1524 lines
51 KiB
C
1524 lines
51 KiB
C
/*
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* Copyright 2014-2020 The OpenSSL Project Authors. All Rights Reserved.
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* Copyright (c) 2014, Intel Corporation. All Rights Reserved.
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* Copyright (c) 2015, CloudFlare, Inc.
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*
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* Licensed under the OpenSSL license (the "License"). You may not use
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* this file except in compliance with the License. You can obtain a copy
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* in the file LICENSE in the source distribution or at
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* https://www.openssl.org/source/license.html
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*
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* Originally written by Shay Gueron (1, 2), and Vlad Krasnov (1, 3)
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* (1) Intel Corporation, Israel Development Center, Haifa, Israel
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* (2) University of Haifa, Israel
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* (3) CloudFlare, Inc.
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*
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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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#include <string.h>
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#include "internal/cryptlib.h"
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#include "crypto/bn.h"
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#include "ec_local.h"
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#include "internal/refcount.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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struct nistz256_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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CRYPTO_REF_COUNT references;
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CRYPTO_RWLOCK *lock;
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};
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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_scatter_w5(P256_POINT *val,
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const P256_POINT *in_t, int idx);
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void ecp_nistz256_gather_w5(P256_POINT *val,
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const P256_POINT *in_t, int idx);
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void ecp_nistz256_scatter_w7(P256_POINT_AFFINE *val,
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const P256_POINT_AFFINE *in_t, int idx);
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void ecp_nistz256_gather_w7(P256_POINT_AFFINE *val,
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const P256_POINT_AFFINE *in_t, int idx);
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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 NISTZ256_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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extern const PRECOMP256_ROW ecp_nistz256_precomputed[37];
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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 = 0-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_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 = bn_get_words(z);
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if (bn_get_top(z) == (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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/*
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* For reference, this macro is used only when new ecp_nistz256 assembly
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* module is being developed. For example, configure with
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* -DECP_NISTZ256_REFERENCE_IMPLEMENTATION and implement only functions
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* performing simplest arithmetic operations on 256-bit vectors. Then
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* work on implementation of higher-level functions performing point
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* operations. Then remove ECP_NISTZ256_REFERENCE_IMPLEMENTATION
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* and never define it again. (The correct macro denoting presence of
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* ecp_nistz256 module is ECP_NISTZ256_ASM.)
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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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* The formulae are incorrect if the points are equal so we check for
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* this and do doubling if this happens.
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*
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* Points here are in Jacobian projective coordinates (Xi, Yi, Zi)
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* that are bound to the affine coordinates (xi, yi) by the following
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* equations:
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* - xi = Xi / (Zi)^2
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* - y1 = Yi / (Zi)^3
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*
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* For the sake of optimization, the algorithm operates over
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* intermediate variables U1, U2 and S1, S2 that are derived from
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* the projective coordinates:
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* - U1 = X1 * (Z2)^2 ; U2 = X2 * (Z1)^2
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* - S1 = Y1 * (Z2)^3 ; S2 = Y2 * (Z1)^3
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*
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* It is easy to prove that is_equal(U1, U2) implies that the affine
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* x-coordinates are equal, or either point is at infinity.
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* Likewise is_equal(S1, S2) implies that the affine y-coordinates are
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* equal, or either point is at infinity.
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*
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* The special case of either point being the point at infinity (Z1 or Z2
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* is zero), is handled separately later on in this function, so we avoid
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* jumping to point_double here in those special cases.
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*
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* When both points are inverse of each other, we know that the affine
