ref: 98c1cd7ae022efe276123898af6b892eade0732c
dir: /third_party/boringssl/src/crypto/fipsmodule/bn/mul.c/
/* Copyright (C) 1995-1998 Eric Young (eay@cryptsoft.com)
* All rights reserved.
*
* This package is an SSL implementation written
* by Eric Young (eay@cryptsoft.com).
* The implementation was written so as to conform with Netscapes SSL.
*
* This library is free for commercial and non-commercial use as long as
* the following conditions are aheared to. The following conditions
* apply to all code found in this distribution, be it the RC4, RSA,
* lhash, DES, etc., code; not just the SSL code. The SSL documentation
* included with this distribution is covered by the same copyright terms
* except that the holder is Tim Hudson (tjh@cryptsoft.com).
*
* Copyright remains Eric Young's, and as such any Copyright notices in
* the code are not to be removed.
* If this package is used in a product, Eric Young should be given attribution
* as the author of the parts of the library used.
* This can be in the form of a textual message at program startup or
* in documentation (online or textual) provided with the package.
*
* Redistribution and use in source and binary forms, with or without
* modification, are permitted provided that the following conditions
* are met:
* 1. Redistributions of source code must retain the copyright
* notice, this list of conditions and the following disclaimer.
* 2. Redistributions in binary form must reproduce the above copyright
* notice, this list of conditions and the following disclaimer in the
* documentation and/or other materials provided with the distribution.
* 3. All advertising materials mentioning features or use of this software
* must display the following acknowledgement:
* "This product includes cryptographic software written by
* Eric Young (eay@cryptsoft.com)"
* The word 'cryptographic' can be left out if the rouines from the library
* being used are not cryptographic related :-).
* 4. If you include any Windows specific code (or a derivative thereof) from
* the apps directory (application code) you must include an acknowledgement:
* "This product includes software written by Tim Hudson (tjh@cryptsoft.com)"
*
* THIS SOFTWARE IS PROVIDED BY ERIC YOUNG ``AS IS'' AND
* ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
* IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
* ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
* FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
* DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
* OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
* HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
* LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
* OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
* SUCH DAMAGE.
*
* The licence and distribution terms for any publically available version or
* derivative of this code cannot be changed. i.e. this code cannot simply be
* copied and put under another distribution licence
* [including the GNU Public Licence.] */
#include <openssl/bn.h>
#include <assert.h>
#include <stdlib.h>
#include <string.h>
#include <openssl/err.h>
#include <openssl/mem.h>
#include <openssl/type_check.h>
#include "internal.h"
#include "../../internal.h"
#define BN_MUL_RECURSIVE_SIZE_NORMAL 16
#define BN_SQR_RECURSIVE_SIZE_NORMAL BN_MUL_RECURSIVE_SIZE_NORMAL
static void bn_abs_sub_words(BN_ULONG *r, const BN_ULONG *a, const BN_ULONG *b,
size_t num, BN_ULONG *tmp) {
BN_ULONG borrow = bn_sub_words(tmp, a, b, num);
bn_sub_words(r, b, a, num);
bn_select_words(r, 0 - borrow, r /* tmp < 0 */, tmp /* tmp >= 0 */, num);
}
static void bn_mul_normal(BN_ULONG *r, const BN_ULONG *a, size_t na,
const BN_ULONG *b, size_t nb) {
if (na < nb) {
size_t itmp = na;
na = nb;
nb = itmp;
const BN_ULONG *ltmp = a;
a = b;
b = ltmp;
}
BN_ULONG *rr = &(r[na]);
if (nb == 0) {
OPENSSL_memset(r, 0, na * sizeof(BN_ULONG));
return;
}
rr[0] = bn_mul_words(r, a, na, b[0]);
for (;;) {
if (--nb == 0) {
return;
}
rr[1] = bn_mul_add_words(&(r[1]), a, na, b[1]);
if (--nb == 0) {
return;
}
rr[2] = bn_mul_add_words(&(r[2]), a, na, b[2]);
if (--nb == 0) {
return;
}
rr[3] = bn_mul_add_words(&(r[3]), a, na, b[3]);
if (--nb == 0) {
return;
}
rr[4] = bn_mul_add_words(&(r[4]), a, na, b[4]);
rr += 4;
r += 4;
b += 4;
}
}
// bn_sub_part_words sets |r| to |a| - |b|. It returns the borrow bit, which is
// one if the operation underflowed and zero otherwise. |cl| is the common
// length, that is, the shorter of len(a) or len(b). |dl| is the delta length,
// that is, len(a) - len(b). |r|'s length matches the larger of |a| and |b|, or
// cl + abs(dl).
