions implemented in assembly */
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/*
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* Most of below mentioned functions *preserve* the property of inputs
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* being fully reduced, i.e. being in [0, modulus) range. Simply put if
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* inputs are fully reduced, then output is too. Note that reverse is
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* not true, in sense that given partially reduced inputs output can be
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* either, not unlikely reduced. And "most" in first sentence refers to
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* the fact that given the calculations flow one can tolerate that
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* addition, 1st function below, produces partially reduced result *if*
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* multiplications by 2 and 3, which customarily use addition, fully
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* reduce it. This effectively gives two options: a) addition produces
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* fully reduced result [as long as inputs are, just like remaining
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* functions]; b) addition is allowed to produce partially reduced
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* result, but multiplications by 2 and 3 perform additional reduction
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* step. Choice between the two can be platform-specific, but it was a)
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* in all cases so far...
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*/
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/* Modular add: res = a+b mod P */
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void ecp_nistz256_add(BN_ULONG res[P256_LIMBS],
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const BN_ULONG a[P256_LIMBS],
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const BN_ULONG b[P256_LIMBS]);
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/* Modular mul by 2: res = 2*a mod P */
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void ecp_nistz256_mul_by_2(BN_ULONG res[P256_LIMBS],
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const BN_ULONG a[P256_LIMBS]);
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/* Modular mul by 3: res = 3*a mod P */
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void ecp_nistz256_mul_by_3(BN_ULONG res[P256_LIMBS],
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const BN_ULONG a[P256_LIMBS]);
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/* Modular div by 2: res = a/2 mod P */
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void ecp_nistz256_div_by_2(BN_ULONG res[P256_LIMBS],
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const BN_ULONG a[P256_LIMBS]);
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/* Modular sub: res = a-b mod P */
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void ecp_nistz256_sub(BN_ULONG res[P256_LIMBS],
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const BN_ULONG a[P256_LIMBS],
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const BN_ULONG b[P256_LIMBS]);
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/* Modular neg: res = -a mod P */
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void ecp_nistz256_neg(BN_ULONG res[P256_LIMBS], const BN_ULONG a[P256_LIMBS]);
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/* Montgomery mul: res = a*b*2^-256 mod P */
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void ecp_nistz256_mul_mont(BN_ULONG res[P256_LIMBS],
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const BN_ULONG a[P256_LIMBS],
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const BN_ULONG b[P256_LIMBS]);
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/* Montgomery sqr: res = a*a*2^-256 mod P */
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void ecp_nistz256_sqr_mont(BN_ULONG res[P256_LIMBS],
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const BN_ULONG a[P256_LIMBS]);
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/* Convert a number from Montgomery domain, by multiplying with 1 */
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void ecp_nistz256_from_mont(BN_ULONG res[P256_LIMBS],
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const BN_ULONG in[P256_LIMBS]);
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/* Convert a number to Montgomery domain, by multiplying with 2^512 mod P*/
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void ecp_nistz256_to_mont(BN_ULONG res[P256_LIMBS],
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const BN_ULONG in[P256_LIMBS]);
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/* Functions that perform constant time access to the precomputed tables */
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void ecp_nistz256_select_w5(P256_POINT * val,
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const P256_POINT * in_t, int index);
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void ecp_nistz256_select_w7(P256_POINT_AFFINE * val,
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const P256_POINT_AFFINE * in_t, int index);
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/* One converted into the Montgomery domain */
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static const BN_ULONG ONE[P256_LIMBS] = {
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TOBN(0x00000000, 0x00000001), TOBN(0xffffffff, 0x00000000),
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TOBN(0xffffffff, 0xffffffff), TOBN(0x00000000, 0xfffffffe)
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};
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static void *ecp_nistz256_pre_comp_dup(void *);
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static void ecp_nistz256_pre_comp_free(void *);
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static void ecp_nistz256_pre_comp_clear_free(void *);
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static EC_PRE_COMP *ecp_nistz256_pre_comp_new(const EC_GROUP *group);
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/* Precomputed tables for the default generator */
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#include "ecp_nistz256_table.c"
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/* Recode window to a signed digit, see ecp_nistputil.c for details */
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static unsigned int _booth_recode_w5(unsigned int in)
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{
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unsigned int s, d;
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s = ~((in >> 5) - 1);
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d = (1 << 6) - in - 1;
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d = (d & s) | (in & ~s);
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d = (d >> 1) + (d & 1);
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return (d << 1) + (s & 1);
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}
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static unsigned int _booth_recode_w7(unsigned int in)
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{
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unsigned int s, d;
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s = ~((in >> 7) - 1);
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d = (1 << 8) - in - 1;
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d = (d & s) | (in & ~s);
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d = (d >> 1) + (d & 1);
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return (d << 1) + (s & 1);
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}
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static void copy_conditional(BN_ULONG dst[P256_LIMBS],
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const BN_ULONG src[P256_LIMBS], BN_ULONG move)
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{
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BN_ULONG mask1 = -move;
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BN_ULONG mask2 = ~mask1;
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dst[0] = (src[0] & mask1) ^ (dst[0] & mask2);
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dst[1] = (src[1] & mask1) ^ (dst[1] & mask2);
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dst[2] = (src[2] & mask1) ^ (dst[2] & mask2);
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dst[3] = (src[3] & mask1) ^ (dst[3] & mask2);
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if (P256_LIMBS == 8) {
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dst[4] = (src[4] & mask1) ^ (dst[4] & mask2);
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dst[5] = (src[5] & mask1) ^ (dst[5] & mask2);
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dst[6] = (src[6] & mask1) ^ (dst[6] & mask2);
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dst[7] = (src[7] & mask1) ^ (dst[7] & mask2);
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}
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}
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static BN_ULONG is_zero(BN_ULONG in)
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{
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in |= (0 - in);
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in = ~in;
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in &= BN_MASK2;
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in >>= BN_BITS2 - 1;
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return in;
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}
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static BN_ULONG is_equal(const BN_ULONG a[P256_LIMBS],
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const BN_ULONG b[P256_LIMBS])
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{
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BN_ULONG res;
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res = a[0] ^ b[0];
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res |= a[1] ^ b[1];
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res |= a[2] ^ b[2];
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res |= a[3] ^ b[3];
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if (P256_LIMBS == 8) {
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res |= a[4] ^ b[4];
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res |= a[5] ^ b[5];
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res |= a[6] ^ b[6];
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res |= a[7] ^ b[7];
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}
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return is_zero(res);
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}
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static BN_ULONG is_one(const BIGNUM *z)
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{
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BN_ULONG res = 0;
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BN_ULONG *a = z->d;
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if (z->top == (P256_LIMBS - P256_LIMBS / 8)) {
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res = a[0] ^ ONE[0];
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res |= a[1] ^ ONE[1];
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res |= a[2] ^ ONE[2];
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res |= a[3] ^ ONE[3];
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if (P256_LIMBS == 8) {
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res |= a[4] ^ ONE[4];
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res |= a[5] ^ ONE[5];
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res |= a[6] ^ ONE[6];
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/*
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* no check for a[7] (being zero) on 32-bit platforms,
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* because value of "one" takes only 7 limbs.