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* x-coordinates are equal, and the y-coordinates have different sign.
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* Therefore since U1 = U2, we know H = 0, and therefore Z3 = H*Z1*Z2
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* will equal 0, thus the result is infinity, if we simply let this
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* function continue normally.
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*
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* We use bitwise operations to avoid potential side-channels introduced by
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* the short-circuiting behaviour of boolean operators.
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*/
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if (is_equal(U1, U2) & ~in1infty & ~in2infty & is_equal(S1, S2)) {
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/*
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* This is obviously not constant-time but it should never happen during
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* single point multiplication, so there is no timing leak for ECDH or
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* ECDSA signing.
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*/
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ecp_nistz256_point_double(r, a);
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return;
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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);
|
|
ecp_nistz256_mul_mont(res_y, R, res_y);
|
|
ecp_nistz256_sub(res_y, res_y, S2);
|
|
|
|
copy_conditional(res_x, in2_x, in1infty);
|
|
copy_conditional(res_y, in2_y, in1infty);
|
|
copy_conditional(res_z, in2_z, in1infty);
|
|
|
|
copy_conditional(res_x, in1_x, in2infty);
|
|
copy_conditional(res_y, in1_y, in2infty);
|
|
copy_conditional(res_z, in1_z, in2infty);
|
|
|
|
memcpy(r->X, res_x, sizeof(res_x));
|
|
memcpy(r->Y, res_y, sizeof(res_y));
|
|
memcpy(r->Z, res_z, sizeof(res_z));
|
|
}
|
|
|
|
/* Point addition when b is known to be affine: r = a+b */
|
|
static void ecp_nistz256_point_add_affine(P256_POINT *r,
|
|
const P256_POINT *a,
|
|
const P256_POINT_AFFINE *b)
|
|
{
|
|
BN_ULONG U2[P256_LIMBS], S2[P256_LIMBS];
|
|
BN_ULONG Z1sqr[P256_LIMBS];
|
|
BN_ULONG H[P256_LIMBS], R[P256_LIMBS];
|
|
BN_ULONG Hsqr[P256_LIMBS];
|
|
BN_ULONG Rsqr[P256_LIMBS];
|
|
BN_ULONG Hcub[P256_LIMBS];
|
|
|
|
BN_ULONG res_x[P256_LIMBS];
|
|
BN_ULONG res_y[P256_LIMBS];
|
|
BN_ULONG res_z[P256_LIMBS];
|
|
|
|
BN_ULONG in1infty, in2infty;
|
|
|
|
const BN_ULONG *in1_x = a->X;
|
|
const BN_ULONG *in1_y = a->Y;
|
|
const BN_ULONG *in1_z = a->Z;
|
|
|
|
const BN_ULONG *in2_x = b->X;
|
|
const BN_ULONG *in2_y = b->Y;
|
|
|
|
/*
|
|
* Infinity in encoded as (,,0)
|
|
*/
|
|
in1infty = (in1_z[0] | in1_z[1] | in1_z[2] | in1_z[3]);
|
|
if (P256_LIMBS == 8)
|
|
in1infty |= (in1_z[4] | in1_z[5] | in1_z[6] | in1_z[7]);
|
|
|
|
/*
|
|
* In affine representation we encode infinity as (0,0), which is
|
|
* not on the curve, so it is OK
|
|
*/
|
|
in2infty = (in2_x[0] | in2_x[1] | in2_x[2] | in2_x[3] |
|
|
in2_y[0] | in2_y[1] | in2_y[2] | in2_y[3]);
|
|
if (P256_LIMBS == 8)
|
|
in2infty |= (in2_x[4] | in2_x[5] | in2_x[6] | in2_x[7] |
|
|
in2_y[4] | in2_y[5] | in2_y[6] | in2_y[7]);
|
|
|
|
in1infty = is_zero(in1infty);
|
|
in2infty = is_zero(in2infty);
|
|
|
|
ecp_nistz256_sqr_mont(Z1sqr, in1_z); /* Z1^2 */
|
|
|
|
ecp_nistz256_mul_mont(U2, in2_x, Z1sqr); /* U2 = X2*Z1^2 */
|
|
ecp_nistz256_sub(H, U2, in1_x); /* H = U2 - U1 */
|
|
|
|
ecp_nistz256_mul_mont(S2, Z1sqr, in1_z); /* S2 = Z1^3 */
|
|
|
|
ecp_nistz256_mul_mont(res_z, H, in1_z); /* Z3 = H*Z1*Z2 */
|
|
|
|
ecp_nistz256_mul_mont(S2, S2, in2_y); /* S2 = Y2*Z1^3 */
|
|
ecp_nistz256_sub(R, S2, in1_y); /* R = S2 - S1 */
|
|
|
|
ecp_nistz256_sqr_mont(Hsqr, H); /* H^2 */
|
|
ecp_nistz256_sqr_mont(Rsqr, R); /* R^2 */
|
|
ecp_nistz256_mul_mont(Hcub, Hsqr, H); /* H^3 */
|
|
|
|
ecp_nistz256_mul_mont(U2, in1_x, Hsqr); /* U1*H^2 */
|
|
ecp_nistz256_mul_by_2(Hsqr, U2); /* 2*U1*H^2 */
|
|
|
|
ecp_nistz256_sub(res_x, Rsqr, Hsqr);
|
|
ecp_nistz256_sub(res_x, res_x, Hcub);
|
|
ecp_nistz256_sub(H, U2, res_x);
|
|
|
|
ecp_nistz256_mul_mont(S2, in1_y, Hcub);
|
|
ecp_nistz256_mul_mont(H, H, R);
|
|
ecp_nistz256_sub(res_y, H, S2);
|
|
|
|
copy_conditional(res_x, in2_x, in1infty);
|
|
copy_conditional(res_x, in1_x, in2infty);
|
|
|
|
copy_conditional(res_y, in2_y, in1infty);
|
|
copy_conditional(res_y, in1_y, in2infty);
|
|
|
|
copy_conditional(res_z, ONE, in1infty);
|
|
copy_conditional(res_z, in1_z, in2infty);
|
|
|
|
memcpy(r->X, res_x, sizeof(res_x));
|
|
memcpy(r->Y, res_y, sizeof(res_y));
|
|
memcpy(r->Z, res_z, sizeof(res_z));
|
|
}
|
|
#endif
|
|
|
|
/* r = in^-1 mod p */
|
|
static void ecp_nistz256_mod_inverse(BN_ULONG r[P256_LIMBS],
|
|
const BN_ULONG in[P256_LIMBS])
|
|
{
|
|
/*
|
|
* The poly is ffffffff 00000001 00000000 00000000 00000000 ffffffff
|
|
* ffffffff ffffffff We use FLT and used poly-2 as exponent
|
|
*/
|
|
BN_ULONG p2[P256_LIMBS];
|
|
BN_ULONG p4[P256_LIMBS];
|
|
BN_ULONG p8[P256_LIMBS];
|
|
BN_ULONG p16[P256_LIMBS];
|
|
BN_ULONG p32[P256_LIMBS];
|
|
BN_ULONG res[P256_LIMBS];
|
|
int i;
|
|
|
|
ecp_nistz256_sqr_mont(res, in);
|
|
ecp_nistz256_mul_mont(p2, res, in); /* 3*p */
|
|
|
|
ecp_nistz256_sqr_mont(res, p2);
|
|
ecp_nistz256_sqr_mont(res, res);
|
|
ecp_nistz256_mul_mont(p4, res, p2); /* f*p */
|
|
|
|
ecp_nistz256_sqr_mont(res, p4);
|
|
ecp_nistz256_sqr_mont(res, res);
|
|
ecp_nistz256_sqr_mont(res, res);
|
|
ecp_nistz256_sqr_mont(res, res);
|
|
ecp_nistz256_mul_mont(p8, res, p4); /* ff*p */
|
|
|
|
ecp_nistz256_sqr_mont(res, p8);
|
|
for (i = 0; i < 7; i++)
|
|
ecp_nistz256_sqr_mont(res, res);
|
|
ecp_nistz256_mul_mont(p16, res, p8); /* ffff*p */
|
|
|
|
ecp_nistz256_sqr_mont(res, p16);
|
|
for (i = 0; i < 15; i++)
|
|
ecp_nistz256_sqr_mont(res, res);
|
|
ecp_nistz256_mul_mont(p32, res, p16); /* ffffffff*p */
|
|
|
|
ecp_nistz256_sqr_mont(res, p32);
|
|
for (i = 0; i < 31; i++)
|
|
ecp_nistz256_sqr_mont(res, res);
|
|
ecp_nistz256_mul_mont(res, res, in);
|
|
|
|
for (i = 0; i < 32 * 4; i++)
|
|
ecp_nistz256_sqr_mont(res, res);
|
|
ecp_nistz256_mul_mont(res, res, p32);
|
|
|
|
for (i = 0; i < 32; i++)
|
|
ecp_nistz256_sqr_mont(res, res);
|
|
ecp_nistz256_mul_mont(res, res, p32);
|
|
|
|
for (i = 0; i < 16; i++)
|
|
ecp_nistz256_sqr_mont(res, res);
|
|
ecp_nistz256_mul_mont(res, res, p16);
|
|
|
|
for (i = 0; i < 8; i++)
|
|
ecp_nistz256_sqr_mont(res, res);
|
|
ecp_nistz256_mul_mont(res, res, p8);
|
|
|
|
ecp_nistz256_sqr_mont(res, res);
|
|
ecp_nistz256_sqr_mont(res, res);
|
|
ecp_nistz256_sqr_mont(res, res);
|
|
ecp_nistz256_sqr_mont(res, res);
|
|
ecp_nistz256_mul_mont(res, res, p4);
|
|
|
|
ecp_nistz256_sqr_mont(res, res);
|
|
ecp_nistz256_sqr_mont(res, res);
|
|
ecp_nistz256_mul_mont(res, res, p2);
|
|
|
|
ecp_nistz256_sqr_mont(res, res);
|
|
ecp_nistz256_sqr_mont(res, res);
|
|
ecp_nistz256_mul_mont(res, res, in);
|
|
|
|
memcpy(r, res, sizeof(res));
|
|
}
|
|
|
|
/*
|
|
* ecp_nistz256_bignum_to_field_elem copies the contents of |in| to |out| and
|
|
* returns one if it fits. Otherwise it returns zero.