//
// TODO(davidben): Make this take |size_t|. The |cl| + |dl| calling convention
// is confusing.
static BN_ULONG bn_sub_part_words(BN_ULONG *r, const BN_ULONG *a,
const BN_ULONG *b, int cl, int dl) {
assert(cl >= 0);
BN_ULONG borrow = bn_sub_words(r, a, b, cl);
if (dl == 0) {
return borrow;
}
r += cl;
a += cl;
b += cl;
if (dl < 0) {
// |a| is shorter than |b|. Complete the subtraction as if the excess words
// in |a| were zeros.
dl = -dl;
for (int i = 0; i < dl; i++) {
r[i] = 0u - b[i] - borrow;
borrow |= r[i] != 0;
}
} else {
// |b| is shorter than |a|. Complete the subtraction as if the excess words
// in |b| were zeros.
for (int i = 0; i < dl; i++) {
// |r| and |a| may alias, so use a temporary.
BN_ULONG tmp = a[i];
r[i] = a[i] - borrow;
borrow = tmp < r[i];
}
}
return borrow;
}
// bn_abs_sub_part_words computes |r| = |a| - |b|, storing the absolute value
// and returning a mask of all ones if the result was negative and all zeros if
// the result was positive. |cl| and |dl| follow the |bn_sub_part_words| calling
// convention.
//
// TODO(davidben): Make this take |size_t|. The |cl| + |dl| calling convention
// is confusing.
static BN_ULONG bn_abs_sub_part_words(BN_ULONG *r, const BN_ULONG *a,
const BN_ULONG *b, int cl, int dl,
BN_ULONG *tmp) {
BN_ULONG borrow = bn_sub_part_words(tmp, a, b, cl, dl);
bn_sub_part_words(r, b, a, cl, -dl);
int r_len = cl + (dl < 0 ? -dl : dl);
borrow = 0 - borrow;
bn_select_words(r, borrow, r /* tmp < 0 */, tmp /* tmp >= 0 */, r_len);
return borrow;
}
int bn_abs_sub_consttime(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
BN_CTX *ctx) {
int cl = a->width < b->width ? a->width : b->width;
int dl = a->width - b->width;
int r_len = a->width < b->width ? b->width : a->width;
BN_CTX_start(ctx);
BIGNUM *tmp = BN_CTX_get(ctx);
int ok = tmp != NULL &&
bn_wexpand(r, r_len) &&
bn_wexpand(tmp, r_len);
if (ok) {
bn_abs_sub_part_words(r->d, a->d, b->d, cl, dl, tmp->d);
r->width = r_len;
}
BN_CTX_end(ctx);
return ok;
}
// Karatsuba recursive multiplication algorithm
// (cf. Knuth, The Art of Computer Programming, Vol. 2)
// bn_mul_recursive sets |r| to |a| * |b|, using |t| as scratch space. |r| has
// length 2*|n2|, |a| has length |n2| + |dna|, |b| has length |n2| + |dnb|, and
// |t| has length 4*|n2|. |n2| must be a power of two. Finally, we must have
// -|BN_MUL_RECURSIVE_SIZE_NORMAL|/2 <= |dna| <= 0 and
// -|BN_MUL_RECURSIVE_SIZE_NORMAL|/2 <= |dnb| <= 0.
//
// TODO(davidben): Simplify and |size_t| the calling convention around lengths
// here.
static void bn_mul_recursive(BN_ULONG *r, const BN_ULONG *a, const BN_ULONG *b,
int n2, int dna, int dnb, BN_ULONG *t) {
// |n2| is a power of two.
assert(n2 != 0 && (n2 & (n2 - 1)) == 0);
// Check |dna| and |dnb| are in range.
assert(-BN_MUL_RECURSIVE_SIZE_NORMAL/2 <= dna && dna <= 0);
assert(-BN_MUL_RECURSIVE_SIZE_NORMAL/2 <= dnb && dnb <= 0);
// Only call bn_mul_comba 8 if n2 == 8 and the
// two arrays are complete [steve]
if (n2 == 8 && dna == 0 && dnb == 0) {
bn_mul_comba8(r, a, b);
return;
}
// Else do normal multiply
if (n2 < BN_MUL_RECURSIVE_SIZE_NORMAL) {
bn_mul_normal(r, a, n2 + dna, b, n2 + dnb);
if (dna + dnb < 0) {
OPENSSL_memset(&r[2 * n2 + dna + dnb], 0,
sizeof(BN_ULONG) * -(dna + dnb));
}
return;
}
// Split |a| and |b| into a0,a1 and b0,b1, where a0 and b0 have size |n|.
