Move some RSA keygen support code into separate files.
This was all new code. There was a request to make this available under ISC. Change-Id: Ibabbe6fbf593c2a781aac47a4de7ac378604dbcf Reviewed-on: https://boringssl-review.googlesource.com/28267 Reviewed-by: Adam Langley <agl@google.com>
This commit is contained in:
David Benjamin
committed by
Adam Langley
Adam Langley
parent
5d626b223b
commit
bb3a456930
@@ -36,8 +36,10 @@
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#include "bn/cmp.c"
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#include "bn/ctx.c"
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#include "bn/div.c"
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#include "bn/div_extra.c"
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#include "bn/exponentiation.c"
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#include "bn/gcd.c"
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#include "bn/gcd_extra.c"
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#include "bn/generic.c"
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#include "bn/jacobi.c"
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#include "bn/montgomery.c"
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@@ -0,0 +1,87 @@
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/* Copyright (c) 2018, Google Inc.
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*
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* Permission to use, copy, modify, and/or distribute this software for any
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* purpose with or without fee is hereby granted, provided that the above
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* copyright notice and this permission notice appear in all copies.
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*
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* THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES
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* WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF
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* MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY
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* SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES
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* WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN ACTION
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* OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF OR IN
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* CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE. */
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#include <openssl/bn.h>
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#include <assert.h>
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#include "internal.h"
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// The following functions use a Barrett reduction variant to avoid leaking the
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// numerator. See http://ridiculousfish.com/blog/posts/labor-of-division-episode-i.html
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//
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// We use 32-bit numerator and 16-bit divisor for simplicity. This allows
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// computing |m| and |q| without architecture-specific code.
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// mod_u16 returns |n| mod |d|. |p| and |m| are the "magic numbers" for |d| (see
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// reference). For proof of correctness in Coq, see
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// https://github.com/davidben/fiat-crypto/blob/barrett/src/Arithmetic/BarrettReduction/RidiculousFish.v
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// Note the Coq version of |mod_u16| additionally includes the computation of
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// |p| and |m| from |bn_mod_u16_consttime| below.
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static uint16_t mod_u16(uint32_t n, uint16_t d, uint32_t p, uint32_t m) {
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// Compute floor(n/d) per steps 3 through 5.
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uint32_t q = ((uint64_t)m * n) >> 32;
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// Note there is a typo in the reference. We right-shift by one, not two.
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uint32_t t = ((n - q) >> 1) + q;
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t = t >> (p - 1);
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// Multiply and subtract to get the remainder.
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n -= d * t;
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assert(n < d);
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return n;
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}
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// shift_and_add_mod_u16 returns |r| * 2^32 + |a| mod |d|. |p| and |m| are the
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// "magic numbers" for |d| (see reference).
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static uint16_t shift_and_add_mod_u16(uint16_t r, uint32_t a, uint16_t d,
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uint32_t p, uint32_t m) {
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// Incorporate |a| in two 16-bit chunks.
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uint32_t t = r;
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t <<= 16;
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t |= a >> 16;
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t = mod_u16(t, d, p, m);
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t <<= 16;
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t |= a & 0xffff;
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t = mod_u16(t, d, p, m);
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return t;
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}
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uint16_t bn_mod_u16_consttime(const BIGNUM *bn, uint16_t d) {
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if (d <= 1) {
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return 0;
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}
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// Compute the "magic numbers" for |d|. See steps 1 and 2.
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// This computes p = ceil(log_2(d)).
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uint32_t p = BN_num_bits_word(d - 1);
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// This operation is not constant-time, but |p| and |d| are public values.
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// Note that |p| is at most 16, so the computation fits in |uint64_t|.
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assert(p <= 16);
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uint32_t m = ((UINT64_C(1) << (32 + p)) + d - 1) / d;
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uint16_t ret = 0;
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for (int i = bn->width - 1; i >= 0; i--) {
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#if BN_BITS2 == 32
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ret = shift_and_add_mod_u16(ret, bn->d[i], d, p, m);
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#elif BN_BITS2 == 64
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ret = shift_and_add_mod_u16(ret, bn->d[i] >> 32, d, p, m);
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ret = shift_and_add_mod_u16(ret, bn->d[i] & 0xffffffff, d, p, m);
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#else
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#error "Unknown BN_ULONG size"
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#endif
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}
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return ret;
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}
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@@ -108,316 +108,11 @@
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#include <openssl/bn.h>
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#include <assert.h>
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#include <openssl/err.h>
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#include "internal.h"
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static BN_ULONG word_is_odd_mask(BN_ULONG a) { return (BN_ULONG)0 - (a & 1); }
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static void maybe_rshift1_words(BN_ULONG *a, BN_ULONG mask, BN_ULONG *tmp,
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size_t num) {
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bn_rshift1_words(tmp, a, num);
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bn_select_words(a, mask, tmp, a, num);
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}
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static void maybe_rshift1_words_carry(BN_ULONG *a, BN_ULONG carry,
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BN_ULONG mask, BN_ULONG *tmp,
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size_t num) {
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maybe_rshift1_words(a, mask, tmp, num);
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if (num != 0) {
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carry &= mask;
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a[num - 1] |= carry << (BN_BITS2-1);
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}
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}
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static BN_ULONG maybe_add_words(BN_ULONG *a, BN_ULONG mask, const BN_ULONG *b,
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BN_ULONG *tmp, size_t num) {
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BN_ULONG carry = bn_add_words(tmp, a, b, num);
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bn_select_words(a, mask, tmp, a, num);
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return carry & mask;
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}
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static int bn_gcd_consttime(BIGNUM *r, unsigned *out_shift, const BIGNUM *x,
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const BIGNUM *y, BN_CTX *ctx) {
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size_t width = x->width > y->width ? x->width : y->width;
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if (width == 0) {
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*out_shift = 0;
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BN_zero(r);
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return 1;
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}
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// This is a constant-time implementation of Stein's algorithm (binary GCD).
