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openssl/crypto/bn/bn_gf2m.c
Viktor Dukhovni 8e008cb8b2 Harden BN_GF2m_poly2arr against misuse. 
The BN_GF2m_poly2arr() function converts characteristic-2 field
(GF_{2^m}) Galois polynomials from a representation as a BIGNUM bitmask,
to a compact array with just the exponents of the non-zero terms.

These polynomials are then used in BN_GF2m_mod_arr() to perform modular
reduction.  A precondition of calling BN_GF2m_mod_arr() is that the
polynomial must have a non-zero constant term (i.e. the array has `0` as
its final element).

Internally, callers of BN_GF2m_poly2arr() did not verify that
precondition, and binary EC curve parameters with an invalid polynomial
could lead to out of bounds memory reads and writes in BN_GF2m_mod_arr().

The precondition is always true for polynomials that arise from the
standard form of EC parameters for characteristic-two fields (X9.62).
See the "Finite Field Identification" section of:

    https://www.itu.int/ITU-T/formal-language/itu-t/x/x894/2018-cor1/ANSI-X9-62.html

The OpenSSL GF(2^m) code supports only the trinomial and pentanomial
basis X9.62 forms.

This commit updates BN_GF2m_poly2arr() to return `0` (failure) when
the constant term is zero (i.e. the input bitmask BIGNUM is not odd).

Additionally, the return value is made unambiguous when there is not
enough space to also pad the array with a final `-1` sentinel value.
The return value is now always the number of elements (including the
final `-1`) that would be filled when the output array is sufficiently
large.  Previously the same count was returned both when the array has
just enough room for the final `-1` and when it had only enough space
for non-sentinel values.

Finally, BN_GF2m_poly2arr() is updated to reject polynomials whose
degree exceeds `OPENSSL_ECC_MAX_FIELD_BITS`, this guards against
CPU exhausition attacks via excessively large inputs.

The above issues do not arise in processing X.509 certificates.  These
generally have EC keys from "named curves", and RFC5840 (Section 2.1.1)
disallows explicit EC parameters.  The TLS code in OpenSSL enforces this
constraint only after the certificate is decoded, but, even if explicit
parameters are specified, they are in X9.62 form, which cannot represent
problem values as noted above.

Initially reported as oss-fuzz issue 71623.

A closely related issue was earlier reported in
<https://github.com/openssl/openssl/issues/19826>.

Severity: Low, CVE-2024-9143

Reviewed-by: Matt Caswell <matt@openssl.org>
Reviewed-by: Bernd Edlinger <bernd.edlinger@hotmail.de>
Reviewed-by: Paul Dale <ppzgs1@gmail.com>
Reviewed-by: Tomas Mraz <tomas@openssl.org>
(Merged from https://github.com/openssl/openssl/pull/25639)
2024-10-16 09:21:33 +02:00

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/*
* Copyright 2002-2021 The OpenSSL Project Authors. All Rights Reserved.
* Copyright (c) 2002, Oracle and/or its affiliates. All rights reserved
*
* Licensed under the Apache License 2.0 (the "License"). You may not use
* this file except in compliance with the License. You can obtain a copy
* in the file LICENSE in the source distribution or at
* https://www.openssl.org/source/license.html
*/
#include <assert.h>
#include <limits.h>
#include <stdio.h>
#include "internal/cryptlib.h"
#include "bn_local.h"
#ifndef OPENSSL_NO_EC2M
# include <openssl/ec.h>
/*
* Maximum number of iterations before BN_GF2m_mod_solve_quad_arr should
* fail.
*/
# define MAX_ITERATIONS 50
# define SQR_nibble(w) ((((w) & 8) << 3) \
| (((w) & 4) << 2) \
| (((w) & 2) << 1) \
| ((w) & 1))
/* Platform-specific macros to accelerate squaring. */
# if defined(SIXTY_FOUR_BIT) || defined(SIXTY_FOUR_BIT_LONG)
# define SQR1(w) \
SQR_nibble((w) >> 60) << 56 | SQR_nibble((w) >> 56) << 48 | \
SQR_nibble((w) >> 52) << 40 | SQR_nibble((w) >> 48) << 32 | \
SQR_nibble((w) >> 44) << 24 | SQR_nibble((w) >> 40) << 16 | \
SQR_nibble((w) >> 36) << 8 | SQR_nibble((w) >> 32)
# define SQR0(w) \
SQR_nibble((w) >> 28) << 56 | SQR_nibble((w) >> 24) << 48 | \
SQR_nibble((w) >> 20) << 40 | SQR_nibble((w) >> 16) << 32 | \
SQR_nibble((w) >> 12) << 24 | SQR_nibble((w) >> 8) << 16 | \
SQR_nibble((w) >> 4) << 8 | SQR_nibble((w) )
# endif
# ifdef THIRTY_TWO_BIT
# define SQR1(w) \
SQR_nibble((w) >> 28) << 24 | SQR_nibble((w) >> 24) << 16 | \
SQR_nibble((w) >> 20) << 8 | SQR_nibble((w) >> 16)
# define SQR0(w) \
SQR_nibble((w) >> 12) << 24 | SQR_nibble((w) >> 8) << 16 | \
SQR_nibble((w) >> 4) << 8 | SQR_nibble((w) )
# endif
# if !defined(OPENSSL_BN_ASM_GF2m)
/*
* Product of two polynomials a, b each with degree < BN_BITS2 - 1, result is
* a polynomial r with degree < 2 * BN_BITS - 1 The caller MUST ensure that
* the variables have the right amount of space allocated.