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*/
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}
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res = is_zero(res);
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}
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return res;
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}
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static int ecp_nistz256_set_words(BIGNUM *a, BN_ULONG words[P256_LIMBS])
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{
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if (bn_wexpand(a, P256_LIMBS) == NULL) {
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ECerr(EC_F_ECP_NISTZ256_SET_WORDS, ERR_R_MALLOC_FAILURE);
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return 0;
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}
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memcpy(a->d, words, sizeof(BN_ULONG) * P256_LIMBS);
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a->top = P256_LIMBS;
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bn_correct_top(a);
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return 1;
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}
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#ifndef ECP_NISTZ256_REFERENCE_IMPLEMENTATION
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void ecp_nistz256_point_double(P256_POINT *r, const P256_POINT *a);
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void ecp_nistz256_point_add(P256_POINT *r,
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const P256_POINT *a, const P256_POINT *b);
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void ecp_nistz256_point_add_affine(P256_POINT *r,
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const P256_POINT *a,
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const P256_POINT_AFFINE *b);
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#else
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/* Point double: r = 2*a */
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static void ecp_nistz256_point_double(P256_POINT *r, const P256_POINT *a)
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{
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BN_ULONG S[P256_LIMBS];
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BN_ULONG M[P256_LIMBS];
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BN_ULONG Zsqr[P256_LIMBS];
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BN_ULONG tmp0[P256_LIMBS];
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const BN_ULONG *in_x = a->X;
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const BN_ULONG *in_y = a->Y;
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const BN_ULONG *in_z = a->Z;
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BN_ULONG *res_x = r->X;
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BN_ULONG *res_y = r->Y;
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BN_ULONG *res_z = r->Z;
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ecp_nistz256_mul_by_2(S, in_y);
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ecp_nistz256_sqr_mont(Zsqr, in_z);
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ecp_nistz256_sqr_mont(S, S);
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ecp_nistz256_mul_mont(res_z, in_z, in_y);
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ecp_nistz256_mul_by_2(res_z, res_z);
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ecp_nistz256_add(M, in_x, Zsqr);
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ecp_nistz256_sub(Zsqr, in_x, Zsqr);
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ecp_nistz256_sqr_mont(res_y, S);
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ecp_nistz256_div_by_2(res_y, res_y);
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ecp_nistz256_mul_mont(M, M, Zsqr);
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ecp_nistz256_mul_by_3(M, M);
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ecp_nistz256_mul_mont(S, S, in_x);
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ecp_nistz256_mul_by_2(tmp0, S);
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ecp_nistz256_sqr_mont(res_x, M);
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ecp_nistz256_sub(res_x, res_x, tmp0);
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ecp_nistz256_sub(S, S, res_x);
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ecp_nistz256_mul_mont(S, S, M);
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ecp_nistz256_sub(res_y, S, res_y);
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}
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/* Point addition: r = a+b */
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static void ecp_nistz256_point_add(P256_POINT *r,
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const P256_POINT *a, const P256_POINT *b)
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{
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BN_ULONG U2[P256_LIMBS], S2[P256_LIMBS];
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BN_ULONG U1[P256_LIMBS], S1[P256_LIMBS];
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BN_ULONG Z1sqr[P256_LIMBS];
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BN_ULONG Z2sqr[P256_LIMBS];
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BN_ULONG H[P256_LIMBS], R[P256_LIMBS];
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BN_ULONG Hsqr[P256_LIMBS];
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BN_ULONG Rsqr[P256_LIMBS];
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BN_ULONG Hcub[P256_LIMBS];
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BN_ULONG res_x[P256_LIMBS];
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BN_ULONG res_y[P256_LIMBS];
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BN_ULONG res_z[P256_LIMBS];
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BN_ULONG in1infty, in2infty;
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const BN_ULONG *in1_x = a->X;
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const BN_ULONG *in1_y = a->Y;
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const BN_ULONG *in1_z = a->Z;
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const BN_ULONG *in2_x = b->X;
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const BN_ULONG *in2_y = b->Y;
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const BN_ULONG *in2_z = b->Z;
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/*
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* Infinity in encoded as (,,0)
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*/
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in1infty = (in1_z[0] | in1_z[1] | in1_z[2] | in1_z[3]);
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if (P256_LIMBS == 8)
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in1infty |= (in1_z[4] | in1_z[5] | in1_z[6] | in1_z[7]);
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in2infty = (in2_z[0] | in2_z[1] | in2_z[2] | in2_z[3]);
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if (P256_LIMBS == 8)
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in2infty |= (in2_z[4] | in2_z[5] | in2_z[6] | in2_z[7]);
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in1infty = is_zero(in1infty);
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in2infty = is_zero(in2infty);
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ecp_nistz256_sqr_mont(Z2sqr, in2_z); /* Z2^2 */
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ecp_nistz256_sqr_mont(Z1sqr, in1_z); /* Z1^2 */
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ecp_nistz256_mul_mont(S1, Z2sqr, in2_z); /* S1 = Z2^3 */
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ecp_nistz256_mul_mont(S2, Z1sqr, in1_z); /* S2 = Z1^3 */
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ecp_nistz256_mul_mont(S1, S1, in1_y); /* S1 = Y1*Z2^3 */
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ecp_nistz256_mul_mont(S2, S2, in2_y); /* S2 = Y2*Z1^3 */
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ecp_nistz256_sub(R, S2, S1); /* R = S2 - S1 */
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ecp_nistz256_mul_mont(U1, in1_x, Z2sqr); /* U1 = X1*Z2^2 */
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ecp_nistz256_mul_mont(U2, in2_x, Z1sqr); /* U2 = X2*Z1^2 */
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ecp_nistz256_sub(H, U2, U1); /* H = U2 - U1 */
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/*
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* This should not happen during sign/ecdh, so no constant time violation
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*/
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if (is_equal(U1, U2) && !in1infty && !in2infty) {
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if (is_equal(S1, S2)) {
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ecp_nistz256_point_double(r, a);
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return;
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} else {
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memset(r, 0, sizeof(*r));
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return;
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}
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}
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ecp_nistz256_sqr_mont(Rsqr, R); /* R^2 */
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ecp_nistz256_mul_mont(res_z, H, in1_z); /* Z3 = H*Z1*Z2 */
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ecp_nistz256_sqr_mont(Hsqr, H); /* H^2 */
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ecp_nistz256_mul_mont(res_z, res_z, in2_z); /* Z3 = H*Z1*Z2 */