|
|
*/
|
|
__owur static int ecp_nistz256_bignum_to_field_elem(BN_ULONG out[P256_LIMBS],
|
|
const BIGNUM *in)
|
|
{
|
|
return bn_copy_words(out, in, P256_LIMBS);
|
|
}
|
|
|
|
/* r = sum(scalar[i]*point[i]) */
|
|
__owur static int ecp_nistz256_windowed_mul(const EC_GROUP *group,
|
|
P256_POINT *r,
|
|
const BIGNUM **scalar,
|
|
const EC_POINT **point,
|
|
size_t num, BN_CTX *ctx)
|
|
{
|
|
size_t i;
|
|
int j, ret = 0;
|
|
unsigned int idx;
|
|
unsigned char (*p_str)[33] = NULL;
|
|
const unsigned int window_size = 5;
|
|
const unsigned int mask = (1 << (window_size + 1)) - 1;
|
|
unsigned int wvalue;
|
|
P256_POINT *temp; /* place for 5 temporary points */
|
|
const BIGNUM **scalars = NULL;
|
|
P256_POINT (*table)[16] = NULL;
|
|
void *table_storage = NULL;
|
|
|
|
if ((num * 16 + 6) > OPENSSL_MALLOC_MAX_NELEMS(P256_POINT)
|
|
|| (table_storage =
|
|
OPENSSL_malloc((num * 16 + 5) * sizeof(P256_POINT) + 64)) == NULL
|
|
|| (p_str =
|
|
OPENSSL_malloc(num * 33 * sizeof(unsigned char))) == NULL
|
|
|| (scalars = OPENSSL_malloc(num * sizeof(BIGNUM *))) == NULL) {
|
|
ECerr(EC_F_ECP_NISTZ256_WINDOWED_MUL, ERR_R_MALLOC_FAILURE);
|
|
goto err;
|
|
}
|
|
|
|
table = (void *)ALIGNPTR(table_storage, 64);
|
|
temp = (P256_POINT *)(table + num);
|
|
|
|
for (i = 0; i < num; i++) {
|
|
P256_POINT *row = table[i];
|
|
|
|
/* This is an unusual input, we don't guarantee constant-timeness. */
|
|
if ((BN_num_bits(scalar[i]) > 256) || BN_is_negative(scalar[i])) {
|
|
BIGNUM *mod;
|
|
|
|
if ((mod = BN_CTX_get(ctx)) == NULL)
|
|
goto err;
|
|
if (!BN_nnmod(mod, scalar[i], group->order, ctx)) {
|
|
ECerr(EC_F_ECP_NISTZ256_WINDOWED_MUL, ERR_R_BN_LIB);
|
|
goto err;
|
|
}
|
|
scalars[i] = mod;
|
|
} else
|
|
scalars[i] = scalar[i];
|
|
|
|
for (j = 0; j < bn_get_top(scalars[i]) * BN_BYTES; j += BN_BYTES) {
|
|
BN_ULONG d = bn_get_words(scalars[i])[j / BN_BYTES];
|
|
|
|
p_str[i][j + 0] = (unsigned char)d;
|
|
p_str[i][j + 1] = (unsigned char)(d >> 8);
|
|
p_str[i][j + 2] = (unsigned char)(d >> 16);
|
|
p_str[i][j + 3] = (unsigned char)(d >>= 24);
|
|
if (BN_BYTES == 8) {
|
|
d >>= 8;
|
|
p_str[i][j + 4] = (unsigned char)d;
|
|
p_str[i][j + 5] = (unsigned char)(d >> 8);
|
|
p_str[i][j + 6] = (unsigned char)(d >> 16);
|
|
p_str[i][j + 7] = (unsigned char)(d >> 24);
|
|
}
|
|
}
|
|
for (; j < 33; j++)
|
|
p_str[i][j] = 0;
|
|
|
|
if (!ecp_nistz256_bignum_to_field_elem(temp[0].X, point[i]->X)
|
|
|| !ecp_nistz256_bignum_to_field_elem(temp[0].Y, point[i]->Y)
|
|
|| !ecp_nistz256_bignum_to_field_elem(temp[0].Z, point[i]->Z)) {
|
|
ECerr(EC_F_ECP_NISTZ256_WINDOWED_MUL,
|
|
EC_R_COORDINATES_OUT_OF_RANGE);
|
|
goto err;
|
|
}
|
|
|
|
/*
|
|
* row[0] is implicitly (0,0,0) (the point at infinity), therefore it
|
|
* is not stored. All other values are actually stored with an offset
|
|
* of -1 in table.
|
|
*/
|
|
|
|
ecp_nistz256_scatter_w5 (row, &temp[0], 1);
|
|
ecp_nistz256_point_double(&temp[1], &temp[0]); /*1+1=2 */
|
|
ecp_nistz256_scatter_w5 (row, &temp[1], 2);
|
|
ecp_nistz256_point_add (&temp[2], &temp[1], &temp[0]); /*2+1=3 */
|
|
ecp_nistz256_scatter_w5 (row, &temp[2], 3);
|
|
ecp_nistz256_point_double(&temp[1], &temp[1]); /*2*2=4 */
|
|
ecp_nistz256_scatter_w5 (row, &temp[1], 4);
|
|
ecp_nistz256_point_double(&temp[2], &temp[2]); /*2*3=6 */
|
|
ecp_nistz256_scatter_w5 (row, &temp[2], 6);
|
|
ecp_nistz256_point_add (&temp[3], &temp[1], &temp[0]); /*4+1=5 */
|
|
ecp_nistz256_scatter_w5 (row, &temp[3], 5);
|
|
ecp_nistz256_point_add (&temp[4], &temp[2], &temp[0]); /*6+1=7 */
|
|
ecp_nistz256_scatter_w5 (row, &temp[4], 7);
|
|
ecp_nistz256_point_double(&temp[1], &temp[1]); /*2*4=8 */
|
|
ecp_nistz256_scatter_w5 (row, &temp[1], 8);
|
|
ecp_nistz256_point_double(&temp[2], &temp[2]); /*2*6=12 */
|
|
ecp_nistz256_scatter_w5 (row, &temp[2], 12);
|
|
ecp_nistz256_point_double(&temp[3], &temp[3]); /*2*5=10 */
|
|
ecp_nistz256_scatter_w5 (row, &temp[3], 10);
|
|
ecp_nistz256_point_double(&temp[4], &temp[4]); /*2*7=14 */
|
|
ecp_nistz256_scatter_w5 (row, &temp[4], 14);
|
|
ecp_nistz256_point_add (&temp[2], &temp[2], &temp[0]); /*12+1=13*/
|
|
ecp_nistz256_scatter_w5 (row, &temp[2], 13);
|
|
ecp_nistz256_point_add (&temp[3], &temp[3], &temp[0]); /*10+1=11*/
|
|
ecp_nistz256_scatter_w5 (row, &temp[3], 11);
|
|
ecp_nistz256_point_add (&temp[4], &temp[4], &temp[0]); /*14+1=15*/
|
|
ecp_nistz256_scatter_w5 (row, &temp[4], 15);
|
|
ecp_nistz256_point_add (&temp[2], &temp[1], &temp[0]); /*8+1=9 */
|
|
ecp_nistz256_scatter_w5 (row, &temp[2], 9);
|
|
ecp_nistz256_point_double(&temp[1], &temp[1]); /*2*8=16 */
|
|
ecp_nistz256_scatter_w5 (row, &temp[1], 16);
|
|
}
|
|
|
|
idx = 255;
|
|
|
|
wvalue = p_str[0][(idx - 1) / 8];
|
|