*/
# ifdef THIRTY_TWO_BIT
static void bn_GF2m_mul_1x1(BN_ULONG *r1, BN_ULONG *r0, const BN_ULONG a,
const BN_ULONG b)
{
register BN_ULONG h, l, s;
BN_ULONG tab[8], top2b = a >> 30;
register BN_ULONG a1, a2, a4;
a1 = a & (0x3FFFFFFF);
a2 = a1 << 1;
a4 = a2 << 1;
tab[0] = 0;
tab[1] = a1;
tab[2] = a2;
tab[3] = a1 ^ a2;
tab[4] = a4;
tab[5] = a1 ^ a4;
tab[6] = a2 ^ a4;
tab[7] = a1 ^ a2 ^ a4;
s = tab[b & 0x7];
l = s;
s = tab[b >> 3 & 0x7];
l ^= s << 3;
h = s >> 29;
s = tab[b >> 6 & 0x7];
l ^= s << 6;
h ^= s >> 26;
s = tab[b >> 9 & 0x7];
l ^= s << 9;
h ^= s >> 23;
s = tab[b >> 12 & 0x7];
l ^= s << 12;
h ^= s >> 20;
s = tab[b >> 15 & 0x7];
l ^= s << 15;
h ^= s >> 17;
s = tab[b >> 18 & 0x7];
l ^= s << 18;
h ^= s >> 14;
s = tab[b >> 21 & 0x7];
l ^= s << 21;
h ^= s >> 11;
s = tab[b >> 24 & 0x7];
l ^= s << 24;
h ^= s >> 8;
s = tab[b >> 27 & 0x7];
l ^= s << 27;
h ^= s >> 5;
s = tab[b >> 30];
l ^= s << 30;
h ^= s >> 2;
/* compensate for the top two bits of a */
if (top2b & 01) {
l ^= b << 30;
h ^= b >> 2;
}
if (top2b & 02) {
l ^= b << 31;
h ^= b >> 1;
}
*r1 = h;
*r0 = l;
}
# endif
# if defined(SIXTY_FOUR_BIT) || defined(SIXTY_FOUR_BIT_LONG)
static void bn_GF2m_mul_1x1(BN_ULONG *r1, BN_ULONG *r0, const BN_ULONG a,
const BN_ULONG b)
{
register BN_ULONG h, l, s;
BN_ULONG tab[16], top3b = a >> 61;
register BN_ULONG a1, a2, a4, a8;
a1 = a & (0x1FFFFFFFFFFFFFFFULL);
a2 = a1 << 1;
a4 = a2 << 1;
a8 = a4 << 1;
tab[0] = 0;
tab[1] = a1;
tab[2] = a2;
tab[3] = a1 ^ a2;
tab[4] = a4;
tab[5] = a1 ^ a4;
tab[6] = a2 ^ a4;
tab[7] = a1 ^ a2 ^ a4;
tab[8] = a8;
tab[9] = a1 ^ a8;
tab[10] = a2 ^ a8;
tab[11] = a1 ^ a2 ^ a8;
tab[12] = a4 ^ a8;
tab[13] = a1 ^ a4 ^ a8;
tab[14] = a2 ^ a4 ^ a8;
tab[15] = a1 ^ a2 ^ a4 ^ a8;
s = tab[b & 0xF];
l = s;
s = tab[b >> 4 & 0xF];
l ^= s << 4;
h = s >> 60;
s = tab[b >> 8 & 0xF];
l ^= s << 8;
h ^= s >> 56;
s = tab[b >> 12 & 0xF];
l ^= s << 12;
h ^= s >> 52;
s = tab[b >> 16 & 0xF];
l ^= s << 16;
h ^= s >> 48;
s = tab[b >> 20 & 0xF];
l ^= s << 20;
h ^= s >> 44;
s = tab[b >> 24 & 0xF];
l ^= s << 24;
h ^= s >> 40;
s = tab[b >> 28 & 0xF];
l ^= s << 28;
h ^= s >> 36;
s = tab[b >> 32 & 0xF];
l ^= s << 32;
h ^= s >> 32;
s = tab[b >> 36 & 0xF];
l ^= s << 36;
h ^= s >> 28;
s = tab[b >> 40 & 0xF];
l ^= s << 40;
h ^= s >> 24;
s = tab[b >> 44 & 0xF];
l ^= s << 44;
h ^= s >> 20;
s = tab[b >> 48 & 0xF];
l ^= s << 48;
h ^= s >> 16;
s = tab[b >> 52 & 0xF];
l ^= s << 52;
h ^= s >> 12;
s = tab[b >> 56 & 0xF];
l ^= s << 56;
h ^= s >> 8;
s = tab[b >> 60];
l ^= s << 60;
h ^= s >> 4;
/* compensate for the top three bits of a */
if (top3b & 01) {
l ^= b << 61;
h ^= b >> 3;
}
if (top3b & 02) {
l ^= b << 62;
h ^= b >> 2;
}
if (top3b & 04) {
l ^= b << 63;
h ^= b >> 1;
}
*r1 = h;
*r0 = l;
}
# endif
/*
* Product of two polynomials a, b each with degree < 2 * BN_BITS2 - 1,
* result is a polynomial r with degree < 4 * BN_BITS2 - 1 The caller MUST
* ensure that the variables have the right amount of space allocated.