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ecp_nistz256_mul_mont(Hcub, Hsqr, H); /* H^3 */
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ecp_nistz256_mul_mont(U2, U1, Hsqr); /* U1*H^2 */
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ecp_nistz256_mul_by_2(Hsqr, U2); /* 2*U1*H^2 */
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ecp_nistz256_sub(res_x, Rsqr, Hsqr);
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ecp_nistz256_sub(res_x, res_x, Hcub);
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ecp_nistz256_sub(res_y, U2, res_x);
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ecp_nistz256_mul_mont(S2, S1, Hcub);
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ecp_nistz256_mul_mont(res_y, R, res_y);
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ecp_nistz256_sub(res_y, res_y, S2);
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copy_conditional(res_x, in2_x, in1infty);
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copy_conditional(res_y, in2_y, in1infty);
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copy_conditional(res_z, in2_z, in1infty);
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copy_conditional(res_x, in1_x, in2infty);
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copy_conditional(res_y, in1_y, in2infty);
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copy_conditional(res_z, in1_z, in2infty);
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memcpy(r->X, res_x, sizeof(res_x));
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memcpy(r->Y, res_y, sizeof(res_y));
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memcpy(r->Z, res_z, sizeof(res_z));
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}
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/* Point addition when b is known to be affine: r = a+b */
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static void ecp_nistz256_point_add_affine(P256_POINT *r,
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const P256_POINT *a,
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const P256_POINT_AFFINE *b)
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{
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BN_ULONG U2[P256_LIMBS], S2[P256_LIMBS];
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BN_ULONG Z1sqr[P256_LIMBS];
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BN_ULONG H[P256_LIMBS], R[P256_LIMBS];
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BN_ULONG Hsqr[P256_LIMBS];
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BN_ULONG Rsqr[P256_LIMBS];
|
|
BN_ULONG Hcub[P256_LIMBS];
|
|
|
|
BN_ULONG res_x[P256_LIMBS];
|
|
BN_ULONG res_y[P256_LIMBS];
|
|
BN_ULONG res_z[P256_LIMBS];
|
|
|
|
BN_ULONG in1infty, in2infty;
|
|
|
|
const BN_ULONG *in1_x = a->X;
|
|
const BN_ULONG *in1_y = a->Y;
|
|
const BN_ULONG *in1_z = a->Z;
|
|
|
|
const BN_ULONG *in2_x = b->X;
|
|
const BN_ULONG *in2_y = b->Y;
|
|
|
|
/*
|
|
* Infinity in encoded as (,,0)
|
|
*/
|
|
in1infty = (in1_z[0] | in1_z[1] | in1_z[2] | in1_z[3]);
|
|
if (P256_LIMBS == 8)
|
|
in1infty |= (in1_z[4] | in1_z[5] | in1_z[6] | in1_z[7]);
|
|
|
|
/*
|
|
* In affine representation we encode infinity as (0,0), which is
|
|
* not on the curve, so it is OK
|
|
*/
|
|
in2infty = (in2_x[0] | in2_x[1] | in2_x[2] | in2_x[3] |
|
|
in2_y[0] | in2_y[1] | in2_y[2] | in2_y[3]);
|
|
if (P256_LIMBS == 8)
|
|
in2infty |= (in2_x[4] | in2_x[5] | in2_x[6] | in2_x[7] |
|
|
in2_y[4] | in2_y[5] | in2_y[6] | in2_y[7]);
|
|
|
|
in1infty = is_zero(in1infty);
|
|
in2infty = is_zero(in2infty);
|
|
|
|
ecp_nistz256_sqr_mont(Z1sqr, in1_z); /* Z1^2 */
|
|
|
|
ecp_nistz256_mul_mont(U2, in2_x, Z1sqr); /* U2 = X2*Z1^2 */
|
|
ecp_nistz256_sub(H, U2, in1_x); /* H = U2 - U1 */
|
|
|
|
ecp_nistz256_mul_mont(S2, Z1sqr, in1_z); /* S2 = Z1^3 */
|
|
|
|
ecp_nistz256_mul_mont(res_z, H, in1_z); /* Z3 = H*Z1*Z2 */
|
|
|
|
ecp_nistz256_mul_mont(S2, S2, in2_y); /* S2 = Y2*Z1^3 */
|
|
ecp_nistz256_sub(R, S2, in1_y); /* R = S2 - S1 */
|
|
|
|
ecp_nistz256_sqr_mont(Hsqr, H); /* H^2 */
|
|
ecp_nistz256_sqr_mont(Rsqr, R); /* R^2 */
|
|
ecp_nistz256_mul_mont(Hcub, Hsqr, H); /* H^3 */
|
|
|
|
ecp_nistz256_mul_mont(U2, in1_x, Hsqr); /* U1*H^2 */
|
|
ecp_nistz256_mul_by_2(Hsqr, U2); /* 2*U1*H^2 */
|
|
|
|
ecp_nistz256_sub(res_x, Rsqr, Hsqr);
|
|
ecp_nistz256_sub(res_x, res_x, Hcub);
|
|
ecp_nistz256_sub(H, U2, res_x);
|
|
|
|
ecp_nistz256_mul_mont(S2, in1_y, Hcub);
|
|
ecp_nistz256_mul_mont(H, H, R);
|
|
ecp_nistz256_sub(res_y, H, S2);
|
|
|
|
copy_conditional(res_x, in2_x, in1infty);
|
|
copy_conditional(res_x, in1_x, in2infty);
|
|
|
|
copy_conditional(res_y, in2_y, in1infty);
|
|
copy_conditional(res_y, in1_y, in2infty);
|
|
|
|
copy_conditional(res_z, ONE, in1infty);
|
|
copy_conditional(res_z, in1_z, in2infty);
|
|
|
|
memcpy(r->X, res_x, sizeof(res_x));
|
|
memcpy(r->Y, res_y, sizeof(res_y));
|
|
memcpy(r->Z, res_z, sizeof(res_z));
|
|
}
|
|
#endif
|
|
|
|
/* r = in^-1 mod p */
|
|
static void ecp_nistz256_mod_inverse(BN_ULONG r[P256_LIMBS],
|
|
const BN_ULONG in[P256_LIMBS])
|
|
{
|
|
/*
|
|
* The poly is ffffffff 00000001 00000000 00000000 00000000 ffffffff
|
|
* ffffffff ffffffff We use FLT and used poly-2 as exponent
|
|
*/
|
|
BN_ULONG p2[P256_LIMBS];
|
|
BN_ULONG p4[P256_LIMBS];
|
|
BN_ULONG p8[P256_LIMBS];
|
|
BN_ULONG p16[P256_LIMBS];
|
|
BN_ULONG p32[P256_LIMBS];
|
|
BN_ULONG res[P256_LIMBS];
|
|
int i;
|
|
|
|
ecp_nistz256_sqr_mont(res, in);
|
|
ecp_nistz256_mul_mont(p2, res, in); /* 3*p */
|
|
|
|
ecp_nistz256_sqr_mont(res, p2);
|
|
ecp_nistz256_sqr_mont(res, res);
|
|
ecp_nistz256_mul_mont(p4, res, p2); /* f*p */
|
|
|
|
ecp_nistz256_sqr_mont(res, p4);
|
|
ecp_nistz256_sqr_mont(res, res);
|
|
ecp_nistz256_sqr_mont(res, res);
|
|
ecp_nistz256_sqr_mont(res, res);
|
|
ecp_nistz256_mul_mont(p8, res, p4); /* ff*p */
|
|
|
|
ecp_nistz256_sqr_mont(res, p8);
|
|
for (i = 0; i < 7; i++)
|
|
ecp_nistz256_sqr_mont(res, res);
|
|
ecp_nistz256_mul_mont(p16, res, p8); /* ffff*p */
|
|
|
|
ecp_nistz256_sqr_mont(res, p16);
|
|
for (i = 0; i < 15; i++)
|
|
ecp_nistz256_sqr_mont(res, res);
|
|
ecp_nistz256_mul_mont(p32, res, p16); /* ffffffff*p */
|
|
|
|
ecp_nistz256_sqr_mont(res, p32);
|
|
for (i = 0; i < 31; i++)
|
|
ecp_nistz256_sqr_mont(res, res);
|
|
ecp_nistz256_mul_mont(res, res, in);
|
|
|
|
for (i = 0; i < 32 * 4; i++)
|
|
ecp_nistz256_sqr_mont(res, res);
|
|
ecp_nistz256_mul_mont(res, res, p32);
|
|
|
|
for (i = 0; i < 32; i++)
|
|
ecp_nistz256_sqr_mont(res, res);
|
|
ecp_nistz256_mul_mont(res, res, p32);
|
|
|
|
for (i = 0; i < 16; i++)
|
|
ecp_nistz256_sqr_mont(res, res);
|
|
ecp_nistz256_mul_mont(res, res, p16);
|
|
|
|
for (i = 0; i < 8; i++)
|
|
ecp_nistz256_sqr_mont(res, res);
|
|
ecp_nistz256_mul_mont(res, res, p8);
|
|
|
|
ecp_nistz256_sqr_mont(res, res);
|
|
ecp_nistz256_sqr_mont(res, res);
|
|
ecp_nistz256_sqr_mont(res, res);
|
|
ecp_nistz256_sqr_mont(res, res);
|
|
ecp_nistz256_mul_mont(res, res, p4);
|
|
|
|
ecp_nistz256_sqr_mont(res, res);
|
|
ecp_nistz256_sqr_mont(res, res);
|
|
ecp_nistz256_mul_mont(res, res, p2);
|
|
|
|
ecp_nistz256_sqr_mont(res, res);
|
|
ecp_nistz256_sqr_mont(res, res);
|
|
ecp_nistz256_mul_mont(res, res, in);
|
|
|
|
memcpy(r, res, sizeof(res));
|
|
}
|
|
|
|
/*
|
|
* ecp_nistz256_bignum_to_field_elem copies the contents of |in| to |out| and
|
|
* returns one if it fits. Otherwise it returns zero.
|
|
*/
|
|
static int ecp_nistz256_bignum_to_field_elem(BN_ULONG out[P256_LIMBS],
|
|
const BIGNUM *in)
|
|
{
|
|
if (in->top > P256_LIMBS)
|
|
return 0;
|
|
|
|
memset(out, 0, sizeof(BN_ULONG) * P256_LIMBS);
|
|
memcpy(out, in->d, sizeof(BN_ULONG) * in->top);
|
|
return 1;
|
|
}
|
|
|
|
/* r = sum(scalar[i]*point[i]) */
|
|
static int ecp_nistz256_windowed_mul(const EC_GROUP *group,
|
|
P256_POINT *r,
|
|
const BIGNUM **scalar,
|
|
const EC_POINT **point,
|
|
int num, BN_CTX *ctx)
|
|
{
|
|
|
|
int i, j, ret = 0;
|
|
unsigned int index;
|
|
unsigned char (*p_str)[33] = NULL;
|
|
const unsigned int window_size = 5;
|
|
const unsigned int mask = (1 << (window_size + 1)) - 1;
|
|
unsigned int wvalue;
|
|
BN_ULONG tmp[P256_LIMBS];
|
|
ALIGN32 P256_POINT h;
|
|
const BIGNUM **scalars = NULL;
|
|
P256_POINT (*table)[16] = NULL;
|
|
void *table_storage = NULL;
|
|
|
|
if ((table_storage =
|
|
OPENSSL_malloc(num * 16 * sizeof(P256_POINT) + 64)) == NULL
|
|
|| (p_str =
|
|
OPENSSL_malloc(num * 33 * sizeof(unsigned char))) == NULL
|
|
|| (scalars = OPENSSL_malloc(num * sizeof(BIGNUM *))) == NULL) {
|
|
ECerr(EC_F_ECP_NISTZ256_WINDOWED_MUL, ERR_R_MALLOC_FAILURE);
|
|
goto err;
|
|
} else {
|
|
table = (void *)ALIGNPTR(table_storage, 64);
|
|
}
|
|
|
|
for (i = 0; i < num; i++) {
|
|
P256_POINT *row = table[i];
|
|
|
|
/* This is an unusual input, we don't guarantee constant-timeness. */
|
|
if ((BN_num_bits(scalar[i]) > 256) || BN_is_negative(scalar[i])) {
|
|
BIGNUM *mod;
|
|
|
|
if ((mod = BN_CTX_get(ctx)) == NULL)
|
|
goto err;
|
|
if (!BN_nnmod(mod, scalar[i], &group->order, ctx)) {
|
|
ECerr(EC_F_ECP_NISTZ256_WINDOWED_MUL, ERR_R_BN_LIB);
|
|
goto err;
|
|
}
|
|
scalars[i] = mod;
|
|
} else
|
|
scalars[i] = scalar[i];
|
|
|
|
for (j = 0; j < scalars[i]->top * BN_BYTES; j += BN_BYTES) {
|
|
BN_ULONG d = scalars[i]->d[j / BN_BYTES];
|
|
|
|
p_str[i][j + 0] = d & 0xff;
|
|
p_str[i][j + 1] = (d >> 8) & 0xff;
|
|
p_str[i][j + 2] = (d >> 16) & 0xff;
|
|
p_str[i][j + 3] = (d >>= 24) & 0xff;
|
|
if (BN_BYTES == 8) {
|
|
d >>= 8;
|
|
p_str[i][j + 4] = d & 0xff;
|
|
p_str[i][j + 5] = (d >> 8) & 0xff;
|
|
p_str[i][j + 6] = (d >> 16) & 0xff;
|
|
p_str[i][j + 7] = (d >> 24) & 0xff;
|
|
}
|
|
}
|
|
for (; j < 33; j++)
|
|
p_str[i][j] = 0;
|
|
|
|
/* table[0] is implicitly (0,0,0) (the point at infinity),
|
|
* therefore it is not stored. All other values are actually
|
|
* stored with an offset of -1 in table.