wvalue = (wvalue >> ((idx - 1) % 8)) & mask;
|
|
|
|
/*
|
|
* We gather to temp[0], because we know it's position relative
|
|
* to table
|
|
*/
|
|
ecp_nistz256_gather_w5(&temp[0], table[0], _booth_recode_w5(wvalue) >> 1);
|
|
memcpy(r, &temp[0], sizeof(temp[0]));
|
|
|
|
while (idx >= 5) {
|
|
for (i = (idx == 255 ? 1 : 0); i < num; i++) {
|
|
unsigned int off = (idx - 1) / 8;
|
|
|
|
wvalue = p_str[i][off] | p_str[i][off + 1] << 8;
|
|
wvalue = (wvalue >> ((idx - 1) % 8)) & mask;
|
|
|
|
wvalue = _booth_recode_w5(wvalue);
|
|
|
|
ecp_nistz256_gather_w5(&temp[0], table[i], wvalue >> 1);
|
|
|
|
ecp_nistz256_neg(temp[1].Y, temp[0].Y);
|
|
copy_conditional(temp[0].Y, temp[1].Y, (wvalue & 1));
|
|
|
|
ecp_nistz256_point_add(r, r, &temp[0]);
|
|
}
|
|
|
|
idx -= window_size;
|
|
|
|
ecp_nistz256_point_double(r, r);
|
|
ecp_nistz256_point_double(r, r);
|
|
ecp_nistz256_point_double(r, r);
|
|
ecp_nistz256_point_double(r, r);
|
|
ecp_nistz256_point_double(r, r);
|
|
}
|
|
|
|
/* Final window */
|
|
for (i = 0; i < num; i++) {
|
|
wvalue = p_str[i][0];
|
|
wvalue = (wvalue << 1) & mask;
|
|
|
|
wvalue = _booth_recode_w5(wvalue);
|
|
|
|
ecp_nistz256_gather_w5(&temp[0], table[i], wvalue >> 1);
|
|
|
|
ecp_nistz256_neg(temp[1].Y, temp[0].Y);
|
|
copy_conditional(temp[0].Y, temp[1].Y, wvalue & 1);
|
|
|
|
ecp_nistz256_point_add(r, r, &temp[0]);
|
|
}
|
|
|
|
ret = 1;
|
|
err:
|
|
OPENSSL_free(table_storage);
|
|
OPENSSL_free(p_str);
|
|
OPENSSL_free(scalars);
|
|
return ret;
|
|
}
|
|
|
|
/* Coordinates of G, for which we have precomputed tables */
|
|
static const BN_ULONG def_xG[P256_LIMBS] = {
|
|
TOBN(0x79e730d4, 0x18a9143c), TOBN(0x75ba95fc, 0x5fedb601),
|
|
TOBN(0x79fb732b, 0x77622510), TOBN(0x18905f76, 0xa53755c6)
|
|
};
|
|
|
|
static const BN_ULONG def_yG[P256_LIMBS] = {
|
|
TOBN(0xddf25357, 0xce95560a), TOBN(0x8b4ab8e4, 0xba19e45c),
|
|
TOBN(0xd2e88688, 0xdd21f325), TOBN(0x8571ff18, 0x25885d85)
|
|
};
|
|
|
|
/*
|
|
* ecp_nistz256_is_affine_G returns one if |generator| is the standard, P-256
|
|
* generator.
|
|
*/
|
|
static int ecp_nistz256_is_affine_G(const EC_POINT *generator)
|
|
{
|
|
return (bn_get_top(generator->X) == P256_LIMBS) &&
|
|
(bn_get_top(generator->Y) == P256_LIMBS) &&
|
|
is_equal(bn_get_words(generator->X), def_xG) &&
|
|
is_equal(bn_get_words(generator->Y), def_yG) &&
|
|
is_one(generator->Z);
|
|
}
|
|
|
|
__owur static int ecp_nistz256_mult_precompute(EC_GROUP *group, BN_CTX *ctx)
|
|
{
|
|
/*
|
|
* We precompute a table for a Booth encoded exponent (wNAF) based
|
|
* computation. Each table holds 64 values for safe access, with an
|
|
* implicit value of infinity at index zero. We use window of size 7, and
|
|
* therefore require ceil(256/7) = 37 tables.
|
|
*/
|
|
const BIGNUM *order;
|
|
EC_POINT *P = NULL, *T = NULL;
|
|
const EC_POINT *generator;
|
|
NISTZ256_PRE_COMP *pre_comp;
|
|
BN_CTX *new_ctx = NULL;
|
|
int i, j, k, ret = 0;
|
|
size_t w;
|
|
|
|
PRECOMP256_ROW *preComputedTable = NULL;
|
|
unsigned char *precomp_storage = NULL;
|
|
|
|
/* if there is an old NISTZ256_PRE_COMP object, throw it away */
|
|
EC_pre_comp_free(group);
|
|
generator = EC_GROUP_get0_generator(group);
|
|
if (generator == NULL) {
|
|
ECerr(EC_F_ECP_NISTZ256_MULT_PRECOMPUTE, EC_R_UNDEFINED_GENERATOR);
|
|
return 0;
|
|
}
|
|
|
|
if (ecp_nistz256_is_affine_G(generator)) {
|
|
/*
|
|
* No need to calculate tables for the standard generator because we
|
|
* have them statically.
|
|
*/
|
|
return 1;
|
|
}
|
|
|
|
if ((pre_comp = ecp_nistz256_pre_comp_new(group)) == NULL)
|
|
return 0;
|
|
|
|
if (ctx == NULL) {
|
|
ctx = new_ctx = BN_CTX_new();
|
|
if (ctx == NULL)
|
|
goto err;
|
|
}
|
|
|
|
BN_CTX_start(ctx);
|
|
|
|
order = EC_GROUP_get0_order(group);
|
|
if (order == NULL)
|
|
goto err;
|
|
|
|
if (BN_is_zero(order)) {
|
|
ECerr(EC_F_ECP_NISTZ256_MULT_PRECOMPUTE, EC_R_UNKNOWN_ORDER);
|
|
goto err;
|
|
}
|
|
|
|
w = 7;
|
|
|
|
if ((precomp_storage =
|
|
OPENSSL_malloc(37 * 64 * sizeof(P256_POINT_AFFINE) + 64)) == NULL) {
|
|
ECerr(EC_F_ECP_NISTZ256_MULT_PRECOMPUTE, ERR_R_MALLOC_FAILURE);
|
|
goto err;
|
|
}
|
|
|
|
preComputedTable = (void *)ALIGNPTR(precomp_storage, 64);
|
|
|
|
P = EC_POINT_new(group);
|
|
T = EC_POINT_new(group);
|
|
if (P == NULL || T == NULL)
|
|
goto err;
|
|
|
|
/*
|
|
* The zero entry is implicitly infinity, and we skip it, storing other
|
|
* values with -1 offset.
|
|
*/
|
|
if (!EC_POINT_copy(T, generator))
|
|
goto err;
|
|
|
|
for (k = 0; k < 64; k++) {
|
|
if (!EC_POINT_copy(P, T))
|
|
goto err;
|
|
for (j = 0; j < 37; j++) {
|
|
P256_POINT_AFFINE temp;
|
|
/*
|
|
* It would be faster to use EC_POINTs_make_affine and
|
|
* make multiple points affine at the same time.