*/
static void bn_GF2m_mul_2x2(BN_ULONG *r, const BN_ULONG a1, const BN_ULONG a0,
const BN_ULONG b1, const BN_ULONG b0)
{
BN_ULONG m1, m0;
/* r[3] = h1, r[2] = h0; r[1] = l1; r[0] = l0 */
bn_GF2m_mul_1x1(r + 3, r + 2, a1, b1);
bn_GF2m_mul_1x1(r + 1, r, a0, b0);
bn_GF2m_mul_1x1(&m1, &m0, a0 ^ a1, b0 ^ b1);
/* Correction on m1 ^= l1 ^ h1; m0 ^= l0 ^ h0; */
r[2] ^= m1 ^ r[1] ^ r[3]; /* h0 ^= m1 ^ l1 ^ h1; */
r[1] = r[3] ^ r[2] ^ r[0] ^ m1 ^ m0; /* l1 ^= l0 ^ h0 ^ m0; */
}
# else
void bn_GF2m_mul_2x2(BN_ULONG *r, BN_ULONG a1, BN_ULONG a0, BN_ULONG b1,
BN_ULONG b0);
# endif
/*
* Add polynomials a and b and store result in r; r could be a or b, a and b
* could be equal; r is the bitwise XOR of a and b.
*/
int BN_GF2m_add(BIGNUM *r, const BIGNUM *a, const BIGNUM *b)
{
int i;
const BIGNUM *at, *bt;
bn_check_top(a);
bn_check_top(b);
if (a->top < b->top) {
at = b;
bt = a;
} else {
at = a;
bt = b;
}
if (bn_wexpand(r, at->top) == NULL)
return 0;
for (i = 0; i < bt->top; i++) {
r->d[i] = at->d[i] ^ bt->d[i];
}
for (; i < at->top; i++) {
r->d[i] = at->d[i];
}
r->top = at->top;
bn_correct_top(r);
return 1;
}
/*-
* Some functions allow for representation of the irreducible polynomials
* as an int[], say p. The irreducible f(t) is then of the form:
* t^p[0] + t^p[1] + ... + t^p[k]
* where m = p[0] > p[1] > ... > p[k] = 0.
*/
/* Performs modular reduction of a and store result in r. r could be a. */
int BN_GF2m_mod_arr(BIGNUM *r, const BIGNUM *a, const int p[])
{
int j, k;
int n, dN, d0, d1;
BN_ULONG zz, *z;
bn_check_top(a);
if (p[0] == 0) {
/* reduction mod 1 => return 0 */
BN_zero(r);
return 1;
}
/*
* Since the algorithm does reduction in the r value, if a != r, copy the
* contents of a into r so we can do reduction in r.
*/
if (a != r) {
if (!bn_wexpand(r, a->top))
return 0;
for (j = 0; j < a->top; j++) {
r->d[j] = a->d[j];
}
r->top = a->top;
}
z = r->d;
/* start reduction */
dN = p[0] / BN_BITS2;
for (j = r->top - 1; j > dN;) {
zz = z[j];
if (z[j] == 0) {
j--;
continue;
}
z[j] = 0;
for (k = 1; p[k] != 0; k++) {
/* reducing component t^p[k] */
n = p[0] - p[k];
d0 = n % BN_BITS2;
d1 = BN_BITS2 - d0;
n /= BN_BITS2;
z[j - n] ^= (zz >> d0);
if (d0)
z[j - n - 1] ^= (zz << d1);
}
/* reducing component t^0 */
n = dN;
d0 = p[0] % BN_BITS2;
d1 = BN_BITS2 - d0;
z[j - n] ^= (zz >> d0);
if (d0)
z[j - n - 1] ^= (zz << d1);
}
/* final round of reduction */
while (j == dN) {
d0 = p[0] % BN_BITS2;
zz = z[dN] >> d0;
if (zz == 0)
break;
d1 = BN_BITS2 - d0;
/* clear up the top d1 bits */
if (d0)
z[dN] = (z[dN] << d1) >> d1;
else
z[dN] = 0;
z[0] ^= zz; /* reduction t^0 component */
for (k = 1; p[k] != 0; k++) {
BN_ULONG tmp_ulong;
/* reducing component t^p[k] */
n = p[k] / BN_BITS2;
d0 = p[k] % BN_BITS2;
d1 = BN_BITS2 - d0;
z[n] ^= (zz << d0);
if (d0 && (tmp_ulong = zz >> d1))
z[n + 1] ^= tmp_ulong;
}
}
bn_correct_top(r);
return 1;
}
/*
* Performs modular reduction of a by p and store result in r. r could be a.