|
|
*/
|
|
|
|
if (!ecp_nistz256_bignum_to_field_elem(row[1 - 1].X, &point[i]->X)
|
|
|| !ecp_nistz256_bignum_to_field_elem(row[1 - 1].Y, &point[i]->Y)
|
|
|| !ecp_nistz256_bignum_to_field_elem(row[1 - 1].Z, &point[i]->Z)) {
|
|
ECerr(EC_F_ECP_NISTZ256_WINDOWED_MUL, EC_R_COORDINATES_OUT_OF_RANGE);
|
|
goto err;
|
|
}
|
|
|
|
ecp_nistz256_point_double(&row[ 2 - 1], &row[ 1 - 1]);
|
|
ecp_nistz256_point_add (&row[ 3 - 1], &row[ 2 - 1], &row[1 - 1]);
|
|
ecp_nistz256_point_double(&row[ 4 - 1], &row[ 2 - 1]);
|
|
ecp_nistz256_point_double(&row[ 6 - 1], &row[ 3 - 1]);
|
|
ecp_nistz256_point_double(&row[ 8 - 1], &row[ 4 - 1]);
|
|
ecp_nistz256_point_double(&row[12 - 1], &row[ 6 - 1]);
|
|
ecp_nistz256_point_add (&row[ 5 - 1], &row[ 4 - 1], &row[1 - 1]);
|
|
ecp_nistz256_point_add (&row[ 7 - 1], &row[ 6 - 1], &row[1 - 1]);
|
|
ecp_nistz256_point_add (&row[ 9 - 1], &row[ 8 - 1], &row[1 - 1]);
|
|
ecp_nistz256_point_add (&row[13 - 1], &row[12 - 1], &row[1 - 1]);
|
|
ecp_nistz256_point_double(&row[14 - 1], &row[ 7 - 1]);
|
|
ecp_nistz256_point_double(&row[10 - 1], &row[ 5 - 1]);
|
|
ecp_nistz256_point_add (&row[15 - 1], &row[14 - 1], &row[1 - 1]);
|
|
ecp_nistz256_point_add (&row[11 - 1], &row[10 - 1], &row[1 - 1]);
|
|
ecp_nistz256_point_add (&row[16 - 1], &row[15 - 1], &row[1 - 1]);
|
|
}
|
|
|
|
index = 255;
|
|
|
|
wvalue = p_str[0][(index - 1) / 8];
|
|
wvalue = (wvalue >> ((index - 1) % 8)) & mask;
|
|
|
|
ecp_nistz256_select_w5(r, table[0], _booth_recode_w5(wvalue) >> 1);
|
|
|
|
while (index >= 5) {
|
|
for (i = (index == 255 ? 1 : 0); i < num; i++) {
|
|
unsigned int off = (index - 1) / 8;
|
|
|
|
wvalue = p_str[i][off] | p_str[i][off + 1] << 8;
|
|
wvalue = (wvalue >> ((index - 1) % 8)) & mask;
|
|
|
|
wvalue = _booth_recode_w5(wvalue);
|
|
|
|
ecp_nistz256_select_w5(&h, table[i], wvalue >> 1);
|
|
|
|
ecp_nistz256_neg(tmp, h.Y);
|
|
copy_conditional(h.Y, tmp, (wvalue & 1));
|
|
|
|
ecp_nistz256_point_add(r, r, &h);
|
|
}
|
|
|
|
index -= window_size;
|
|
|
|
ecp_nistz256_point_double(r, r);
|
|
ecp_nistz256_point_double(r, r);
|
|
ecp_nistz256_point_double(r, r);
|
|
ecp_nistz256_point_double(r, r);
|
|
ecp_nistz256_point_double(r, r);
|
|
}
|
|
|
|
/* Final window */
|
|
for (i = 0; i < num; i++) {
|
|
wvalue = p_str[i][0];
|
|
wvalue = (wvalue << 1) & mask;
|
|
|
|
wvalue = _booth_recode_w5(wvalue);
|
|
|
|
ecp_nistz256_select_w5(&h, table[i], wvalue >> 1);
|
|
|
|
ecp_nistz256_neg(tmp, h.Y);
|
|
copy_conditional(h.Y, tmp, wvalue & 1);
|
|
|
|
ecp_nistz256_point_add(r, r, &h);
|
|
}
|
|
|
|
ret = 1;
|
|
err:
|
|
if (table_storage)
|
|
OPENSSL_free(table_storage);
|
|
if (p_str)
|
|
OPENSSL_free(p_str);
|
|
if (scalars)
|
|
OPENSSL_free(scalars);
|
|
return ret;
|
|
}
|
|
|
|
/* Coordinates of G, for which we have precomputed tables */
|
|
const static BN_ULONG def_xG[P256_LIMBS] = {
|
|
TOBN(0x79e730d4, 0x18a9143c), TOBN(0x75ba95fc, 0x5fedb601),
|
|
TOBN(0x79fb732b, 0x77622510), TOBN(0x18905f76, 0xa53755c6)
|
|
};
|
|
|
|
const static BN_ULONG def_yG[P256_LIMBS] = {
|
|
TOBN(0xddf25357, 0xce95560a), TOBN(0x8b4ab8e4, 0xba19e45c),
|
|
TOBN(0xd2e88688, 0xdd21f325), TOBN(0x8571ff18, 0x25885d85)
|
|
};
|
|
|
|
/*
|
|
* ecp_nistz256_is_affine_G returns one if |generator| is the standard, P-256
|
|
* generator.
|
|
*/
|
|
static int ecp_nistz256_is_affine_G(const EC_POINT *generator)
|
|
{
|
|
return (generator->X.top == P256_LIMBS) &&
|
|
(generator->Y.top == P256_LIMBS) &&
|
|
is_equal(generator->X.d, def_xG) &&
|
|
is_equal(generator->Y.d, def_yG) && is_one(&generator->Z);
|
|
}
|
|
|
|
static int ecp_nistz256_mult_precompute(EC_GROUP *group, BN_CTX *ctx)
|
|
{
|
|
/*
|
|
* We precompute a table for a Booth encoded exponent (wNAF) based
|
|
* computation. Each table holds 64 values for safe access, with an
|
|
* implicit value of infinity at index zero. We use window of size 7, and
|
|
* therefore require ceil(256/7) = 37 tables.
|
|
*/
|
|
BIGNUM *order;
|
|
EC_POINT *P = NULL, *T = NULL;
|
|
const EC_POINT *generator;
|
|
EC_PRE_COMP *pre_comp;
|
|
BN_CTX *new_ctx = NULL;
|
|
int i, j, k, ret = 0;
|
|
size_t w;
|
|
|
|
PRECOMP256_ROW *preComputedTable = NULL;
|
|
unsigned char *precomp_storage = NULL;
|
|
|
|
/* if there is an old EC_PRE_COMP object, throw it away */
|
|
EC_EX_DATA_free_data(&group->extra_data, ecp_nistz256_pre_comp_dup,
|
|
ecp_nistz256_pre_comp_free,
|
|
ecp_nistz256_pre_comp_clear_free);
|
|
|
|
generator = EC_GROUP_get0_generator(group);
|
|
if (generator == NULL) {
|
|
ECerr(EC_F_ECP_NISTZ256_MULT_PRECOMPUTE, EC_R_UNDEFINED_GENERATOR);
|
|
return 0;
|
|
}
|
|
|
|
if (ecp_nistz256_is_affine_G(generator)) {
|
|
/*
|
|
* No need to calculate tables for the standard generator because we
|
|
* have them statically.
|
|
*/
|
|
return 1;
|
|
}
|
|
|
|
if ((pre_comp = ecp_nistz256_pre_comp_new(group)) == NULL)
|
|
return 0;
|
|
|
|
if (ctx == NULL) {
|
|
ctx = new_ctx = BN_CTX_new();
|
|
if (ctx == NULL)
|
|
goto err;
|
|
}
|
|
|
|
BN_CTX_start(ctx);
|
|
order = BN_CTX_get(ctx);
|
|
|
|
if (order == NULL)
|
|
goto err;
|
|
|
|
if (!EC_GROUP_get_order(group, order, ctx))
|
|
goto err;
|
|
|
|
if (BN_is_zero(order)) {
|
|
ECerr(EC_F_ECP_NISTZ256_MULT_PRECOMPUTE, EC_R_UNKNOWN_ORDER);
|
|
goto err;
|
|
}
|
|
|
|
w = 7;
|
|
|
|
if ((precomp_storage =
|
|
OPENSSL_malloc(37 * 64 * sizeof(P256_POINT_AFFINE) + 64)) == NULL) {
|
|
ECerr(EC_F_ECP_NISTZ256_MULT_PRECOMPUTE, ERR_R_MALLOC_FAILURE);
|
|
goto err;
|
|
} else {
|
|
preComputedTable = (void *)ALIGNPTR(precomp_storage, 64);
|
|
}
|
|
|
|
P = EC_POINT_new(group);
|
|
T = EC_POINT_new(group);
|
|
if (P == NULL || T == NULL)
|
|
goto err;
|
|
|
|
/*
|
|
* The zero entry is implicitly infinity, and we skip it, storing other
|
|
* values with -1 offset.