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int ret = 0;
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BN_CTX_start(ctx);
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BIGNUM *u = BN_CTX_get(ctx);
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BIGNUM *v = BN_CTX_get(ctx);
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BIGNUM *tmp = BN_CTX_get(ctx);
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if (u == NULL || v == NULL || tmp == NULL ||
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!BN_copy(u, x) ||
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!BN_copy(v, y) ||
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!bn_resize_words(u, width) ||
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!bn_resize_words(v, width) ||
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!bn_resize_words(tmp, width)) {
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goto err;
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}
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// Each loop iteration halves at least one of |u| and |v|. Thus we need at
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// most the combined bit width of inputs for at least one value to be zero.
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unsigned x_bits = x->width * BN_BITS2, y_bits = y->width * BN_BITS2;
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unsigned num_iters = x_bits + y_bits;
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if (num_iters < x_bits) {
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OPENSSL_PUT_ERROR(BN, BN_R_BIGNUM_TOO_LONG);
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goto err;
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}
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unsigned shift = 0;
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for (unsigned i = 0; i < num_iters; i++) {
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BN_ULONG both_odd = word_is_odd_mask(u->d[0]) & word_is_odd_mask(v->d[0]);
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// If both |u| and |v| are odd, subtract the smaller from the larger.
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BN_ULONG u_less_than_v =
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(BN_ULONG)0 - bn_sub_words(tmp->d, u->d, v->d, width);
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bn_select_words(u->d, both_odd & ~u_less_than_v, tmp->d, u->d, width);
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bn_sub_words(tmp->d, v->d, u->d, width);
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bn_select_words(v->d, both_odd & u_less_than_v, tmp->d, v->d, width);
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// At least one of |u| and |v| is now even.
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BN_ULONG u_is_odd = word_is_odd_mask(u->d[0]);
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BN_ULONG v_is_odd = word_is_odd_mask(v->d[0]);
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assert(!(u_is_odd & v_is_odd));
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// If both are even, the final GCD gains a factor of two.
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shift += 1 & (~u_is_odd & ~v_is_odd);
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// Halve any which are even.
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maybe_rshift1_words(u->d, ~u_is_odd, tmp->d, width);
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maybe_rshift1_words(v->d, ~v_is_odd, tmp->d, width);
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}
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// One of |u| or |v| is zero at this point. The algorithm usually makes |u|
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// zero, unless |y| was already zero on input. Fix this by combining the
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// values.
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assert(BN_is_zero(u) || BN_is_zero(v));
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for (size_t i = 0; i < width; i++) {
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v->d[i] |= u->d[i];
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}
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*out_shift = shift;
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ret = bn_set_words(r, v->d, width);
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err:
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BN_CTX_end(ctx);
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return ret;
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}
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int BN_gcd(BIGNUM *r, const BIGNUM *x, const BIGNUM *y, BN_CTX *ctx) {
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unsigned shift;
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return bn_gcd_consttime(r, &shift, x, y, ctx) &&
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BN_lshift(r, r, shift);
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}
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int bn_is_relatively_prime(int *out_relatively_prime, const BIGNUM *x,
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const BIGNUM *y, BN_CTX *ctx) {
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int ret = 0;
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BN_CTX_start(ctx);
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unsigned shift;
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BIGNUM *gcd = BN_CTX_get(ctx);
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if (gcd == NULL ||
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!bn_gcd_consttime(gcd, &shift, x, y, ctx)) {
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goto err;
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}
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// Check that 2^|shift| * |gcd| is one.