* This function calls down to the BN_GF2m_mod_arr implementation; this wrapper
* function is only provided for convenience; for best performance, use the
* BN_GF2m_mod_arr function.
*/
int BN_GF2m_mod(BIGNUM *r, const BIGNUM *a, const BIGNUM *p)
{
int ret = 0;
int arr[6];
bn_check_top(a);
bn_check_top(p);
ret = BN_GF2m_poly2arr(p, arr, OSSL_NELEM(arr));
if (!ret || ret > (int)OSSL_NELEM(arr)) {
ERR_raise(ERR_LIB_BN, BN_R_INVALID_LENGTH);
return 0;
}
ret = BN_GF2m_mod_arr(r, a, arr);
bn_check_top(r);
return ret;
}
/*
* Compute the product of two polynomials a and b, reduce modulo p, and store
* the result in r. r could be a or b; a could be b.
*/
int BN_GF2m_mod_mul_arr(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
const int p[], BN_CTX *ctx)
{
int zlen, i, j, k, ret = 0;
BIGNUM *s;
BN_ULONG x1, x0, y1, y0, zz[4];
bn_check_top(a);
bn_check_top(b);
if (a == b) {
return BN_GF2m_mod_sqr_arr(r, a, p, ctx);
}
BN_CTX_start(ctx);
if ((s = BN_CTX_get(ctx)) == NULL)
goto err;
zlen = a->top + b->top + 4;
if (!bn_wexpand(s, zlen))
goto err;
s->top = zlen;
for (i = 0; i < zlen; i++)
s->d[i] = 0;
for (j = 0; j < b->top; j += 2) {
y0 = b->d[j];
y1 = ((j + 1) == b->top) ? 0 : b->d[j + 1];
for (i = 0; i < a->top; i += 2) {
x0 = a->d[i];
x1 = ((i + 1) == a->top) ? 0 : a->d[i + 1];
bn_GF2m_mul_2x2(zz, x1, x0, y1, y0);
for (k = 0; k < 4; k++)
s->d[i + j + k] ^= zz[k];
}
}
bn_correct_top(s);
if (BN_GF2m_mod_arr(r, s, p))
ret = 1;
bn_check_top(r);
err:
BN_CTX_end(ctx);
return ret;
}
/*
* Compute the product of two polynomials a and b, reduce modulo p, and store
* the result in r. r could be a or b; a could equal b. This function calls
* down to the BN_GF2m_mod_mul_arr implementation; this wrapper function is
* only provided for convenience; for best performance, use the
* BN_GF2m_mod_mul_arr function.
*/
int BN_GF2m_mod_mul(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
const BIGNUM *p, BN_CTX *ctx)
{
int ret = 0;
const int max = BN_num_bits(p) + 1;
int *arr;
bn_check_top(a);
bn_check_top(b);
bn_check_top(p);
arr = OPENSSL_malloc(sizeof(*arr) * max);
if (arr == NULL)
return 0;
ret = BN_GF2m_poly2arr(p, arr, max);
if (!ret || ret > max) {
ERR_raise(ERR_LIB_BN, BN_R_INVALID_LENGTH);
goto err;
}
ret = BN_GF2m_mod_mul_arr(r, a, b, arr, ctx);
bn_check_top(r);
err:
OPENSSL_free(arr);
return ret;
}
/* Square a, reduce the result mod p, and store it in a. r could be a. */
int BN_GF2m_mod_sqr_arr(BIGNUM *r, const BIGNUM *a, const int p[],
BN_CTX *ctx)
{
int i, ret = 0;
BIGNUM *s;
bn_check_top(a);
BN_CTX_start(ctx);
if ((s = BN_CTX_get(ctx)) == NULL)
goto err;
if (!bn_wexpand(s, 2 * a->top))
goto err;
for (i = a->top - 1; i >= 0; i--) {
s->d[2 * i + 1] = SQR1(a->d[i]);
s->d[2 * i] = SQR0(a->d[i]);
}
s->top = 2 * a->top;
bn_correct_top(s);
if (!BN_GF2m_mod_arr(r, s, p))
goto err;
bn_check_top(r);
ret = 1;
err:
BN_CTX_end(ctx);
return ret;
}
/*
* Square a, reduce the result mod p, and store it in a. r could be a. This
* function calls down to the BN_GF2m_mod_sqr_arr implementation; this
* wrapper function is only provided for convenience; for best performance,
* use the BN_GF2m_mod_sqr_arr function.