|
|
*/
|
|
if (!EC_POINT_copy(T, generator))
|
|
goto err;
|
|
|
|
for (k = 0; k < 64; k++) {
|
|
if (!EC_POINT_copy(P, T))
|
|
goto err;
|
|
for (j = 0; j < 37; j++) {
|
|
/*
|
|
* It would be faster to use EC_POINTs_make_affine and
|
|
* make multiple points affine at the same time.
|
|
*/
|
|
if (!EC_POINT_make_affine(group, P, ctx))
|
|
goto err;
|
|
if (!ecp_nistz256_bignum_to_field_elem(preComputedTable[j][k].X,
|
|
&P->X) ||
|
|
!ecp_nistz256_bignum_to_field_elem(preComputedTable[j][k].Y,
|
|
&P->Y)) {
|
|
ECerr(EC_F_ECP_NISTZ256_MULT_PRECOMPUTE,
|
|
EC_R_COORDINATES_OUT_OF_RANGE);
|
|
goto err;
|
|
}
|
|
for (i = 0; i < 7; i++) {
|
|
if (!EC_POINT_dbl(group, P, P, ctx))
|
|
goto err;
|
|
}
|
|
}
|
|
if (!EC_POINT_add(group, T, T, generator, ctx))
|
|
goto err;
|
|
}
|
|
|
|
pre_comp->group = group;
|
|
pre_comp->w = w;
|
|
pre_comp->precomp = preComputedTable;
|
|
pre_comp->precomp_storage = precomp_storage;
|
|
|
|
precomp_storage = NULL;
|
|
|
|
if (!EC_EX_DATA_set_data(&group->extra_data, pre_comp,
|
|
ecp_nistz256_pre_comp_dup,
|
|
ecp_nistz256_pre_comp_free,
|
|
ecp_nistz256_pre_comp_clear_free)) {
|
|
goto err;
|
|
}
|
|
|
|
pre_comp = NULL;
|
|
|
|
ret = 1;
|
|
|
|
err:
|
|
if (ctx != NULL)
|
|
BN_CTX_end(ctx);
|
|
BN_CTX_free(new_ctx);
|
|
|
|
if (pre_comp)
|
|
ecp_nistz256_pre_comp_free(pre_comp);
|
|
if (precomp_storage)
|
|
OPENSSL_free(precomp_storage);
|
|
if (P)
|
|
EC_POINT_free(P);
|
|
if (T)
|
|
EC_POINT_free(T);
|
|
return ret;
|
|
}
|
|
|
|
/*
|
|
* Note that by default ECP_NISTZ256_AVX2 is undefined. While it's great
|
|
* code processing 4 points in parallel, corresponding serial operation
|
|
* is several times slower, because it uses 29x29=58-bit multiplication
|
|
* as opposite to 64x64=128-bit in integer-only scalar case. As result
|
|
* it doesn't provide *significant* performance improvement. Note that
|
|
* just defining ECP_NISTZ256_AVX2 is not sufficient to make it work,
|
|
* you'd need to compile even asm/ecp_nistz256-avx.pl module.
|
|
*/
|
|
#if defined(ECP_NISTZ256_AVX2)
|
|
# if !(defined(__x86_64) || defined(__x86_64__)) || \
|
|
defined(_M_AMD64) || defined(_MX64)) || \
|
|
!(defined(__GNUC__) || defined(_MSC_VER)) /* this is for ALIGN32 */
|
|
# undef ECP_NISTZ256_AVX2
|
|
# else
|
|
/* Constant time access, loading four values, from four consecutive tables */
|
|
void ecp_nistz256_avx2_select_w7(P256_POINT_AFFINE * val,
|
|
const P256_POINT_AFFINE * in_t, int index);
|
|
void ecp_nistz256_avx2_multi_select_w7(void *result, const void *in, int index0,
|
|
int index1, int index2, int index3);
|
|
void ecp_nistz256_avx2_transpose_convert(void *RESULTx4, const void *in);
|
|
void ecp_nistz256_avx2_convert_transpose_back(void *result, const void *Ax4);
|
|
void ecp_nistz256_avx2_point_add_affine_x4(void *RESULTx4, const void *Ax4,
|
|
const void *Bx4);
|
|
void ecp_nistz256_avx2_point_add_affines_x4(void *RESULTx4, const void *Ax4,
|
|
const void *Bx4);
|
|
void ecp_nistz256_avx2_to_mont(void *RESULTx4, const void *Ax4);
|
|
void ecp_nistz256_avx2_from_mont(void *RESULTx4, const void *Ax4);
|
|
void ecp_nistz256_avx2_set1(void *RESULTx4);
|
|
int ecp_nistz_avx2_eligible(void);
|
|
|
|
static void booth_recode_w7(unsigned char *sign,
|
|
unsigned char *digit, unsigned char in)
|
|
{
|
|
unsigned char s, d;
|
|
|
|
s = ~((in >> 7) - 1);
|
|
d = (1 << 8) - in - 1;
|
|
d = (d & s) | (in & ~s);
|
|
d = (d >> 1) + (d & 1);
|
|
|
|
*sign = s & 1;
|
|
*digit = d;
|
|
}
|
|
|
|
/*
|
|
* ecp_nistz256_avx2_mul_g performs multiplication by G, using only the
|
|
* precomputed table. It does 4 affine point additions in parallel,
|
|
* significantly speeding up point multiplication for a fixed value.
|
|
*/
|
|
static void ecp_nistz256_avx2_mul_g(P256_POINT *r,
|
|
unsigned char p_str[33],
|
|
const P256_POINT_AFFINE(*preComputedTable)[64])
|
|
{
|
|
const unsigned int window_size = 7;
|
|
const unsigned int mask = (1 << (window_size + 1)) - 1;
|
|
unsigned int wvalue;
|
|
/* Using 4 windows at a time */
|
|
unsigned char sign0, digit0;
|
|
unsigned char sign1, digit1;
|
|
unsigned char sign2, digit2;
|
|
unsigned char sign3, digit3;
|
|
unsigned int index = 0;
|
|
BN_ULONG tmp[P256_LIMBS];
|
|
int i;
|
|
|
|
ALIGN32 BN_ULONG aX4[4 * 9 * 3] = { 0 };
|
|
ALIGN32 BN_ULONG bX4[4 * 9 * 2] = { 0 };
|
|
ALIGN32 P256_POINT_AFFINE point_arr[P256_LIMBS];
|
|
ALIGN32 P256_POINT res_point_arr[P256_LIMBS];
|
|
|
|
/* Initial four windows */
|
|
wvalue = *((u16 *) & p_str[0]);
|
|
wvalue = (wvalue << 1) & mask;
|
|
index += window_size;
|
|
booth_recode_w7(&sign0, &digit0, wvalue);
|
|
wvalue = *((u16 *) & p_str[(index - 1) / 8]);
|
|
wvalue = (wvalue >> ((index - 1) % 8)) & mask;
|
|
index += window_size;
|
|
booth_recode_w7(&sign1, &digit1, wvalue);
|
|
wvalue = *((u16 *) & p_str[(index - 1) / 8]);
|
|
wvalue = (wvalue >> ((index - 1) % 8)) & mask;
|
|
index += window_size;
|
|
booth_recode_w7(&sign2, &digit2, wvalue);
|
|
wvalue = *((u16 *) & p_str[(index - 1) / 8]);
|
|
wvalue = (wvalue >> ((index - 1) % 8)) & mask;
|
|
index += window_size;
|
|
booth_recode_w7(&sign3, &digit3, wvalue);
|
|
|
|
ecp_nistz256_avx2_multi_select_w7(point_arr, preComputedTable[0],
|
|
digit0, digit1, digit2, digit3);
|
|
|
|
ecp_nistz256_neg(tmp, point_arr[0].Y);
|
|
copy_conditional(point_arr[0].Y, tmp, sign0);
|
|
ecp_nistz256_neg(tmp, point_arr[1].Y);
|
|
copy_conditional(point_arr[1].Y, tmp, sign1);
|
|
ecp_nistz256_neg(tmp, point_arr[2].Y);
|
|
copy_conditional(point_arr[2].Y, tmp, sign2);
|
|
ecp_nistz256_neg(tmp, point_arr[3].Y);
|
|
copy_conditional(point_arr[3].Y, tmp, sign3);
|
|
|
|
ecp_nistz256_avx2_transpose_convert(aX4, point_arr);
|
|
ecp_nistz256_avx2_to_mont(aX4, aX4);
|
|
ecp_nistz256_avx2_to_mont(&aX4[4 * 9], &aX4[4 * 9]);
|
|
ecp_nistz256_avx2_set1(&aX4[4 * 9 * 2]);
|
|
|
|
wvalue = *((u16 *) & p_str[(index - 1) / 8]);
|
|
wvalue = (wvalue >> ((index - 1) % 8)) & mask;
|
|
index += window_size;
|
|
booth_recode_w7(&sign0, &digit0, wvalue);
|
|
wvalue = *((u16 *) & p_str[(index - 1) / 8]);
|
|
wvalue = (wvalue >> ((index - 1) % 8)) & mask;
|
|
index += window_size;