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if (gcd->width == 0) {
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*out_relatively_prime = 0;
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} else {
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BN_ULONG mask = shift | (gcd->d[0] ^ 1);
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for (int i = 1; i < gcd->width; i++) {
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mask |= gcd->d[i];
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}
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*out_relatively_prime = mask == 0;
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}
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ret = 1;
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err:
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BN_CTX_end(ctx);
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return ret;
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}
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int bn_lcm_consttime(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx) {
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BN_CTX_start(ctx);
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unsigned shift;
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BIGNUM *gcd = BN_CTX_get(ctx);
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int ret = gcd != NULL &&
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bn_mul_consttime(r, a, b, ctx) &&
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bn_gcd_consttime(gcd, &shift, a, b, ctx) &&
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bn_div_consttime(r, NULL, r, gcd, ctx) &&
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bn_rshift_secret_shift(r, r, shift, ctx);
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BN_CTX_end(ctx);
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return ret;
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}
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int bn_mod_inverse_consttime(BIGNUM *r, int *out_no_inverse, const BIGNUM *a,
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const BIGNUM *n, BN_CTX *ctx) {
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*out_no_inverse = 0;
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if (BN_is_negative(a) || BN_ucmp(a, n) >= 0) {
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OPENSSL_PUT_ERROR(BN, BN_R_INPUT_NOT_REDUCED);
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return 0;
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}
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if (BN_is_zero(a)) {
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if (BN_is_one(n)) {
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BN_zero(r);
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return 1;
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}
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*out_no_inverse = 1;
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OPENSSL_PUT_ERROR(BN, BN_R_NO_INVERSE);
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return 0;
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}
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// This is a constant-time implementation of the extended binary GCD
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// algorithm. It is adapted from the Handbook of Applied Cryptography, section
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// 14.4.3, algorithm 14.51, and modified to bound coefficients and avoid
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// negative numbers.
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//
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// For more details and proof of correctness, see
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// https://github.com/mit-plv/fiat-crypto/pull/333. In particular, see |step|
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// and |mod_inverse_consttime| for the algorithm in Gallina and see
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// |mod_inverse_consttime_spec| for the correctness result.
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if (!BN_is_odd(a) && !BN_is_odd(n)) {
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*out_no_inverse = 1;
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OPENSSL_PUT_ERROR(BN, BN_R_NO_INVERSE);
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return 0;
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}
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// This function exists to compute the RSA private exponent, where |a| is one
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// word. We'll thus use |a_width| when available.
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size_t n_width = n->width, a_width = a->width;
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if (a_width > n_width) {
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a_width = n_width;
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}
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int ret = 0;
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BN_CTX_start(ctx);
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BIGNUM *u = BN_CTX_get(ctx);
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BIGNUM *v = BN_CTX_get(ctx);
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BIGNUM *A = BN_CTX_get(ctx);
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BIGNUM *B = BN_CTX_get(ctx);
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BIGNUM *C = BN_CTX_get(ctx);
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BIGNUM *D = BN_CTX_get(ctx);
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BIGNUM *tmp = BN_CTX_get(ctx);
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BIGNUM *tmp2 = BN_CTX_get(ctx);
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if (u == NULL || v == NULL || A == NULL || B == NULL || C == NULL ||
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D == NULL || tmp == NULL || tmp2 == NULL ||
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!BN_copy(u, a) ||
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!BN_copy(v, n) ||
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!BN_one(A) ||
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!BN_one(D) ||
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// For convenience, size |u| and |v| equivalently.
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!bn_resize_words(u, n_width) ||
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!bn_resize_words(v, n_width) ||
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// |A| and |C| are bounded by |m|.
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!bn_resize_words(A, n_width) ||
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!bn_resize_words(C, n_width) ||
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// |B| and |D| are bounded by |a|.
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!bn_resize_words(B, a_width) ||
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!bn_resize_words(D, a_width) ||
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// |tmp| and |tmp2| may be used at either size.
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!bn_resize_words(tmp, n_width) ||
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!bn_resize_words(tmp2, n_width)) {
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goto err;
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}
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// Each loop iteration halves at least one of |u| and |v|. Thus we need at
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// most the combined bit width of inputs for at least one value to be zero.
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unsigned a_bits = a_width * BN_BITS2, n_bits = n_width * BN_BITS2;
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unsigned num_iters = a_bits + n_bits;
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if (num_iters < a_bits) {
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OPENSSL_PUT_ERROR(BN, BN_R_BIGNUM_TOO_LONG);
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goto err;
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}
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// Before and after each loop iteration, the following hold:
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//
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// u = A*a - B*n
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// v = D*n - C*a
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// 0 < u <= a
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// 0 <= v <= n
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// 0 <= A < n
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// 0 <= B <= a
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// 0 <= C < n
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// 0 <= D <= a
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//
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// After each loop iteration, u and v only get smaller, and at least one of
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// them shrinks by at least a factor of two.
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for (unsigned i = 0; i < num_iters; i++) {
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BN_ULONG both_odd = word_is_odd_mask(u->d[0]) & word_is_odd_mask(v->d[0]);
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// If both |u| and |v| are odd, subtract the smaller from the larger.
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BN_ULONG v_less_than_u =
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(BN_ULONG)0 - bn_sub_words(tmp->d, v->d, u->d, n_width);
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bn_select_words(v->d, both_odd & ~v_less_than_u, tmp->d, v->d, n_width);
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bn_sub_words(tmp->d, u->d, v->d, n_width);
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bn_select_words(u->d, both_odd & v_less_than_u, tmp->d, u->d, n_width);
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// If we updated one of the values, update the corresponding coefficient.