*/
int BN_GF2m_mod_sqr(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, BN_CTX *ctx)
{
int ret = 0;
const int max = BN_num_bits(p) + 1;
int *arr;
bn_check_top(a);
bn_check_top(p);
arr = OPENSSL_malloc(sizeof(*arr) * max);
if (arr == NULL)
return 0;
ret = BN_GF2m_poly2arr(p, arr, max);
if (!ret || ret > max) {
ERR_raise(ERR_LIB_BN, BN_R_INVALID_LENGTH);
goto err;
}
ret = BN_GF2m_mod_sqr_arr(r, a, arr, ctx);
bn_check_top(r);
err:
OPENSSL_free(arr);
return ret;
}
/*
* Invert a, reduce modulo p, and store the result in r. r could be a. Uses
* Modified Almost Inverse Algorithm (Algorithm 10) from Hankerson, D.,
* Hernandez, J.L., and Menezes, A. "Software Implementation of Elliptic
* Curve Cryptography Over Binary Fields".
*/
static int BN_GF2m_mod_inv_vartime(BIGNUM *r, const BIGNUM *a,
const BIGNUM *p, BN_CTX *ctx)
{
BIGNUM *b, *c = NULL, *u = NULL, *v = NULL, *tmp;
int ret = 0;
bn_check_top(a);
bn_check_top(p);
BN_CTX_start(ctx);
b = BN_CTX_get(ctx);
c = BN_CTX_get(ctx);
u = BN_CTX_get(ctx);
v = BN_CTX_get(ctx);
if (v == NULL)
goto err;
if (!BN_GF2m_mod(u, a, p))
goto err;
if (BN_is_zero(u))
goto err;
if (!BN_copy(v, p))
goto err;
# if 0
if (!BN_one(b))
goto err;
while (1) {
while (!BN_is_odd(u)) {
if (BN_is_zero(u))
goto err;
if (!BN_rshift1(u, u))
goto err;
if (BN_is_odd(b)) {
if (!BN_GF2m_add(b, b, p))
goto err;
}
if (!BN_rshift1(b, b))
goto err;
}
if (BN_abs_is_word(u, 1))
break;
if (BN_num_bits(u) < BN_num_bits(v)) {
tmp = u;
u = v;
v = tmp;
tmp = b;
b = c;
c = tmp;
}
if (!BN_GF2m_add(u, u, v))
goto err;
if (!BN_GF2m_add(b, b, c))
goto err;
}
# else
{
int i;
int ubits = BN_num_bits(u);
int vbits = BN_num_bits(v); /* v is copy of p */
int top = p->top;
BN_ULONG *udp, *bdp, *vdp, *cdp;
if (!bn_wexpand(u, top))
goto err;
udp = u->d;
for (i = u->top; i < top; i++)
udp[i] = 0;
u->top = top;
if (!bn_wexpand(b, top))
goto err;
bdp = b->d;
bdp[0] = 1;
for (i = 1; i < top; i++)
bdp[i] = 0;
b->top = top;
if (!bn_wexpand(c, top))
goto err;
cdp = c->d;
for (i = 0; i < top; i++)
cdp[i] = 0;
c->top = top;
vdp = v->d; /* It pays off to "cache" *->d pointers,
* because it allows optimizer to be more
* aggressive. But we don't have to "cache"
* p->d, because *p is declared 'const'... */
while (1) {
while (ubits && !(udp[0] & 1)) {
BN_ULONG u0, u1, b0, b1, mask;
u0 = udp[0];
b0 = bdp[0];
mask = (BN_ULONG)0 - (b0 & 1);
b0 ^= p->d[0] & mask;
for (i = 0; i < top - 1; i++) {
u1 = udp[i + 1];
udp[i] = ((u0 >> 1) | (u1 << (BN_BITS2 - 1))) & BN_MASK2;
u0 = u1;
b1 = bdp[i + 1] ^ (p->d[i + 1] & mask);
bdp[i] = ((b0 >> 1) | (b1 << (BN_BITS2 - 1))) & BN_MASK2;
b0 = b1;
}
udp[i] = u0 >> 1;
bdp[i] = b0 >> 1;
ubits--;
}
if (ubits <= BN_BITS2) {
if (udp[0] == 0) /* poly was reducible */
goto err;
if (udp[0] == 1)
break;
}
if (ubits < vbits) {
i = ubits;
ubits = vbits;
vbits = i;
tmp = u;
u = v;
v = tmp;
tmp = b;
b = c;
c = tmp;
udp = vdp;
vdp = v->d;
bdp = cdp;
cdp = c->d;
}
for (i = 0; i < top; i++) {
udp[i] ^= vdp[i];
bdp[i] ^= cdp[i];
}
if (ubits == vbits) {
BN_ULONG ul;
int utop = (ubits - 1) / BN_BITS2;
while ((ul = udp[utop]) == 0 && utop)
utop--;
ubits = utop * BN_BITS2 + BN_num_bits_word(ul);
}
}
bn_correct_top(b);
}
# endif
if (!BN_copy(r, b))
goto err;
bn_check_top(r);
ret = 1;
err:
# ifdef BN_DEBUG
/* BN_CTX_end would complain about the expanded form */
bn_correct_top(c);
bn_correct_top(u);
bn_correct_top(v);
# endif
BN_CTX_end(ctx);
return ret;
}
/*-
* Wrapper for BN_GF2m_mod_inv_vartime that blinds the input before calling.