|
|
*/
|
|
if (!EC_POINT_make_affine(group, P, ctx))
|
|
goto err;
|
|
if (!ecp_nistz256_bignum_to_field_elem(temp.X, P->X) ||
|
|
!ecp_nistz256_bignum_to_field_elem(temp.Y, P->Y)) {
|
|
ECerr(EC_F_ECP_NISTZ256_MULT_PRECOMPUTE,
|
|
EC_R_COORDINATES_OUT_OF_RANGE);
|
|
goto err;
|
|
}
|
|
ecp_nistz256_scatter_w7(preComputedTable[j], &temp, k);
|
|
for (i = 0; i < 7; i++) {
|
|
if (!EC_POINT_dbl(group, P, P, ctx))
|
|
goto err;
|
|
}
|
|
}
|
|
if (!EC_POINT_add(group, T, T, generator, ctx))
|
|
goto err;
|
|
}
|
|
|
|
pre_comp->group = group;
|
|
pre_comp->w = w;
|
|
pre_comp->precomp = preComputedTable;
|
|
pre_comp->precomp_storage = precomp_storage;
|
|
precomp_storage = NULL;
|
|
SETPRECOMP(group, nistz256, pre_comp);
|
|
pre_comp = NULL;
|
|
ret = 1;
|
|
|
|
err:
|
|
BN_CTX_end(ctx);
|
|
BN_CTX_free(new_ctx);
|
|
|
|
EC_nistz256_pre_comp_free(pre_comp);
|
|
OPENSSL_free(precomp_storage);
|
|
EC_POINT_free(P);
|
|
EC_POINT_free(T);
|
|
return ret;
|
|
}
|
|
|
|
__owur static int ecp_nistz256_set_from_affine(EC_POINT *out, const EC_GROUP *group,
|
|
const P256_POINT_AFFINE *in,
|
|
BN_CTX *ctx)
|
|
{
|
|
int ret = 0;
|
|
|
|
if ((ret = bn_set_words(out->X, in->X, P256_LIMBS))
|
|
&& (ret = bn_set_words(out->Y, in->Y, P256_LIMBS))
|
|
&& (ret = bn_set_words(out->Z, ONE, P256_LIMBS)))
|
|
out->Z_is_one = 1;
|
|
|
|
return ret;
|
|
}
|
|
|
|
/* r = scalar*G + sum(scalars[i]*points[i]) */
|
|
__owur static int ecp_nistz256_points_mul(const EC_GROUP *group,
|
|
EC_POINT *r,
|
|
const BIGNUM *scalar,
|
|
size_t num,
|
|
const EC_POINT *points[],
|
|
const BIGNUM *scalars[], BN_CTX *ctx)
|
|
{
|
|
int i = 0, ret = 0, no_precomp_for_generator = 0, p_is_infinity = 0;
|
|
unsigned char p_str[33] = { 0 };
|
|
const PRECOMP256_ROW *preComputedTable = NULL;
|
|
const NISTZ256_PRE_COMP *pre_comp = NULL;
|
|
const EC_POINT *generator = NULL;
|
|
const BIGNUM **new_scalars = NULL;
|
|
const EC_POINT **new_points = NULL;
|
|
unsigned int idx = 0;
|
|
const unsigned int window_size = 7;
|
|
const unsigned int mask = (1 << (window_size + 1)) - 1;
|
|
unsigned int wvalue;
|
|
ALIGN32 union {
|
|
P256_POINT p;
|
|
P256_POINT_AFFINE a;
|
|
} t, p;
|
|
BIGNUM *tmp_scalar;
|
|
|
|
if ((num + 1) == 0 || (num + 1) > OPENSSL_MALLOC_MAX_NELEMS(void *)) {
|
|
ECerr(EC_F_ECP_NISTZ256_POINTS_MUL, ERR_R_MALLOC_FAILURE);
|
|
return 0;
|
|
}
|
|
|
|
BN_CTX_start(ctx);
|
|
|
|
if (scalar) {
|
|
generator = EC_GROUP_get0_generator(group);
|
|
if (generator == NULL) {
|
|
ECerr(EC_F_ECP_NISTZ256_POINTS_MUL, EC_R_UNDEFINED_GENERATOR);
|
|
goto err;
|
|
}
|
|
|
|
/* look if we can use precomputed multiples of generator */
|
|
pre_comp = group->pre_comp.nistz256;
|
|
|
|
if (pre_comp) {
|
|
/*
|
|
* If there is a precomputed table for the generator, check that
|
|
* it was generated with the same generator.
|
|
*/
|
|
EC_POINT *pre_comp_generator = EC_POINT_new(group);
|
|
if (pre_comp_generator == NULL)
|
|
goto err;
|
|
|
|
ecp_nistz256_gather_w7(&p.a, pre_comp->precomp[0], 1);
|
|
if (!ecp_nistz256_set_from_affine(pre_comp_generator,
|
|
group, &p.a, ctx)) {
|
|
EC_POINT_free(pre_comp_generator);
|
|
goto err;
|
|
}
|
|
|
|
if (0 == EC_POINT_cmp(group, generator, pre_comp_generator, ctx))
|
|
preComputedTable = (const PRECOMP256_ROW *)pre_comp->precomp;
|
|
|
|
EC_POINT_free(pre_comp_generator);
|
|
}
|
|
|
|
if (preComputedTable == NULL && ecp_nistz256_is_affine_G(generator)) {
|
|
/*
|
|
* If there is no precomputed data, but the generator is the
|
|
* default, a hardcoded table of precomputed data is used. This
|
|
* is because applications, such as Apache, do not use
|
|
* EC_KEY_precompute_mult.
|
|
*/
|
|
preComputedTable = ecp_nistz256_precomputed;
|
|
}
|
|
|
|
if (preComputedTable) {
|
|
BN_ULONG infty;
|
|
|
|
if ((BN_num_bits(scalar) > 256)
|
|
|| BN_is_negative(scalar)) {
|
|
if ((tmp_scalar = BN_CTX_get(ctx)) == NULL)
|
|
goto err;
|
|
|
|
if (!BN_nnmod(tmp_scalar, scalar, group->order, ctx)) {
|
|
ECerr(EC_F_ECP_NISTZ256_POINTS_MUL, ERR_R_BN_LIB);
|
|
goto err;
|
|
}
|
|
scalar = tmp_scalar;
|
|
}
|
|
|
|
for (i = 0; i < bn_get_top(scalar) * BN_BYTES; i += BN_BYTES) {
|
|
BN_ULONG d = bn_get_words(scalar)[i / BN_BYTES];
|
|
|
|
p_str[i + 0] = (unsigned char)d;
|
|
p_str[i + 1] = (unsigned char)(d >> 8);
|
|
p_str[i + 2] = (unsigned char)(d >> 16);
|
|
p_str[i + 3] = (unsigned char)(d >>= 24);
|
|
if (BN_BYTES == 8) {
|
|
d >>= 8;
|
|
p_str[i + 4] = (unsigned char)d;
|
|
p_str[i + 5] = (unsigned char)(d >> 8);
|
|
p_str[i + 6] = (unsigned char)(d >> 16);
|
|
p_str[i + 7] = (unsigned char)(d >> 24);
|
|
}
|
|
}
|
|
|
|
for (; i < 33; i++)
|
|
p_str[i] = 0;
|
|
|
|
/* First window */
|
|
wvalue = (p_str[0] << 1) & mask;
|
|
idx += window_size;
|
|
|
|
wvalue = _booth_recode_w7(wvalue);
|
|
|
|
ecp_nistz256_gather_w7(&p.a, preComputedTable[0],
|
|
wvalue >> 1);
|
|
|
|
ecp_nistz256_neg(p.p.Z, p.p.Y);
|
|
copy_conditional(p.p.Y, p.p.Z, wvalue & 1);
|
|
|
|
/*
|
|
* Since affine infinity is encoded as (0,0) and
|
|
* Jacobian is (,,0), we need to harmonize them
|
|
* by assigning "one" or zero to Z.