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BN_ULONG carry = bn_add_words(tmp->d, A->d, C->d, n_width);
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carry -= bn_sub_words(tmp2->d, tmp->d, n->d, n_width);
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bn_select_words(tmp->d, carry, tmp->d, tmp2->d, n_width);
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bn_select_words(A->d, both_odd & v_less_than_u, tmp->d, A->d, n_width);
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bn_select_words(C->d, both_odd & ~v_less_than_u, tmp->d, C->d, n_width);
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bn_add_words(tmp->d, B->d, D->d, a_width);
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bn_sub_words(tmp2->d, tmp->d, a->d, a_width);
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bn_select_words(tmp->d, carry, tmp->d, tmp2->d, a_width);
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bn_select_words(B->d, both_odd & v_less_than_u, tmp->d, B->d, a_width);
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bn_select_words(D->d, both_odd & ~v_less_than_u, tmp->d, D->d, a_width);
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// Our loop invariants hold at this point. Additionally, exactly one of |u|
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// and |v| is now even.
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BN_ULONG u_is_even = ~word_is_odd_mask(u->d[0]);
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BN_ULONG v_is_even = ~word_is_odd_mask(v->d[0]);
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assert(u_is_even != v_is_even);
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// Halve the even one and adjust the corresponding coefficient.
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maybe_rshift1_words(u->d, u_is_even, tmp->d, n_width);
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BN_ULONG A_or_B_is_odd =
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word_is_odd_mask(A->d[0]) | word_is_odd_mask(B->d[0]);
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BN_ULONG A_carry =
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maybe_add_words(A->d, A_or_B_is_odd & u_is_even, n->d, tmp->d, n_width);
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BN_ULONG B_carry =
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maybe_add_words(B->d, A_or_B_is_odd & u_is_even, a->d, tmp->d, a_width);
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maybe_rshift1_words_carry(A->d, A_carry, u_is_even, tmp->d, n_width);
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maybe_rshift1_words_carry(B->d, B_carry, u_is_even, tmp->d, a_width);
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|
||||
maybe_rshift1_words(v->d, v_is_even, tmp->d, n_width);
|
||||
BN_ULONG C_or_D_is_odd =
|
||||
word_is_odd_mask(C->d[0]) | word_is_odd_mask(D->d[0]);
|
||||
BN_ULONG C_carry =
|
||||
maybe_add_words(C->d, C_or_D_is_odd & v_is_even, n->d, tmp->d, n_width);
|
||||
BN_ULONG D_carry =
|
||||
maybe_add_words(D->d, C_or_D_is_odd & v_is_even, a->d, tmp->d, a_width);
|
||||
maybe_rshift1_words_carry(C->d, C_carry, v_is_even, tmp->d, n_width);
|
||||
maybe_rshift1_words_carry(D->d, D_carry, v_is_even, tmp->d, a_width);
|
||||
}
|
||||
|
||||
assert(BN_is_zero(v));
|
||||
if (!BN_is_one(u)) {
|
||||
*out_no_inverse = 1;
|
||||
OPENSSL_PUT_ERROR(BN, BN_R_NO_INVERSE);
|
||||
goto err;
|
||||
}
|
||||
|
||||
ret = BN_copy(r, A) != NULL;
|
||||
|
||||
err:
|
||||
BN_CTX_end(ctx);
|
||||
return ret;
|
||||
}
|
||||
|
||||
int BN_mod_inverse_odd(BIGNUM *out, int *out_no_inverse, const BIGNUM *a,
|
||||
const BIGNUM *n, BN_CTX *ctx) {
|
||||
*out_no_inverse = 0;
|
||||
|
||||
@@ -0,0 +1,325 @@
|
||||
/* Copyright (c) 2018, Google Inc.
|
||||
*
|
||||
* Permission to use, copy, modify, and/or distribute this software for any
|
||||
* purpose with or without fee is hereby granted, provided that the above
|
||||
* copyright notice and this permission notice appear in all copies.
|
||||
*
|
||||
* THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES
|
||||
* WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF
|
||||
* MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY
|
||||
* SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES
|
||||
* WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN ACTION
|
||||
* OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF OR IN
|
||||
* CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE. */
|
||||
|
||||
#include <openssl/bn.h>
|
||||
|
||||
#include <assert.h>
|
||||
|
||||
#include <openssl/err.h>
|
||||
|
||||
#include "internal.h"
|
||||
|
||||
|
||||
static BN_ULONG word_is_odd_mask(BN_ULONG a) { return (BN_ULONG)0 - (a & 1); }
|
||||
|
||||
static void maybe_rshift1_words(BN_ULONG *a, BN_ULONG mask, BN_ULONG *tmp,
|
||||
size_t num) {
|
||||
bn_rshift1_words(tmp, a, num);
|
||||
bn_select_words(a, mask, tmp, a, num);
|
||||
}
|
||||
|
||||
static void maybe_rshift1_words_carry(BN_ULONG *a, BN_ULONG carry,
|
||||
BN_ULONG mask, BN_ULONG *tmp,
|
||||
size_t num) {
|
||||
maybe_rshift1_words(a, mask, tmp, num);
|
||||
if (num != 0) {
|
||||
carry &= mask;
|
||||
a[num - 1] |= carry << (BN_BITS2-1);
|
||||
}
|
||||
}
|
||||
|
||||
static BN_ULONG maybe_add_words(BN_ULONG *a, BN_ULONG mask, const BN_ULONG *b,
|
||||
BN_ULONG *tmp, size_t num) {
|
||||
BN_ULONG carry = bn_add_words(tmp, a, b, num);
|
||||
bn_select_words(a, mask, tmp, a, num);
|
||||
return carry & mask;
|
||||
}
|
||||
|
||||
static int bn_gcd_consttime(BIGNUM *r, unsigned *out_shift, const BIGNUM *x,
|
||||
const BIGNUM *y, BN_CTX *ctx) {
|
||||
size_t width = x->width > y->width ? x->width : y->width;
|
||||
if (width == 0) {
|
||||
*out_shift = 0;
|
||||
BN_zero(r);
|
||||
return 1;
|
||||
}
|
||||
|
||||
// This is a constant-time implementation of Stein's algorithm (binary GCD).