|
|
booth_recode_w7(&sign1, &digit1, wvalue);
|
|
wvalue = *((u16 *) & p_str[(index - 1) / 8]);
|
|
wvalue = (wvalue >> ((index - 1) % 8)) & mask;
|
|
index += window_size;
|
|
booth_recode_w7(&sign2, &digit2, wvalue);
|
|
wvalue = *((u16 *) & p_str[(index - 1) / 8]);
|
|
wvalue = (wvalue >> ((index - 1) % 8)) & mask;
|
|
index += window_size;
|
|
booth_recode_w7(&sign3, &digit3, wvalue);
|
|
|
|
ecp_nistz256_avx2_multi_select_w7(point_arr, preComputedTable[4 * 1],
|
|
digit0, digit1, digit2, digit3);
|
|
|
|
ecp_nistz256_neg(tmp, point_arr[0].Y);
|
|
copy_conditional(point_arr[0].Y, tmp, sign0);
|
|
ecp_nistz256_neg(tmp, point_arr[1].Y);
|
|
copy_conditional(point_arr[1].Y, tmp, sign1);
|
|
ecp_nistz256_neg(tmp, point_arr[2].Y);
|
|
copy_conditional(point_arr[2].Y, tmp, sign2);
|
|
ecp_nistz256_neg(tmp, point_arr[3].Y);
|
|
copy_conditional(point_arr[3].Y, tmp, sign3);
|
|
|
|
ecp_nistz256_avx2_transpose_convert(bX4, point_arr);
|
|
ecp_nistz256_avx2_to_mont(bX4, bX4);
|
|
ecp_nistz256_avx2_to_mont(&bX4[4 * 9], &bX4[4 * 9]);
|
|
/* Optimized when both inputs are affine */
|
|
ecp_nistz256_avx2_point_add_affines_x4(aX4, aX4, bX4);
|
|
|
|
for (i = 2; i < 9; i++) {
|
|
wvalue = *((u16 *) & p_str[(index - 1) / 8]);
|
|
wvalue = (wvalue >> ((index - 1) % 8)) & mask;
|
|
index += window_size;
|
|
booth_recode_w7(&sign0, &digit0, wvalue);
|
|
wvalue = *((u16 *) & p_str[(index - 1) / 8]);
|
|
wvalue = (wvalue >> ((index - 1) % 8)) & mask;
|
|
index += window_size;
|
|
booth_recode_w7(&sign1, &digit1, wvalue);
|
|
wvalue = *((u16 *) & p_str[(index - 1) / 8]);
|
|
wvalue = (wvalue >> ((index - 1) % 8)) & mask;
|
|
index += window_size;
|
|
booth_recode_w7(&sign2, &digit2, wvalue);
|
|
wvalue = *((u16 *) & p_str[(index - 1) / 8]);
|
|
wvalue = (wvalue >> ((index - 1) % 8)) & mask;
|
|
index += window_size;
|
|
booth_recode_w7(&sign3, &digit3, wvalue);
|
|
|
|
ecp_nistz256_avx2_multi_select_w7(point_arr,
|
|
preComputedTable[4 * i],
|
|
digit0, digit1, digit2, digit3);
|
|
|
|
ecp_nistz256_neg(tmp, point_arr[0].Y);
|
|
copy_conditional(point_arr[0].Y, tmp, sign0);
|
|
ecp_nistz256_neg(tmp, point_arr[1].Y);
|
|
copy_conditional(point_arr[1].Y, tmp, sign1);
|
|
ecp_nistz256_neg(tmp, point_arr[2].Y);
|
|
copy_conditional(point_arr[2].Y, tmp, sign2);
|
|
ecp_nistz256_neg(tmp, point_arr[3].Y);
|
|
copy_conditional(point_arr[3].Y, tmp, sign3);
|
|
|
|
ecp_nistz256_avx2_transpose_convert(bX4, point_arr);
|
|
ecp_nistz256_avx2_to_mont(bX4, bX4);
|
|
ecp_nistz256_avx2_to_mont(&bX4[4 * 9], &bX4[4 * 9]);
|
|
|
|
ecp_nistz256_avx2_point_add_affine_x4(aX4, aX4, bX4);
|
|
}
|
|
|
|
ecp_nistz256_avx2_from_mont(&aX4[4 * 9 * 0], &aX4[4 * 9 * 0]);
|
|
ecp_nistz256_avx2_from_mont(&aX4[4 * 9 * 1], &aX4[4 * 9 * 1]);
|
|
ecp_nistz256_avx2_from_mont(&aX4[4 * 9 * 2], &aX4[4 * 9 * 2]);
|
|
|
|
ecp_nistz256_avx2_convert_transpose_back(res_point_arr, aX4);
|
|
/* Last window is performed serially */
|
|
wvalue = *((u16 *) & p_str[(index - 1) / 8]);
|
|
wvalue = (wvalue >> ((index - 1) % 8)) & mask;
|
|
booth_recode_w7(&sign0, &digit0, wvalue);
|
|
ecp_nistz256_avx2_select_w7((P256_POINT_AFFINE *) r,
|
|
preComputedTable[36], digit0);
|
|
ecp_nistz256_neg(tmp, r->Y);
|
|
copy_conditional(r->Y, tmp, sign0);
|
|
memcpy(r->Z, ONE, sizeof(ONE));
|
|
/* Sum the four windows */
|
|
ecp_nistz256_point_add(r, r, &res_point_arr[0]);
|
|
ecp_nistz256_point_add(r, r, &res_point_arr[1]);
|
|
ecp_nistz256_point_add(r, r, &res_point_arr[2]);
|
|
ecp_nistz256_point_add(r, r, &res_point_arr[3]);
|
|
}
|
|
# endif
|
|
#endif
|
|
|
|
static int ecp_nistz256_set_from_affine(EC_POINT *out, const EC_GROUP *group,
|
|
const P256_POINT_AFFINE *in,
|
|
BN_CTX *ctx)
|
|
{
|
|
BIGNUM x, y;
|
|
BN_ULONG d_x[P256_LIMBS], d_y[P256_LIMBS];
|
|
int ret = 0;
|
|
|
|
memcpy(d_x, in->X, sizeof(d_x));
|
|
x.d = d_x;
|
|
x.dmax = x.top = P256_LIMBS;
|
|
x.neg = 0;
|
|
x.flags = BN_FLG_STATIC_DATA;
|
|
|
|
memcpy(d_y, in->Y, sizeof(d_y));
|
|
y.d = d_y;
|
|
y.dmax = y.top = P256_LIMBS;
|
|
y.neg = 0;
|
|
y.flags = BN_FLG_STATIC_DATA;
|
|
|
|
ret = EC_POINT_set_affine_coordinates_GFp(group, out, &x, &y, ctx);
|
|
|
|
return ret;
|
|
}
|
|
|
|
/* r = scalar*G + sum(scalars[i]*points[i]) */
|
|
static int ecp_nistz256_points_mul(const EC_GROUP *group,
|
|
EC_POINT *r,
|
|
const BIGNUM *scalar,
|
|
size_t num,
|
|
const EC_POINT *points[],
|
|
const BIGNUM *scalars[], BN_CTX *ctx)
|
|
{
|
|
int i = 0, ret = 0, no_precomp_for_generator = 0, p_is_infinity = 0;
|
|
size_t j;
|
|
unsigned char p_str[33] = { 0 };
|
|
const PRECOMP256_ROW *preComputedTable = NULL;
|
|
const EC_PRE_COMP *pre_comp = NULL;
|
|
const EC_POINT *generator = NULL;
|
|
unsigned int index = 0;
|
|
BN_CTX *new_ctx = NULL;
|
|
const BIGNUM **new_scalars = NULL;
|
|
const EC_POINT **new_points = NULL;
|
|
const unsigned int window_size = 7;
|
|
const unsigned int mask = (1 << (window_size + 1)) - 1;
|
|
unsigned int wvalue;
|
|
ALIGN32 union {
|
|
P256_POINT p;
|
|
P256_POINT_AFFINE a;
|
|
} t, p;
|
|
BIGNUM *tmp_scalar;
|
|
|
|
if (group->meth != r->meth) {
|
|
ECerr(EC_F_ECP_NISTZ256_POINTS_MUL, EC_R_INCOMPATIBLE_OBJECTS);
|
|
return 0;
|
|
}
|
|
|
|
if ((scalar == NULL) && (num == 0))
|
|
return EC_POINT_set_to_infinity(group, r);
|
|
|
|
for (j = 0; j < num; j++) {
|
|
if (group->meth != points[j]->meth) {
|
|
ECerr(EC_F_ECP_NISTZ256_POINTS_MUL, EC_R_INCOMPATIBLE_OBJECTS);
|
|
return 0;
|
|
}
|
|
}
|
|
|
|
if (ctx == NULL) {
|
|
ctx = new_ctx = BN_CTX_new();
|
|
if (ctx == NULL)
|
|
goto err;
|
|
}
|
|
|
|
BN_CTX_start(ctx);
|
|
|
|
if (scalar) {
|
|
generator = EC_GROUP_get0_generator(group);
|
|
if (generator == NULL) {
|
|
ECerr(EC_F_ECP_NISTZ256_POINTS_MUL, EC_R_UNDEFINED_GENERATOR);
|
|
goto err;
|
|
}
|
|
|
|
/* look if we can use precomputed multiples of generator */
|
|
pre_comp =
|
|
EC_EX_DATA_get_data(group->extra_data, ecp_nistz256_pre_comp_dup,
|
|
ecp_nistz256_pre_comp_free,
|
|
ecp_nistz256_pre_comp_clear_free);
|
|
|
|
if (pre_comp) {
|
|
/*
|
|
* If there is a precomputed table for the generator, check that
|
|
* it was generated with the same generator.