|
|
*/
|
|
infty = (p.p.X[0] | p.p.X[1] | p.p.X[2] | p.p.X[3] |
|
|
p.p.Y[0] | p.p.Y[1] | p.p.Y[2] | p.p.Y[3]);
|
|
if (P256_LIMBS == 8)
|
|
infty |= (p.p.X[4] | p.p.X[5] | p.p.X[6] | p.p.X[7] |
|
|
p.p.Y[4] | p.p.Y[5] | p.p.Y[6] | p.p.Y[7]);
|
|
|
|
infty = 0 - is_zero(infty);
|
|
infty = ~infty;
|
|
|
|
p.p.Z[0] = ONE[0] & infty;
|
|
p.p.Z[1] = ONE[1] & infty;
|
|
p.p.Z[2] = ONE[2] & infty;
|
|
p.p.Z[3] = ONE[3] & infty;
|
|
if (P256_LIMBS == 8) {
|
|
p.p.Z[4] = ONE[4] & infty;
|
|
p.p.Z[5] = ONE[5] & infty;
|
|
p.p.Z[6] = ONE[6] & infty;
|
|
p.p.Z[7] = ONE[7] & infty;
|
|
}
|
|
|
|
for (i = 1; i < 37; i++) {
|
|
unsigned int off = (idx - 1) / 8;
|
|
wvalue = p_str[off] | p_str[off + 1] << 8;
|
|
wvalue = (wvalue >> ((idx - 1) % 8)) & mask;
|
|
idx += window_size;
|
|
|
|
wvalue = _booth_recode_w7(wvalue);
|
|
|
|
ecp_nistz256_gather_w7(&t.a,
|
|
preComputedTable[i], wvalue >> 1);
|
|
|
|
ecp_nistz256_neg(t.p.Z, t.a.Y);
|
|
copy_conditional(t.a.Y, t.p.Z, wvalue & 1);
|
|
|
|
ecp_nistz256_point_add_affine(&p.p, &p.p, &t.a);
|
|
}
|
|
} else {
|
|
p_is_infinity = 1;
|
|
no_precomp_for_generator = 1;
|
|
}
|
|
} else
|
|
p_is_infinity = 1;
|
|
|
|
if (no_precomp_for_generator) {
|
|
/*
|
|
* Without a precomputed table for the generator, it has to be
|
|
* handled like a normal point.
|
|
*/
|
|
new_scalars = OPENSSL_malloc((num + 1) * sizeof(BIGNUM *));
|
|
if (new_scalars == NULL) {
|
|
ECerr(EC_F_ECP_NISTZ256_POINTS_MUL, ERR_R_MALLOC_FAILURE);
|
|
goto err;
|
|
}
|
|
|
|
new_points = OPENSSL_malloc((num + 1) * sizeof(EC_POINT *));
|
|
if (new_points == NULL) {
|
|
ECerr(EC_F_ECP_NISTZ256_POINTS_MUL, ERR_R_MALLOC_FAILURE);
|
|
goto err;
|
|
}
|
|
|
|
memcpy(new_scalars, scalars, num * sizeof(BIGNUM *));
|
|
new_scalars[num] = scalar;
|
|
memcpy(new_points, points, num * sizeof(EC_POINT *));
|
|
new_points[num] = generator;
|
|
|
|
scalars = new_scalars;
|
|
points = new_points;
|
|
num++;
|
|
}
|
|
|
|
if (num) {
|
|
P256_POINT *out = &t.p;
|
|
if (p_is_infinity)
|
|
out = &p.p;
|
|
|
|
if (!ecp_nistz256_windowed_mul(group, out, scalars, points, num, ctx))
|
|
goto err;
|
|
|
|
if (!p_is_infinity)
|
|
ecp_nistz256_point_add(&p.p, &p.p, out);
|
|
}
|
|
|
|
/* Not constant-time, but we're only operating on the public output. */
|
|
if (!bn_set_words(r->X, p.p.X, P256_LIMBS) ||
|
|
!bn_set_words(r->Y, p.p.Y, P256_LIMBS) ||
|
|
!bn_set_words(r->Z, p.p.Z, P256_LIMBS)) {
|
|
goto err;
|
|
}
|
|
r->Z_is_one = is_one(r->Z) & 1;
|
|
|
|
ret = 1;
|
|
|
|
err:
|
|
BN_CTX_end(ctx);
|
|
OPENSSL_free(new_points);
|
|
OPENSSL_free(new_scalars);
|
|
return ret;
|
|
}
|
|
|
|
__owur static int ecp_nistz256_get_affine(const EC_GROUP *group,
|
|
const EC_POINT *point,
|
|
BIGNUM *x, BIGNUM *y, BN_CTX *ctx)
|
|
{
|
|
BN_ULONG z_inv2[P256_LIMBS];
|
|
BN_ULONG z_inv3[P256_LIMBS];
|
|
BN_ULONG x_aff[P256_LIMBS];
|
|
BN_ULONG y_aff[P256_LIMBS];
|
|
BN_ULONG point_x[P256_LIMBS], point_y[P256_LIMBS], point_z[P256_LIMBS];
|
|
BN_ULONG x_ret[P256_LIMBS], y_ret[P256_LIMBS];
|
|
|
|
if (EC_POINT_is_at_infinity(group, point)) {
|
|
ECerr(EC_F_ECP_NISTZ256_GET_AFFINE, EC_R_POINT_AT_INFINITY);
|
|
return 0;
|
|
}
|
|
|
|
if (!ecp_nistz256_bignum_to_field_elem(point_x, point->X) ||
|
|
!ecp_nistz256_bignum_to_field_elem(point_y, point->Y) ||
|
|
!ecp_nistz256_bignum_to_field_elem(point_z, point->Z)) {
|
|
ECerr(EC_F_ECP_NISTZ256_GET_AFFINE, EC_R_COORDINATES_OUT_OF_RANGE);
|
|
return 0;
|
|
}
|
|
|
|
ecp_nistz256_mod_inverse(z_inv3, point_z);
|
|
ecp_nistz256_sqr_mont(z_inv2, z_inv3);
|
|
ecp_nistz256_mul_mont(x_aff, z_inv2, point_x);
|
|
|
|
if (x != NULL) {
|
|
ecp_nistz256_from_mont(x_ret, x_aff);
|
|
if (!bn_set_words(x, x_ret, P256_LIMBS))
|
|
return 0;
|
|
}
|
|
|
|
if (y != NULL) {
|
|
ecp_nistz256_mul_mont(z_inv3, z_inv3, z_inv2);
|
|
ecp_nistz256_mul_mont(y_aff, z_inv3, point_y);
|
|
ecp_nistz256_from_mont(y_ret, y_aff);
|
|
if (!bn_set_words(y, y_ret, P256_LIMBS))
|
|
return 0;
|
|
}
|
|
|
|
return 1;
|
|
}
|
|
|
|
static NISTZ256_PRE_COMP *ecp_nistz256_pre_comp_new(const EC_GROUP *group)
|
|
{
|
|
NISTZ256_PRE_COMP *ret = NULL;
|
|
|
|
if (!group)
|
|
return NULL;
|
|
|
|
ret = OPENSSL_zalloc(sizeof(*ret));
|
|
|
|
if (ret == NULL) {
|
|
ECerr(EC_F_ECP_NISTZ256_PRE_COMP_NEW, ERR_R_MALLOC_FAILURE);
|
|
return ret;
|
|
}
|
|
|
|
ret->group = group;
|
|
ret->w = 6; /* default */
|
|
ret->references = 1;
|
|
|
|
ret->lock = CRYPTO_THREAD_lock_new();
|
|
if (ret->lock == NULL) {
|
|
ECerr(EC_F_ECP_NISTZ256_PRE_COMP_NEW, ERR_R_MALLOC_FAILURE);
|
|
OPENSSL_free(ret);
|
|
return NULL;
|
|
}
|
|
return ret;
|
|
}
|
|
|
|
NISTZ256_PRE_COMP *EC_nistz256_pre_comp_dup(NISTZ256_PRE_COMP *p)
|
|
{
|
|
int i;
|
|
if (p != NULL)
|
|
CRYPTO_UP_REF(&p->references, &i, p->lock);
|
|
return p;