|
||||
int ret = 0;
|
||||
BN_CTX_start(ctx);
|
||||
BIGNUM *u = BN_CTX_get(ctx);
|
||||
BIGNUM *v = BN_CTX_get(ctx);
|
||||
BIGNUM *tmp = BN_CTX_get(ctx);
|
||||
if (u == NULL || v == NULL || tmp == NULL ||
|
||||
!BN_copy(u, x) ||
|
||||
!BN_copy(v, y) ||
|
||||
!bn_resize_words(u, width) ||
|
||||
!bn_resize_words(v, width) ||
|
||||
!bn_resize_words(tmp, width)) {
|
||||
goto err;
|
||||
}
|
||||
|
||||
// Each loop iteration halves at least one of |u| and |v|. Thus we need at
|
||||
// most the combined bit width of inputs for at least one value to be zero.
|
||||
unsigned x_bits = x->width * BN_BITS2, y_bits = y->width * BN_BITS2;
|
||||
unsigned num_iters = x_bits + y_bits;
|
||||
if (num_iters < x_bits) {
|
||||
OPENSSL_PUT_ERROR(BN, BN_R_BIGNUM_TOO_LONG);
|
||||
goto err;
|
||||
}
|
||||
|
||||
unsigned shift = 0;
|
||||
for (unsigned i = 0; i < num_iters; i++) {
|
||||
BN_ULONG both_odd = word_is_odd_mask(u->d[0]) & word_is_odd_mask(v->d[0]);
|
||||
|
||||
// If both |u| and |v| are odd, subtract the smaller from the larger.
|
||||
BN_ULONG u_less_than_v =
|
||||
(BN_ULONG)0 - bn_sub_words(tmp->d, u->d, v->d, width);
|
||||
bn_select_words(u->d, both_odd & ~u_less_than_v, tmp->d, u->d, width);
|
||||
bn_sub_words(tmp->d, v->d, u->d, width);
|
||||
bn_select_words(v->d, both_odd & u_less_than_v, tmp->d, v->d, width);
|
||||
|
||||
// At least one of |u| and |v| is now even.
|
||||
BN_ULONG u_is_odd = word_is_odd_mask(u->d[0]);
|
||||
BN_ULONG v_is_odd = word_is_odd_mask(v->d[0]);
|
||||
assert(!(u_is_odd & v_is_odd));
|
||||
|
||||
// If both are even, the final GCD gains a factor of two.
|
||||
shift += 1 & (~u_is_odd & ~v_is_odd);
|
||||
|
||||
// Halve any which are even.
|
||||
maybe_rshift1_words(u->d, ~u_is_odd, tmp->d, width);
|
||||
maybe_rshift1_words(v->d, ~v_is_odd, tmp->d, width);
|
||||
}
|
||||
|
||||
// One of |u| or |v| is zero at this point. The algorithm usually makes |u|
|
||||
// zero, unless |y| was already zero on input. Fix this by combining the
|
||||
// values.
|
||||
assert(BN_is_zero(u) || BN_is_zero(v));
|
||||
for (size_t i = 0; i < width; i++) {
|
||||
v->d[i] |= u->d[i];
|
||||
}
|
||||
|
||||
*out_shift = shift;
|
||||
ret = bn_set_words(r, v->d, width);
|
||||
|
||||
err:
|
||||
BN_CTX_end(ctx);
|
||||
return ret;
|
||||
}
|
||||
|
||||
int BN_gcd(BIGNUM *r, const BIGNUM *x, const BIGNUM *y, BN_CTX *ctx) {
|
||||
unsigned shift;
|
||||
return bn_gcd_consttime(r, &shift, x, y, ctx) &&
|
||||
BN_lshift(r, r, shift);
|
||||
}
|
||||
|
||||
int bn_is_relatively_prime(int *out_relatively_prime, const BIGNUM *x,
|
||||
const BIGNUM *y, BN_CTX *ctx) {
|
||||
int ret = 0;
|
||||
BN_CTX_start(ctx);
|
||||
unsigned shift;
|
||||
BIGNUM *gcd = BN_CTX_get(ctx);
|
||||
if (gcd == NULL ||
|
||||
!bn_gcd_consttime(gcd, &shift, x, y, ctx)) {
|
||||
goto err;
|
||||
}
|
||||
|
||||
// Check that 2^|shift| * |gcd| is one.