* This is not constant time.
* But it does eliminate first order deduction on the input.
*/
int BN_GF2m_mod_inv(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, BN_CTX *ctx)
{
BIGNUM *b = NULL;
int ret = 0;
int numbits;
BN_CTX_start(ctx);
if ((b = BN_CTX_get(ctx)) == NULL)
goto err;
/* Fail on a non-sensical input p value */
numbits = BN_num_bits(p);
if (numbits <= 1)
goto err;
/* generate blinding value */
do {
if (!BN_priv_rand_ex(b, numbits - 1,
BN_RAND_TOP_ANY, BN_RAND_BOTTOM_ANY, 0, ctx))
goto err;
} while (BN_is_zero(b));
/* r := a * b */
if (!BN_GF2m_mod_mul(r, a, b, p, ctx))
goto err;
/* r := 1/(a * b) */
if (!BN_GF2m_mod_inv_vartime(r, r, p, ctx))
goto err;
/* r := b/(a * b) = 1/a */
if (!BN_GF2m_mod_mul(r, r, b, p, ctx))
goto err;
ret = 1;
err:
BN_CTX_end(ctx);
return ret;
}
/*
* Invert xx, reduce modulo p, and store the result in r. r could be xx.
* This function calls down to the BN_GF2m_mod_inv implementation; this
* wrapper function is only provided for convenience; for best performance,
* use the BN_GF2m_mod_inv function.
*/
int BN_GF2m_mod_inv_arr(BIGNUM *r, const BIGNUM *xx, const int p[],
BN_CTX *ctx)
{
BIGNUM *field;
int ret = 0;
bn_check_top(xx);
BN_CTX_start(ctx);
if ((field = BN_CTX_get(ctx)) == NULL)
goto err;
if (!BN_GF2m_arr2poly(p, field))
goto err;
ret = BN_GF2m_mod_inv(r, xx, field, ctx);
bn_check_top(r);
err:
BN_CTX_end(ctx);
return ret;
}
/*
* Divide y by x, reduce modulo p, and store the result in r. r could be x
* or y, x could equal y.
*/
int BN_GF2m_mod_div(BIGNUM *r, const BIGNUM *y, const BIGNUM *x,
const BIGNUM *p, BN_CTX *ctx)
{
BIGNUM *xinv = NULL;
int ret = 0;
bn_check_top(y);
bn_check_top(x);
bn_check_top(p);
BN_CTX_start(ctx);
xinv = BN_CTX_get(ctx);
if (xinv == NULL)
goto err;
if (!BN_GF2m_mod_inv(xinv, x, p, ctx))
goto err;
if (!BN_GF2m_mod_mul(r, y, xinv, p, ctx))
goto err;
bn_check_top(r);
ret = 1;
err:
BN_CTX_end(ctx);
return ret;
}
/*
* Divide yy by xx, reduce modulo p, and store the result in r. r could be xx
* * or yy, xx could equal yy. This function calls down to the
* BN_GF2m_mod_div implementation; this wrapper function is only provided for
* convenience; for best performance, use the BN_GF2m_mod_div function.
*/
int BN_GF2m_mod_div_arr(BIGNUM *r, const BIGNUM *yy, const BIGNUM *xx,
const int p[], BN_CTX *ctx)
{
BIGNUM *field;
int ret = 0;
bn_check_top(yy);
bn_check_top(xx);
BN_CTX_start(ctx);
if ((field = BN_CTX_get(ctx)) == NULL)
goto err;
if (!BN_GF2m_arr2poly(p, field))
goto err;
ret = BN_GF2m_mod_div(r, yy, xx, field, ctx);
bn_check_top(r);
err:
BN_CTX_end(ctx);
return ret;
}
/*
* Compute the bth power of a, reduce modulo p, and store the result in r. r
* could be a. Uses simple square-and-multiply algorithm A.5.1 from IEEE
* P1363.