|
|
}
|
|
|
|
void EC_nistz256_pre_comp_free(NISTZ256_PRE_COMP *pre)
|
|
{
|
|
int i;
|
|
|
|
if (pre == NULL)
|
|
return;
|
|
|
|
CRYPTO_DOWN_REF(&pre->references, &i, pre->lock);
|
|
REF_PRINT_COUNT("EC_nistz256", x);
|
|
if (i > 0)
|
|
return;
|
|
REF_ASSERT_ISNT(i < 0);
|
|
|
|
OPENSSL_free(pre->precomp_storage);
|
|
CRYPTO_THREAD_lock_free(pre->lock);
|
|
OPENSSL_free(pre);
|
|
}
|
|
|
|
|
|
static int ecp_nistz256_window_have_precompute_mult(const EC_GROUP *group)
|
|
{
|
|
/* There is a hard-coded table for the default generator. */
|
|
const EC_POINT *generator = EC_GROUP_get0_generator(group);
|
|
|
|
if (generator != NULL && ecp_nistz256_is_affine_G(generator)) {
|
|
/* There is a hard-coded table for the default generator. */
|
|
return 1;
|
|
}
|
|
|
|
return HAVEPRECOMP(group, nistz256);
|
|
}
|
|
|
|
#if defined(__x86_64) || defined(__x86_64__) || \
|
|
defined(_M_AMD64) || defined(_M_X64) || \
|
|
defined(__powerpc64__) || defined(_ARCH_PP64) || \
|
|
defined(__aarch64__)
|
|
/*
|
|
* Montgomery mul modulo Order(P): res = a*b*2^-256 mod Order(P)
|
|
*/
|
|
void ecp_nistz256_ord_mul_mont(BN_ULONG res[P256_LIMBS],
|
|
const BN_ULONG a[P256_LIMBS],
|
|
const BN_ULONG b[P256_LIMBS]);
|
|
void ecp_nistz256_ord_sqr_mont(BN_ULONG res[P256_LIMBS],
|
|
const BN_ULONG a[P256_LIMBS],
|
|
int rep);
|
|
|
|
static int ecp_nistz256_inv_mod_ord(const EC_GROUP *group, BIGNUM *r,
|
|
const BIGNUM *x, BN_CTX *ctx)
|
|
{
|
|
/* RR = 2^512 mod ord(p256) */
|
|
static const BN_ULONG RR[P256_LIMBS] = {
|
|
TOBN(0x83244c95,0xbe79eea2), TOBN(0x4699799c,0x49bd6fa6),
|
|
TOBN(0x2845b239,0x2b6bec59), TOBN(0x66e12d94,0xf3d95620)
|
|
};
|
|
/* The constant 1 (unlike ONE that is one in Montgomery representation) */
|
|
static const BN_ULONG one[P256_LIMBS] = {
|
|
TOBN(0,1), TOBN(0,0), TOBN(0,0), TOBN(0,0)
|
|
};
|
|
/*
|
|
* We don't use entry 0 in the table, so we omit it and address
|
|
* with -1 offset.
|
|
*/
|
|
BN_ULONG table[15][P256_LIMBS];
|
|
BN_ULONG out[P256_LIMBS], t[P256_LIMBS];
|
|
int i, ret = 0;
|
|
enum {
|
|
i_1 = 0, i_10, i_11, i_101, i_111, i_1010, i_1111,
|
|
i_10101, i_101010, i_101111, i_x6, i_x8, i_x16, i_x32
|
|
};
|
|
|
|
/*
|
|
* Catch allocation failure early.
|
|
*/
|
|
if (bn_wexpand(r, P256_LIMBS) == NULL) {
|
|
ECerr(EC_F_ECP_NISTZ256_INV_MOD_ORD, ERR_R_BN_LIB);
|
|
goto err;
|
|
}
|
|
|
|
if ((BN_num_bits(x) > 256) || BN_is_negative(x)) {
|
|
BIGNUM *tmp;
|
|
|
|
if ((tmp = BN_CTX_get(ctx)) == NULL
|
|
|| !BN_nnmod(tmp, x, group->order, ctx)) {
|
|
ECerr(EC_F_ECP_NISTZ256_INV_MOD_ORD, ERR_R_BN_LIB);
|
|
goto err;
|
|
}
|
|
x = tmp;
|
|
}
|
|
|
|
if (!ecp_nistz256_bignum_to_field_elem(t, x)) {
|
|
ECerr(EC_F_ECP_NISTZ256_INV_MOD_ORD, EC_R_COORDINATES_OUT_OF_RANGE);
|
|
goto err;
|
|
}
|
|
|
|
ecp_nistz256_ord_mul_mont(table[0], t, RR);
|
|
#if 0
|
|
/*
|
|
* Original sparse-then-fixed-window algorithm, retained for reference.
|
|
*/
|
|
for (i = 2; i < 16; i += 2) {
|
|
ecp_nistz256_ord_sqr_mont(table[i-1], table[i/2-1], 1);
|
|
ecp_nistz256_ord_mul_mont(table[i], table[i-1], table[0]);
|
|
}
|
|
|
|
/*
|
|
* The top 128bit of the exponent are highly redudndant, so we
|
|
* perform an optimized flow
|
|
*/
|
|
ecp_nistz256_ord_sqr_mont(t, table[15-1], 4); /* f0 */
|
|
ecp_nistz256_ord_mul_mont(t, t, table[15-1]); /* ff */
|
|
|
|
ecp_nistz256_ord_sqr_mont(out, t, 8); /* ff00 */
|
|
ecp_nistz256_ord_mul_mont(out, out, t); /* ffff */
|
|
|
|
ecp_nistz256_ord_sqr_mont(t, out, 16); /* ffff0000 */
|
|
ecp_nistz256_ord_mul_mont(t, t, out); /* ffffffff */
|
|
|
|
ecp_nistz256_ord_sqr_mont(out, t, 64); /* ffffffff0000000000000000 */
|
|
ecp_nistz256_ord_mul_mont(out, out, t); /* ffffffff00000000ffffffff */
|
|
|
|
ecp_nistz256_ord_sqr_mont(out, out, 32); /* ffffffff00000000ffffffff00000000 */
|
|
ecp_nistz256_ord_mul_mont(out, out, t); /* ffffffff00000000ffffffffffffffff */
|
|
|
|
/*
|
|
* The bottom 128 bit of the exponent are processed with fixed 4-bit window
|
|
*/
|
|
for(i = 0; i < 32; i++) {
|
|
/* expLo - the low 128 bits of the exponent we use (ord(p256) - 2),
|
|
* split into nibbles */
|
|
static const unsigned char expLo[32] = {
|
|
0xb,0xc,0xe,0x6,0xf,0xa,0xa,0xd,0xa,0x7,0x1,0x7,0x9,0xe,0x8,0x4,
|
|
0xf,0x3,0xb,0x9,0xc,0xa,0xc,0x2,0xf,0xc,0x6,0x3,0x2,0x5,0x4,0xf
|
|
};
|
|
|
|
ecp_nistz256_ord_sqr_mont(out, out, 4);
|
|
/* The exponent is public, no need in constant-time access */
|
|
ecp_nistz256_ord_mul_mont(out, out, table[expLo[i]-1]);
|
|
}
|
|
#else
|
|
/*
|
|
* https://briansmith.org/ecc-inversion-addition-chains-01#p256_scalar_inversion
|
|
*
|
|
* Even though this code path spares 12 squarings, 4.5%, and 13
|
|
* multiplications, 25%, on grand scale sign operation is not that
|
|
* much faster, not more that 2%...