|
||||
if (gcd->width == 0) {
|
||||
*out_relatively_prime = 0;
|
||||
} else {
|
||||
BN_ULONG mask = shift | (gcd->d[0] ^ 1);
|
||||
for (int i = 1; i < gcd->width; i++) {
|
||||
mask |= gcd->d[i];
|
||||
}
|
||||
*out_relatively_prime = mask == 0;
|
||||
}
|
||||
ret = 1;
|
||||
|
||||
err:
|
||||
BN_CTX_end(ctx);
|
||||
return ret;
|
||||
}
|
||||
|
||||
int bn_lcm_consttime(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx) {
|
||||
BN_CTX_start(ctx);
|
||||
unsigned shift;
|
||||
BIGNUM *gcd = BN_CTX_get(ctx);
|
||||
int ret = gcd != NULL &&
|
||||
bn_mul_consttime(r, a, b, ctx) &&
|
||||
bn_gcd_consttime(gcd, &shift, a, b, ctx) &&
|
||||
bn_div_consttime(r, NULL, r, gcd, ctx) &&
|
||||
bn_rshift_secret_shift(r, r, shift, ctx);
|
||||
BN_CTX_end(ctx);
|
||||
return ret;
|
||||
}
|
||||
|
||||
int bn_mod_inverse_consttime(BIGNUM *r, int *out_no_inverse, const BIGNUM *a,
|
||||
const BIGNUM *n, BN_CTX *ctx) {
|
||||
*out_no_inverse = 0;
|
||||
if (BN_is_negative(a) || BN_ucmp(a, n) >= 0) {
|
||||
OPENSSL_PUT_ERROR(BN, BN_R_INPUT_NOT_REDUCED);
|
||||
return 0;
|
||||
}
|
||||
if (BN_is_zero(a)) {
|
||||
if (BN_is_one(n)) {
|
||||
BN_zero(r);
|
||||
return 1;
|
||||
}
|
||||
*out_no_inverse = 1;
|
||||
OPENSSL_PUT_ERROR(BN, BN_R_NO_INVERSE);
|
||||
return 0;
|
||||
}
|
||||
|
||||
// This is a constant-time implementation of the extended binary GCD
|
||||
// algorithm. It is adapted from the Handbook of Applied Cryptography, section
|
||||
// 14.4.3, algorithm 14.51, and modified to bound coefficients and avoid
|
||||
// negative numbers.
|
||||
//
|
||||
// For more details and proof of correctness, see
|
||||
// https://github.com/mit-plv/fiat-crypto/pull/333. In particular, see |step|
|
||||
// and |mod_inverse_consttime| for the algorithm in Gallina and see
|
||||
// |mod_inverse_consttime_spec| for the correctness result.
|
||||
|
||||
if (!BN_is_odd(a) && !BN_is_odd(n)) {
|
||||
*out_no_inverse = 1;
|
||||
OPENSSL_PUT_ERROR(BN, BN_R_NO_INVERSE);
|
||||
return 0;
|
||||
}
|
||||
|
||||
// This function exists to compute the RSA private exponent, where |a| is one
|
||||
// word. We'll thus use |a_width| when available.
|
||||
size_t n_width = n->width, a_width = a->width;
|
||||
if (a_width > n_width) {
|
||||
a_width = n_width;
|
||||
}
|
||||
|
||||
int ret = 0;
|
||||
BN_CTX_start(ctx);
|
||||
BIGNUM *u = BN_CTX_get(ctx);
|
||||
BIGNUM *v = BN_CTX_get(ctx);
|
||||
BIGNUM *A = BN_CTX_get(ctx);
|
||||
BIGNUM *B = BN_CTX_get(ctx);
|
||||
BIGNUM *C = BN_CTX_get(ctx);
|
||||
BIGNUM *D = BN_CTX_get(ctx);
|
||||
BIGNUM *tmp = BN_CTX_get(ctx);
|
||||
BIGNUM *tmp2 = BN_CTX_get(ctx);
|
||||
if (u == NULL || v == NULL || A == NULL || B == NULL || C == NULL ||
|
||||
D == NULL || tmp == NULL || tmp2 == NULL ||
|
||||
!BN_copy(u, a) ||
|
||||
!BN_copy(v, n) ||
|
||||
!BN_one(A) ||
|
||||
!BN_one(D) ||
|
||||
// For convenience, size |u| and |v| equivalently.
|
||||
!bn_resize_words(u, n_width) ||
|
||||
!bn_resize_words(v, n_width) ||
|
||||
// |A| and |C| are bounded by |m|.