*/
int BN_GF2m_mod_exp_arr(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
const int p[], BN_CTX *ctx)
{
int ret = 0, i, n;
BIGNUM *u;
bn_check_top(a);
bn_check_top(b);
if (BN_is_zero(b))
return BN_one(r);
if (BN_abs_is_word(b, 1))
return (BN_copy(r, a) != NULL);
BN_CTX_start(ctx);
if ((u = BN_CTX_get(ctx)) == NULL)
goto err;
if (!BN_GF2m_mod_arr(u, a, p))
goto err;
n = BN_num_bits(b) - 1;
for (i = n - 1; i >= 0; i--) {
if (!BN_GF2m_mod_sqr_arr(u, u, p, ctx))
goto err;
if (BN_is_bit_set(b, i)) {
if (!BN_GF2m_mod_mul_arr(u, u, a, p, ctx))
goto err;
}
}
if (!BN_copy(r, u))
goto err;
bn_check_top(r);
ret = 1;
err:
BN_CTX_end(ctx);
return ret;
}
/*
* Compute the bth power of a, reduce modulo p, and store the result in r. r
* could be a. This function calls down to the BN_GF2m_mod_exp_arr
* implementation; this wrapper function is only provided for convenience;
* for best performance, use the BN_GF2m_mod_exp_arr function.
*/
int BN_GF2m_mod_exp(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
const BIGNUM *p, BN_CTX *ctx)
{
int ret = 0;
const int max = BN_num_bits(p) + 1;
int *arr;
bn_check_top(a);
bn_check_top(b);
bn_check_top(p);
arr = OPENSSL_malloc(sizeof(*arr) * max);
if (arr == NULL)
return 0;
ret = BN_GF2m_poly2arr(p, arr, max);
if (!ret || ret > max) {
ERR_raise(ERR_LIB_BN, BN_R_INVALID_LENGTH);
goto err;
}
ret = BN_GF2m_mod_exp_arr(r, a, b, arr, ctx);
bn_check_top(r);
err:
OPENSSL_free(arr);
return ret;
}
/*
* Compute the square root of a, reduce modulo p, and store the result in r.
* r could be a. Uses exponentiation as in algorithm A.4.1 from IEEE P1363.
*/
int BN_GF2m_mod_sqrt_arr(BIGNUM *r, const BIGNUM *a, const int p[],
BN_CTX *ctx)
{
int ret = 0;
BIGNUM *u;
bn_check_top(a);
if (p[0] == 0) {
/* reduction mod 1 => return 0 */
BN_zero(r);
return 1;
}
BN_CTX_start(ctx);
if ((u = BN_CTX_get(ctx)) == NULL)
goto err;
if (!BN_set_bit(u, p[0] - 1))
goto err;
ret = BN_GF2m_mod_exp_arr(r, a, u, p, ctx);
bn_check_top(r);
err:
BN_CTX_end(ctx);
return ret;
}
/*
* Compute the square root of a, reduce modulo p, and store the result in r.
* r could be a. This function calls down to the BN_GF2m_mod_sqrt_arr
* implementation; this wrapper function is only provided for convenience;
* for best performance, use the BN_GF2m_mod_sqrt_arr function.
*/
int BN_GF2m_mod_sqrt(BIGNUM *r, const BIGNUM *a, const BIGNUM *p, BN_CTX *ctx)
{
int ret = 0;
const int max = BN_num_bits(p) + 1;
int *arr;
bn_check_top(a);
bn_check_top(p);
arr = OPENSSL_malloc(sizeof(*arr) * max);
if (arr == NULL)
return 0;
ret = BN_GF2m_poly2arr(p, arr, max);
if (!ret || ret > max) {
ERR_raise(ERR_LIB_BN, BN_R_INVALID_LENGTH);
goto err;
}
ret = BN_GF2m_mod_sqrt_arr(r, a, arr, ctx);
bn_check_top(r);
err:
OPENSSL_free(arr);
return ret;
}
/*
* Find r such that r^2 + r = a mod p. r could be a. If no r exists returns
* 0. Uses algorithms A.4.7 and A.4.6 from IEEE P1363.