|
|
*/
|
|
EC_POINT *pre_comp_generator = EC_POINT_new(group);
|
|
if (pre_comp_generator == NULL)
|
|
goto err;
|
|
|
|
if (!ecp_nistz256_set_from_affine
|
|
(pre_comp_generator, group, pre_comp->precomp[0], ctx)) {
|
|
EC_POINT_free(pre_comp_generator);
|
|
goto err;
|
|
}
|
|
|
|
if (0 == EC_POINT_cmp(group, generator, pre_comp_generator, ctx))
|
|
preComputedTable = (const PRECOMP256_ROW *)pre_comp->precomp;
|
|
|
|
EC_POINT_free(pre_comp_generator);
|
|
}
|
|
|
|
if (preComputedTable == NULL && ecp_nistz256_is_affine_G(generator)) {
|
|
/*
|
|
* If there is no precomputed data, but the generator
|
|
* is the default, a hardcoded table of precomputed
|
|
* data is used. This is because applications, such as
|
|
* Apache, do not use EC_KEY_precompute_mult.
|
|
*/
|
|
preComputedTable = (const PRECOMP256_ROW *)ecp_nistz256_precomputed;
|
|
}
|
|
|
|
if (preComputedTable) {
|
|
if ((BN_num_bits(scalar) > 256)
|
|
|| BN_is_negative(scalar)) {
|
|
if ((tmp_scalar = BN_CTX_get(ctx)) == NULL)
|
|
goto err;
|
|
|
|
if (!BN_nnmod(tmp_scalar, scalar, &group->order, ctx)) {
|
|
ECerr(EC_F_ECP_NISTZ256_POINTS_MUL, ERR_R_BN_LIB);
|
|
goto err;
|
|
}
|
|
scalar = tmp_scalar;
|
|
}
|
|
|
|
for (i = 0; i < scalar->top * BN_BYTES; i += BN_BYTES) {
|
|
BN_ULONG d = scalar->d[i / BN_BYTES];
|
|
|
|
p_str[i + 0] = d & 0xff;
|
|
p_str[i + 1] = (d >> 8) & 0xff;
|
|
p_str[i + 2] = (d >> 16) & 0xff;
|
|
p_str[i + 3] = (d >>= 24) & 0xff;
|
|
if (BN_BYTES == 8) {
|
|
d >>= 8;
|
|
p_str[i + 4] = d & 0xff;
|
|
p_str[i + 5] = (d >> 8) & 0xff;
|
|
p_str[i + 6] = (d >> 16) & 0xff;
|
|
p_str[i + 7] = (d >> 24) & 0xff;
|
|
}
|
|
}
|
|
|
|
for (; i < 33; i++)
|
|
p_str[i] = 0;
|
|
|
|
#if defined(ECP_NISTZ256_AVX2)
|
|
if (ecp_nistz_avx2_eligible()) {
|
|
ecp_nistz256_avx2_mul_g(&p.p, p_str, preComputedTable);
|
|
} else
|
|
#endif
|
|
{
|
|
BN_ULONG infty;
|
|
|
|
/* First window */
|
|
wvalue = (p_str[0] << 1) & mask;
|
|
index += window_size;
|
|
|
|
wvalue = _booth_recode_w7(wvalue);
|
|
|
|
ecp_nistz256_select_w7(&p.a, preComputedTable[0], wvalue >> 1);
|
|
|
|
ecp_nistz256_neg(p.p.Z, p.p.Y);
|
|
copy_conditional(p.p.Y, p.p.Z, wvalue & 1);
|
|
|
|
/*
|
|
* Since affine infinity is encoded as (0,0) and
|
|
* Jacobian ias (,,0), we need to harmonize them
|
|
* by assigning "one" or zero to Z.
|
|
*/
|
|
infty = (p.p.X[0] | p.p.X[1] | p.p.X[2] | p.p.X[3] |
|
|
p.p.Y[0] | p.p.Y[1] | p.p.Y[2] | p.p.Y[3]);
|
|
if (P256_LIMBS == 8)
|
|
infty |= (p.p.X[4] | p.p.X[5] | p.p.X[6] | p.p.X[7] |
|
|
p.p.Y[4] | p.p.Y[5] | p.p.Y[6] | p.p.Y[7]);
|
|
|
|
infty = 0 - is_zero(infty);
|
|
infty = ~infty;
|
|
|
|
p.p.Z[0] = ONE[0] & infty;
|
|
p.p.Z[1] = ONE[1] & infty;
|
|
p.p.Z[2] = ONE[2] & infty;
|
|
p.p.Z[3] = ONE[3] & infty;
|
|
if (P256_LIMBS == 8) {
|
|
p.p.Z[4] = ONE[4] & infty;
|
|
p.p.Z[5] = ONE[5] & infty;
|
|
p.p.Z[6] = ONE[6] & infty;
|
|
p.p.Z[7] = ONE[7] & infty;
|
|
}
|
|
|
|
for (i = 1; i < 37; i++) {
|
|
unsigned int off = (index - 1) / 8;
|
|
wvalue = p_str[off] | p_str[off + 1] << 8;
|
|
wvalue = (wvalue >> ((index - 1) % 8)) & mask;
|
|
index += window_size;
|
|
|
|
wvalue = _booth_recode_w7(wvalue);
|
|
|
|
ecp_nistz256_select_w7(&t.a,
|
|
preComputedTable[i], wvalue >> 1);
|
|
|
|
ecp_nistz256_neg(t.p.Z, t.a.Y);
|
|
copy_conditional(t.a.Y, t.p.Z, wvalue & 1);
|
|
|
|
ecp_nistz256_point_add_affine(&p.p, &p.p, &t.a);
|
|
}
|
|
}
|
|
} else {
|
|
p_is_infinity = 1;
|
|
no_precomp_for_generator = 1;
|
|
}
|
|
} else
|
|
p_is_infinity = 1;
|
|
|
|
if (no_precomp_for_generator) {
|
|
/*
|
|
* Without a precomputed table for the generator, it has to be
|
|
* handled like a normal point.