|
||||
!bn_resize_words(A, n_width) ||
|
||||
!bn_resize_words(C, n_width) ||
|
||||
// |B| and |D| are bounded by |a|.
|
||||
!bn_resize_words(B, a_width) ||
|
||||
!bn_resize_words(D, a_width) ||
|
||||
// |tmp| and |tmp2| may be used at either size.
|
||||
!bn_resize_words(tmp, n_width) ||
|
||||
!bn_resize_words(tmp2, n_width)) {
|
||||
goto err;
|
||||
}
|
||||
|
||||
// Each loop iteration halves at least one of |u| and |v|. Thus we need at
|
||||
// most the combined bit width of inputs for at least one value to be zero.
|
||||
unsigned a_bits = a_width * BN_BITS2, n_bits = n_width * BN_BITS2;
|
||||
unsigned num_iters = a_bits + n_bits;
|
||||
if (num_iters < a_bits) {
|
||||
OPENSSL_PUT_ERROR(BN, BN_R_BIGNUM_TOO_LONG);
|
||||
goto err;
|
||||
}
|
||||
|
||||
// Before and after each loop iteration, the following hold:
|
||||
//
|
||||
// u = A*a - B*n
|
||||
// v = D*n - C*a
|
||||
// 0 < u <= a
|
||||
// 0 <= v <= n
|
||||
// 0 <= A < n
|
||||
// 0 <= B <= a
|
||||
// 0 <= C < n
|
||||
// 0 <= D <= a
|
||||
//
|
||||
// After each loop iteration, u and v only get smaller, and at least one of
|
||||
// them shrinks by at least a factor of two.
|
||||
for (unsigned i = 0; i < num_iters; i++) {
|
||||
BN_ULONG both_odd = word_is_odd_mask(u->d[0]) & word_is_odd_mask(v->d[0]);
|
||||
|
||||
// If both |u| and |v| are odd, subtract the smaller from the larger.
|
||||
BN_ULONG v_less_than_u =
|
||||
(BN_ULONG)0 - bn_sub_words(tmp->d, v->d, u->d, n_width);
|
||||
bn_select_words(v->d, both_odd & ~v_less_than_u, tmp->d, v->d, n_width);
|
||||
bn_sub_words(tmp->d, u->d, v->d, n_width);
|
||||
bn_select_words(u->d, both_odd & v_less_than_u, tmp->d, u->d, n_width);
|
||||
|
||||
// If we updated one of the values, update the corresponding coefficient.
|
||||
BN_ULONG carry = bn_add_words(tmp->d, A->d, C->d, n_width);
|
||||
carry -= bn_sub_words(tmp2->d, tmp->d, n->d, n_width);
|
||||
bn_select_words(tmp->d, carry, tmp->d, tmp2->d, n_width);
|
||||
bn_select_words(A->d, both_odd & v_less_than_u, tmp->d, A->d, n_width);
|
||||
bn_select_words(C->d, both_odd & ~v_less_than_u, tmp->d, C->d, n_width);
|
||||
|
||||
bn_add_words(tmp->d, B->d, D->d, a_width);
|
||||
bn_sub_words(tmp2->d, tmp->d, a->d, a_width);
|
||||
bn_select_words(tmp->d, carry, tmp->d, tmp2->d, a_width);
|
||||
bn_select_words(B->d, both_odd & v_less_than_u, tmp->d, B->d, a_width);
|
||||
bn_select_words(D->d, both_odd & ~v_less_than_u, tmp->d, D->d, a_width);
|
||||
|
||||
// Our loop invariants hold at this point. Additionally, exactly one of |u|
|
||||
// and |v| is now even.
|
||||
BN_ULONG u_is_even = ~word_is_odd_mask(u->d[0]);
|
||||
BN_ULONG v_is_even = ~word_is_odd_mask(v->d[0]);
|
||||
assert(u_is_even != v_is_even);
|
||||
|
||||
// Halve the even one and adjust the corresponding coefficient.