*/
int BN_GF2m_mod_solve_quad_arr(BIGNUM *r, const BIGNUM *a_, const int p[],
BN_CTX *ctx)
{
int ret = 0, count = 0, j;
BIGNUM *a, *z, *rho, *w, *w2, *tmp;
bn_check_top(a_);
if (p[0] == 0) {
/* reduction mod 1 => return 0 */
BN_zero(r);
return 1;
}
BN_CTX_start(ctx);
a = BN_CTX_get(ctx);
z = BN_CTX_get(ctx);
w = BN_CTX_get(ctx);
if (w == NULL)
goto err;
if (!BN_GF2m_mod_arr(a, a_, p))
goto err;
if (BN_is_zero(a)) {
BN_zero(r);
ret = 1;
goto err;
}
if (p[0] & 0x1) { /* m is odd */
/* compute half-trace of a */
if (!BN_copy(z, a))
goto err;
for (j = 1; j <= (p[0] - 1) / 2; j++) {
if (!BN_GF2m_mod_sqr_arr(z, z, p, ctx))
goto err;
if (!BN_GF2m_mod_sqr_arr(z, z, p, ctx))
goto err;
if (!BN_GF2m_add(z, z, a))
goto err;
}
} else { /* m is even */
rho = BN_CTX_get(ctx);
w2 = BN_CTX_get(ctx);
tmp = BN_CTX_get(ctx);
if (tmp == NULL)
goto err;
do {
if (!BN_priv_rand_ex(rho, p[0], BN_RAND_TOP_ONE, BN_RAND_BOTTOM_ANY,
0, ctx))
goto err;
if (!BN_GF2m_mod_arr(rho, rho, p))
goto err;
BN_zero(z);
if (!BN_copy(w, rho))
goto err;
for (j = 1; j <= p[0] - 1; j++) {
if (!BN_GF2m_mod_sqr_arr(z, z, p, ctx))
goto err;
if (!BN_GF2m_mod_sqr_arr(w2, w, p, ctx))
goto err;
if (!BN_GF2m_mod_mul_arr(tmp, w2, a, p, ctx))
goto err;
if (!BN_GF2m_add(z, z, tmp))
goto err;
if (!BN_GF2m_add(w, w2, rho))
goto err;
}
count++;
} while (BN_is_zero(w) && (count < MAX_ITERATIONS));
if (BN_is_zero(w)) {
ERR_raise(ERR_LIB_BN, BN_R_TOO_MANY_ITERATIONS);
goto err;
}
}
if (!BN_GF2m_mod_sqr_arr(w, z, p, ctx))
goto err;
if (!BN_GF2m_add(w, z, w))
goto err;
if (BN_GF2m_cmp(w, a)) {
ERR_raise(ERR_LIB_BN, BN_R_NO_SOLUTION);
goto err;
}
if (!BN_copy(r, z))
goto err;
bn_check_top(r);
ret = 1;
err:
BN_CTX_end(ctx);
return ret;
}
/*
* Find r such that r^2 + r = a mod p. r could be a. If no r exists returns
* 0. This function calls down to the BN_GF2m_mod_solve_quad_arr
* implementation; this wrapper function is only provided for convenience;
* for best performance, use the BN_GF2m_mod_solve_quad_arr function.
*/
int BN_GF2m_mod_solve_quad(BIGNUM *r, const BIGNUM *a, const BIGNUM *p,
BN_CTX *ctx)
{
int ret = 0;
const int max = BN_num_bits(p) + 1;
int *arr;
bn_check_top(a);
bn_check_top(p);
arr = OPENSSL_malloc(sizeof(*arr) * max);
if (arr == NULL)
goto err;
ret = BN_GF2m_poly2arr(p, arr, max);
if (!ret || ret > max) {
ERR_raise(ERR_LIB_BN, BN_R_INVALID_LENGTH);
goto err;
}
ret = BN_GF2m_mod_solve_quad_arr(r, a, arr, ctx);
bn_check_top(r);
err:
OPENSSL_free(arr);
return ret;
}
/*
* Convert the bit-string representation of a polynomial ( \sum_{i=0}^n a_i *
* x^i) into an array of integers corresponding to the bits with non-zero
* coefficient. The array is intended to be suitable for use with
* `BN_GF2m_mod_arr()`, and so the constant term of the polynomial must not be
* zero. This translates to a requirement that the input BIGNUM `a` is odd.
*
* Given sufficient room, the array is terminated with -1. Up to max elements
* of the array will be filled.
*
* The return value is total number of array elements that would be filled if
* array was large enough, including the terminating `-1`. It is `0` when `a`
* is not odd or the constant term is zero contrary to requirement.
*
* The return value is also `0` when the leading exponent exceeds
* `OPENSSL_ECC_MAX_FIELD_BITS`, this guards against CPU exhaustion attacks,
*/
int BN_GF2m_poly2arr(const BIGNUM *a, int p[], int max)
{
int i, j, k = 0;
BN_ULONG mask;
if (!BN_is_odd(a))
return 0;
for (i = a->top - 1; i >= 0; i--) {
if (!a->d[i])
/* skip word if a->d[i] == 0 */
continue;
mask = BN_TBIT;
for (j = BN_BITS2 - 1; j >= 0; j--) {
if (a->d[i] & mask) {
if (k < max)
p[k] = BN_BITS2 * i + j;
k++;
}
mask >>= 1;
}
}
if (k > 0 && p[0] > OPENSSL_ECC_MAX_FIELD_BITS)
return 0;
if (k < max)
p[k] = -1;
return k + 1;
}
/*
* Convert the coefficient array representation of a polynomial to a
* bit-string. The array must be terminated by -1.
*/
int BN_GF2m_arr2poly(const int p[], BIGNUM *a)
{
int i;
bn_check_top(a);
BN_zero(a);
for (i = 0; p[i] != -1; i++) {
if (BN_set_bit(a, p[i]) == 0)
return 0;
}
bn_check_top(a);
return 1;
}
#endif
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