|
|
*/
|
|
|
|
/* pre-calculate powers */
|
|
ecp_nistz256_ord_sqr_mont(table[i_10], table[i_1], 1);
|
|
|
|
ecp_nistz256_ord_mul_mont(table[i_11], table[i_1], table[i_10]);
|
|
|
|
ecp_nistz256_ord_mul_mont(table[i_101], table[i_11], table[i_10]);
|
|
|
|
ecp_nistz256_ord_mul_mont(table[i_111], table[i_101], table[i_10]);
|
|
|
|
ecp_nistz256_ord_sqr_mont(table[i_1010], table[i_101], 1);
|
|
|
|
ecp_nistz256_ord_mul_mont(table[i_1111], table[i_1010], table[i_101]);
|
|
|
|
ecp_nistz256_ord_sqr_mont(table[i_10101], table[i_1010], 1);
|
|
ecp_nistz256_ord_mul_mont(table[i_10101], table[i_10101], table[i_1]);
|
|
|
|
ecp_nistz256_ord_sqr_mont(table[i_101010], table[i_10101], 1);
|
|
|
|
ecp_nistz256_ord_mul_mont(table[i_101111], table[i_101010], table[i_101]);
|
|
|
|
ecp_nistz256_ord_mul_mont(table[i_x6], table[i_101010], table[i_10101]);
|
|
|
|
ecp_nistz256_ord_sqr_mont(table[i_x8], table[i_x6], 2);
|
|
ecp_nistz256_ord_mul_mont(table[i_x8], table[i_x8], table[i_11]);
|
|
|
|
ecp_nistz256_ord_sqr_mont(table[i_x16], table[i_x8], 8);
|
|
ecp_nistz256_ord_mul_mont(table[i_x16], table[i_x16], table[i_x8]);
|
|
|
|
ecp_nistz256_ord_sqr_mont(table[i_x32], table[i_x16], 16);
|
|
ecp_nistz256_ord_mul_mont(table[i_x32], table[i_x32], table[i_x16]);
|
|
|
|
/* calculations */
|
|
ecp_nistz256_ord_sqr_mont(out, table[i_x32], 64);
|
|
ecp_nistz256_ord_mul_mont(out, out, table[i_x32]);
|
|
|
|
for (i = 0; i < 27; i++) {
|
|
static const struct { unsigned char p, i; } chain[27] = {
|
|
{ 32, i_x32 }, { 6, i_101111 }, { 5, i_111 },
|
|
{ 4, i_11 }, { 5, i_1111 }, { 5, i_10101 },
|
|
{ 4, i_101 }, { 3, i_101 }, { 3, i_101 },
|
|
{ 5, i_111 }, { 9, i_101111 }, { 6, i_1111 },
|
|
{ 2, i_1 }, { 5, i_1 }, { 6, i_1111 },
|
|
{ 5, i_111 }, { 4, i_111 }, { 5, i_111 },
|
|
{ 5, i_101 }, { 3, i_11 }, { 10, i_101111 },
|
|
{ 2, i_11 }, { 5, i_11 }, { 5, i_11 },
|
|
{ 3, i_1 }, { 7, i_10101 }, { 6, i_1111 }
|
|
};
|
|
|
|
ecp_nistz256_ord_sqr_mont(out, out, chain[i].p);
|
|
ecp_nistz256_ord_mul_mont(out, out, table[chain[i].i]);
|
|
}
|
|
#endif
|
|
ecp_nistz256_ord_mul_mont(out, out, one);
|
|
|
|
/*
|
|
* Can't fail, but check return code to be consistent anyway.
|
|
*/
|
|
if (!bn_set_words(r, out, P256_LIMBS))
|
|
goto err;
|
|
|
|
ret = 1;
|
|
err:
|
|
return ret;
|
|
}
|
|
#else
|
|
# define ecp_nistz256_inv_mod_ord NULL
|
|
#endif
|
|
|
|
const EC_METHOD *EC_GFp_nistz256_method(void)
|
|
{
|
|
static const EC_METHOD ret = {
|
|
EC_FLAGS_DEFAULT_OCT,
|
|
NID_X9_62_prime_field,
|
|
ec_GFp_mont_group_init,
|
|
ec_GFp_mont_group_finish,
|
|
ec_GFp_mont_group_clear_finish,
|
|
ec_GFp_mont_group_copy,
|
|
ec_GFp_mont_group_set_curve,
|
|
ec_GFp_simple_group_get_curve,
|
|
ec_GFp_simple_group_get_degree,
|
|
ec_group_simple_order_bits,
|
|
ec_GFp_simple_group_check_discriminant,
|
|
ec_GFp_simple_point_init,
|
|
ec_GFp_simple_point_finish,
|
|
ec_GFp_simple_point_clear_finish,
|
|
ec_GFp_simple_point_copy,
|
|
ec_GFp_simple_point_set_to_infinity,
|
|
ec_GFp_simple_set_Jprojective_coordinates_GFp,
|
|
ec_GFp_simple_get_Jprojective_coordinates_GFp,
|
|
ec_GFp_simple_point_set_affine_coordinates,
|
|
ecp_nistz256_get_affine,
|
|
0, 0, 0,
|
|
ec_GFp_simple_add,
|
|
ec_GFp_simple_dbl,
|
|
ec_GFp_simple_invert,
|
|
ec_GFp_simple_is_at_infinity,
|
|
ec_GFp_simple_is_on_curve,
|
|
ec_GFp_simple_cmp,
|
|
ec_GFp_simple_make_affine,
|
|
ec_GFp_simple_points_make_affine,
|
|
ecp_nistz256_points_mul, /* mul */
|
|
ecp_nistz256_mult_precompute, /* precompute_mult */
|
|
ecp_nistz256_window_have_precompute_mult, /* have_precompute_mult */
|
|
ec_GFp_mont_field_mul,
|
|
ec_GFp_mont_field_sqr,
|
|
0, /* field_div */
|
|
ec_GFp_mont_field_inv,
|
|
ec_GFp_mont_field_encode,
|
|
ec_GFp_mont_field_decode,
|
|
ec_GFp_mont_field_set_to_one,
|
|
ec_key_simple_priv2oct,
|
|
ec_key_simple_oct2priv,
|
|
0, /* set private */
|
|
ec_key_simple_generate_key,
|
|
ec_key_simple_check_key,
|
|
ec_key_simple_generate_public_key,
|
|
0, /* keycopy */
|
|
0, /* keyfinish */
|
|
ecdh_simple_compute_key,
|
|
ecp_nistz256_inv_mod_ord, /* can be #define-d NULL */
|
|
0, /* blind_coordinates */
|
|
0, /* ladder_pre */
|
|
0, /* ladder_step */
|
|
0 /* ladder_post */
|
|
};
|
|
|
|
return &ret;
|
|
}
|