|
||||
maybe_rshift1_words(u->d, u_is_even, tmp->d, n_width);
|
||||
BN_ULONG A_or_B_is_odd =
|
||||
word_is_odd_mask(A->d[0]) | word_is_odd_mask(B->d[0]);
|
||||
BN_ULONG A_carry =
|
||||
maybe_add_words(A->d, A_or_B_is_odd & u_is_even, n->d, tmp->d, n_width);
|
||||
BN_ULONG B_carry =
|
||||
maybe_add_words(B->d, A_or_B_is_odd & u_is_even, a->d, tmp->d, a_width);
|
||||
maybe_rshift1_words_carry(A->d, A_carry, u_is_even, tmp->d, n_width);
|
||||
maybe_rshift1_words_carry(B->d, B_carry, u_is_even, tmp->d, a_width);
|
||||
|
||||
maybe_rshift1_words(v->d, v_is_even, tmp->d, n_width);
|
||||
BN_ULONG C_or_D_is_odd =
|
||||
word_is_odd_mask(C->d[0]) | word_is_odd_mask(D->d[0]);
|
||||
BN_ULONG C_carry =
|
||||
maybe_add_words(C->d, C_or_D_is_odd & v_is_even, n->d, tmp->d, n_width);
|
||||
BN_ULONG D_carry =
|
||||
maybe_add_words(D->d, C_or_D_is_odd & v_is_even, a->d, tmp->d, a_width);
|
||||
maybe_rshift1_words_carry(C->d, C_carry, v_is_even, tmp->d, n_width);
|
||||
maybe_rshift1_words_carry(D->d, D_carry, v_is_even, tmp->d, a_width);
|
||||
}
|
||||
|
||||
assert(BN_is_zero(v));
|
||||
if (!BN_is_one(u)) {
|
||||
*out_no_inverse = 1;
|
||||
OPENSSL_PUT_ERROR(BN, BN_R_NO_INVERSE);
|
||||
goto err;
|
||||
}
|
||||
|
||||
ret = BN_copy(r, A) != NULL;
|
||||
|
||||
err:
|
||||
BN_CTX_end(ctx);
|
||||
return ret;
|
||||
}
|
||||
@@ -532,73 +532,6 @@ err:
|
||||
return found;
|
||||
}
|
||||
|
||||
// The following functions use a Barrett reduction variant to avoid leaking the
|
||||
// numerator. See http://ridiculousfish.com/blog/posts/labor-of-division-episode-i.html
|
||||
//
|
||||
// We use 32-bit numerator and 16-bit divisor for simplicity. This allows
|
||||
// computing |m| and |q| without architecture-specific code.
|
||||
|
||||
// mod_u16 returns |n| mod |d|. |p| and |m| are the "magic numbers" for |d| (see
|
||||
// reference). For proof of correctness in Coq, see
|
||||
// https://github.com/davidben/fiat-crypto/blob/barrett/src/Arithmetic/BarrettReduction/RidiculousFish.v
|
||||
// Note the Coq version of |mod_u16| additionally includes the computation of
|
||||
// |p| and |m| from |bn_mod_u16_consttime| below.
|
||||
static uint16_t mod_u16(uint32_t n, uint16_t d, uint32_t p, uint32_t m) {
|
||||
// Compute floor(n/d) per steps 3 through 5.
|
||||
uint32_t q = ((uint64_t)m * n) >> 32;
|
||||
// Note there is a typo in the reference. We right-shift by one, not two.
|
||||
uint32_t t = ((n - q) >> 1) + q;
|
||||
t = t >> (p - 1);
|
||||
|
||||
// Multiply and subtract to get the remainder.
|
||||
n -= d * t;
|
||||
assert(n < d);
|
||||
return n;
|
||||
}
|
||||
|
||||
// shift_and_add_mod_u16 returns |r| * 2^32 + |a| mod |d|. |p| and |m| are the
|
||||
// "magic numbers" for |d| (see reference).
|
||||
static uint16_t shift_and_add_mod_u16(uint16_t r, uint32_t a, uint16_t d,
|
||||
uint32_t p, uint32_t m) {
|
||||
// Incorporate |a| in two 16-bit chunks.
|
||||
uint32_t t = r;
|
||||
t <<= 16;
|
||||
t |= a >> 16;
|
||||
t = mod_u16(t, d, p, m);
|
||||
|
||||
t <<= 16;
|
||||
t |= a & 0xffff;
|
||||
t = mod_u16(t, d, p, m);
|
||||
return t;
|
||||
}
|
||||
|
||||
uint16_t bn_mod_u16_consttime(const BIGNUM *bn, uint16_t d) {
|
||||
if (d <= 1) {
|
||||
return 0;
|
||||
}
|
||||
|
||||
// Compute the "magic numbers" for |d|. See steps 1 and 2.
|
||||
// This computes p = ceil(log_2(d)).
|
||||
uint32_t p = BN_num_bits_word(d - 1);
|
||||
// This operation is not constant-time, but |p| and |d| are public values.
|
||||
// Note that |p| is at most 16, so the computation fits in |uint64_t|.
|
||||
assert(p <= 16);
|
||||
uint32_t m = ((UINT64_C(1) << (32 + p)) + d - 1) / d;
|
||||
|
||||
uint16_t ret = 0;
|
||||
for (int i = bn->width - 1; i >= 0; i--) {
|
||||
#if BN_BITS2 == 32
|
||||
ret = shift_and_add_mod_u16(ret, bn->d[i], d, p, m);
|
||||
#elif BN_BITS2 == 64
|
||||
ret = shift_and_add_mod_u16(ret, bn->d[i] >> 32, d, p, m);
|
||||
ret = shift_and_add_mod_u16(ret, bn->d[i] & 0xffffffff, d, p, m);
|
||||
#else
|
||||
#error "Unknown BN_ULONG size"
|
||||
#endif
|
||||
}
|
||||
return ret;
|
||||
}
|
||||
|
||||
static int bn_trial_division(uint16_t *out, const BIGNUM *bn) {
|
||||
const size_t num_primes = num_trial_division_primes(bn);
|
||||
for (size_t i = 1; i < num_primes; i++) {
|
||||
|
||||
Reference in New Issue
Block a user