|
|
*/
|
|
new_scalars = OPENSSL_malloc((num + 1) * sizeof(BIGNUM *));
|
|
if (!new_scalars) {
|
|
ECerr(EC_F_ECP_NISTZ256_POINTS_MUL, ERR_R_MALLOC_FAILURE);
|
|
goto err;
|
|
}
|
|
|
|
new_points = OPENSSL_malloc((num + 1) * sizeof(EC_POINT *));
|
|
if (!new_points) {
|
|
ECerr(EC_F_ECP_NISTZ256_POINTS_MUL, ERR_R_MALLOC_FAILURE);
|
|
goto err;
|
|
}
|
|
|
|
memcpy(new_scalars, scalars, num * sizeof(BIGNUM *));
|
|
new_scalars[num] = scalar;
|
|
memcpy(new_points, points, num * sizeof(EC_POINT *));
|
|
new_points[num] = generator;
|
|
|
|
scalars = new_scalars;
|
|
points = new_points;
|
|
num++;
|
|
}
|
|
|
|
if (num) {
|
|
P256_POINT *out = &t.p;
|
|
if (p_is_infinity)
|
|
out = &p.p;
|
|
|
|
if (!ecp_nistz256_windowed_mul(group, out, scalars, points, num, ctx))
|
|
goto err;
|
|
|
|
if (!p_is_infinity)
|
|
ecp_nistz256_point_add(&p.p, &p.p, out);
|
|
}
|
|
|
|
/* Not constant-time, but we're only operating on the public output. */
|
|
if (!ecp_nistz256_set_words(&r->X, p.p.X) ||
|
|
!ecp_nistz256_set_words(&r->Y, p.p.Y) ||
|
|
!ecp_nistz256_set_words(&r->Z, p.p.Z)) {
|
|
goto err;
|
|
}
|
|
r->Z_is_one = is_one(&r->Z) & 1;
|
|
|
|
ret = 1;
|
|
|
|
err:
|
|
if (ctx)
|
|
BN_CTX_end(ctx);
|
|
BN_CTX_free(new_ctx);
|
|
if (new_points)
|
|
OPENSSL_free(new_points);
|
|
if (new_scalars)
|
|
OPENSSL_free(new_scalars);
|
|
return ret;
|
|
}
|
|
|
|
static int ecp_nistz256_get_affine(const EC_GROUP *group,
|
|
const EC_POINT *point,
|
|
BIGNUM *x, BIGNUM *y, BN_CTX *ctx)
|
|
{
|
|
BN_ULONG z_inv2[P256_LIMBS];
|
|
BN_ULONG z_inv3[P256_LIMBS];
|
|
BN_ULONG x_aff[P256_LIMBS];
|
|
BN_ULONG y_aff[P256_LIMBS];
|
|
BN_ULONG point_x[P256_LIMBS], point_y[P256_LIMBS], point_z[P256_LIMBS];
|
|
BN_ULONG x_ret[P256_LIMBS], y_ret[P256_LIMBS];
|
|
|
|
if (EC_POINT_is_at_infinity(group, point)) {
|
|
ECerr(EC_F_ECP_NISTZ256_GET_AFFINE, EC_R_POINT_AT_INFINITY);
|
|
return 0;
|
|
}
|
|
|
|
if (!ecp_nistz256_bignum_to_field_elem(point_x, &point->X) ||
|
|
!ecp_nistz256_bignum_to_field_elem(point_y, &point->Y) ||
|
|
!ecp_nistz256_bignum_to_field_elem(point_z, &point->Z)) {
|
|
ECerr(EC_F_ECP_NISTZ256_GET_AFFINE, EC_R_COORDINATES_OUT_OF_RANGE);
|
|
return 0;
|
|
}
|
|
|
|
ecp_nistz256_mod_inverse(z_inv3, point_z);
|
|
ecp_nistz256_sqr_mont(z_inv2, z_inv3);
|
|
ecp_nistz256_mul_mont(x_aff, z_inv2, point_x);
|
|
|
|
if (x != NULL) {
|
|
ecp_nistz256_from_mont(x_ret, x_aff);
|
|
if (!ecp_nistz256_set_words(x, x_ret))
|
|
return 0;
|
|
}
|
|
|
|
if (y != NULL) {
|
|
ecp_nistz256_mul_mont(z_inv3, z_inv3, z_inv2);
|
|
ecp_nistz256_mul_mont(y_aff, z_inv3, point_y);
|
|
ecp_nistz256_from_mont(y_ret, y_aff);
|
|
if (!ecp_nistz256_set_words(y, y_ret))
|
|
return 0;
|
|
}
|
|
|
|
return 1;
|
|
}
|
|
|
|
static EC_PRE_COMP *ecp_nistz256_pre_comp_new(const EC_GROUP *group)
|
|
{
|
|
EC_PRE_COMP *ret = NULL;
|
|
|
|
if (!group)
|
|
return NULL;
|
|
|
|
ret = (EC_PRE_COMP *)OPENSSL_malloc(sizeof(EC_PRE_COMP));
|
|
|
|
if (!ret) {
|
|
ECerr(EC_F_ECP_NISTZ256_PRE_COMP_NEW, ERR_R_MALLOC_FAILURE);
|
|
return ret;
|
|
}
|
|
|
|
ret->group = group;
|
|
ret->w = 6; /* default */
|
|
ret->precomp = NULL;
|
|
ret->precomp_storage = NULL;
|
|
ret->references = 1;
|
|
return ret;
|
|
}
|
|
|
|
static void *ecp_nistz256_pre_comp_dup(void *src_)
|
|
{
|
|
EC_PRE_COMP *src = src_;
|
|
|
|
/* no need to actually copy, these objects never change! */
|
|
CRYPTO_add(&src->references, 1, CRYPTO_LOCK_EC_PRE_COMP);
|
|
|
|
return src_;
|
|
}
|
|
|
|
static void ecp_nistz256_pre_comp_free(void *pre_)
|
|
{
|
|
int i;
|
|
EC_PRE_COMP *pre = pre_;
|
|
|
|
if (!pre)
|
|
return;
|
|
|
|
i = CRYPTO_add(&pre->references, -1, CRYPTO_LOCK_EC_PRE_COMP);
|
|
if (i > 0)
|
|
return;
|
|
|
|
if (pre->precomp_storage)
|
|
OPENSSL_free(pre->precomp_storage);
|
|
|
|
OPENSSL_free(pre);
|
|
}
|
|
|
|
static void ecp_nistz256_pre_comp_clear_free(void *pre_)
|
|
{
|
|
int i;
|
|
EC_PRE_COMP *pre = pre_;
|
|
|
|
if (!pre)
|
|
return;
|
|
|
|
i = CRYPTO_add(&pre->references, -1, CRYPTO_LOCK_EC_PRE_COMP);
|
|
if (i > 0)
|
|
return;
|
|
|
|
if (pre->precomp_storage) {
|
|
OPENSSL_cleanse(pre->precomp,
|
|
32 * sizeof(unsigned char) * (1 << pre->w) * 2 * 37);
|
|
OPENSSL_free(pre->precomp_storage);
|
|
}
|
|
OPENSSL_cleanse(pre, sizeof *pre);
|
|
OPENSSL_free(pre);
|
|
}
|
|
|
|
static int ecp_nistz256_window_have_precompute_mult(const EC_GROUP *group)
|
|
{
|
|
/* There is a hard-coded table for the default generator. */
|
|
const EC_POINT *generator = EC_GROUP_get0_generator(group);
|
|
if (generator != NULL && ecp_nistz256_is_affine_G(generator)) {
|
|
/* There is a hard-coded table for the default generator. */
|
|
return 1;
|
|
}
|
|
|
|
return EC_EX_DATA_get_data(group->extra_data, ecp_nistz256_pre_comp_dup,
|
|
ecp_nistz256_pre_comp_free,
|
|
ecp_nistz256_pre_comp_clear_free) != NULL;
|
|
}
|
|
|
|
const EC_METHOD *EC_GFp_nistz256_method(void)
|
|
{
|
|
static const EC_METHOD ret = {
|
|
EC_FLAGS_DEFAULT_OCT,
|
|
NID_X9_62_prime_field,
|
|
ec_GFp_mont_group_init,
|
|
ec_GFp_mont_group_finish,
|
|
ec_GFp_mont_group_clear_finish,
|
|
ec_GFp_mont_group_copy,
|
|
ec_GFp_mont_group_set_curve,
|
|
ec_GFp_simple_group_get_curve,
|
|
ec_GFp_simple_group_get_degree,
|
|
ec_GFp_simple_group_check_discriminant,
|
|
ec_GFp_simple_point_init,
|
|
ec_GFp_simple_point_finish,
|
|
ec_GFp_simple_point_clear_finish,
|
|
ec_GFp_simple_point_copy,
|
|
ec_GFp_simple_point_set_to_infinity,
|
|
ec_GFp_simple_set_Jprojective_coordinates_GFp,
|
|
ec_GFp_simple_get_Jprojective_coordinates_GFp,
|
|
ec_GFp_simple_point_set_affine_coordinates,
|
|
ecp_nistz256_get_affine,
|
|
0, 0, 0,
|
|
ec_GFp_simple_add,
|
|
ec_GFp_simple_dbl,
|
|
ec_GFp_simple_invert,
|
|
ec_GFp_simple_is_at_infinity,
|
|
ec_GFp_simple_is_on_curve,
|
|
ec_GFp_simple_cmp,
|
|
ec_GFp_simple_make_affine,
|
|
ec_GFp_simple_points_make_affine,
|
|
ecp_nistz256_points_mul, /* mul */
|
|
ecp_nistz256_mult_precompute, /* precompute_mult */
|
|
ecp_nistz256_window_have_precompute_mult, /* have_precompute_mult */
|
|
ec_GFp_mont_field_mul,
|
|
ec_GFp_mont_field_sqr,
|
|
0, /* field_div */
|
|
ec_GFp_mont_field_encode,
|
|
ec_GFp_mont_field_decode,
|
|
ec_GFp_mont_field_set_to_one
|
|
};
|
|
|
|
return &ret;
|
|
}
|