// Split |t| into t0,t1,t2,t3, each of size |n|, with the remaining 4*|n| used
// for recursive calls.
// Split |r| into r0,r1,r2,r3. We must contribute a0*b0 to r0,r1, a0*a1+b0*b1
// to r1,r2, and a1*b1 to r2,r3. The middle term we will compute as:
//
// a0*a1 + b0*b1 = (a0 - a1)*(b1 - b0) + a1*b1 + a0*b0
//
// Note that we know |n| >= |BN_MUL_RECURSIVE_SIZE_NORMAL|/2 above, so
// |tna| and |tnb| are non-negative.
int n = n2 / 2, tna = n + dna, tnb = n + dnb;
// t0 = a0 - a1 and t1 = b1 - b0. The result will be multiplied, so we XOR
// their sign masks, giving the sign of (a0 - a1)*(b1 - b0). t0 and t1
// themselves store the absolute value.
BN_ULONG neg = bn_abs_sub_part_words(t, a, &a[n], tna, n - tna, &t[n2]);
neg ^= bn_abs_sub_part_words(&t[n], &b[n], b, tnb, tnb - n, &t[n2]);
// Compute:
// t2,t3 = t0 * t1 = |(a0 - a1)*(b1 - b0)|
// r0,r1 = a0 * b0
// r2,r3 = a1 * b1
if (n == 4 && dna == 0 && dnb == 0) {
bn_mul_comba4(&t[n2], t, &t[n]);
bn_mul_comba4(r, a, b);
bn_mul_comba4(&r[n2], &a[n], &b[n]);
} else if (n == 8 && dna == 0 && dnb == 0) {
bn_mul_comba8(&t[n2], t, &t[n]);
bn_mul_comba8(r, a, b);
bn_mul_comba8(&r[n2], &a[n], &b[n]);
} else {
BN_ULONG *p = &t[n2 * 2];
bn_mul_recursive(&t[n2], t, &t[n], n, 0, 0, p);
bn_mul_recursive(r, a, b, n, 0, 0, p);
bn_mul_recursive(&r[n2], &a[n], &b[n], n, dna, dnb, p);
}
// t0,t1,c = r0,r1 + r2,r3 = a0*b0 + a1*b1
BN_ULONG c = bn_add_words(t, r, &r[n2], n2);
// t2,t3,c = t0,t1,c + neg*t2,t3 = (a0 - a1)*(b1 - b0) + a1*b1 + a0*b0.
// The second term is stored as the absolute value, so we do this with a
// constant-time select.
BN_ULONG c_neg = c - bn_sub_words(&t[n2 * 2], t, &t[n2], n2);
BN_ULONG c_pos = c + bn_add_words(&t[n2], t, &t[n2], n2);
bn_select_words(&t[n2], neg, &t[n2 * 2], &t[n2], n2);
OPENSSL_STATIC_ASSERT(sizeof(BN_ULONG) <= sizeof(crypto_word_t),
"crypto_word_t is too small");
c = constant_time_select_w(neg, c_neg, c_pos);
// We now have our three components. Add them together.
// r1,r2,c = r1,r2 + t2,t3,c
c += bn_add_words(&r[n], &r[n], &t[n2], n2);
// Propagate the carry bit to the end.
for (int i = n + n2; i < n2 + n2; i++) {
BN_ULONG old = r[i];
r[i] = old + c;
c = r[i] < old;
}
// The product should fit without carries.
assert(c == 0);
}
// bn_mul_part_recursive sets |r| to |a| * |b|, using |t| as scratch space. |r|
// has length 4*|n|, |a| has length |n| + |tna|, |b| has length |n| + |tnb|, and
// |t| has length 8*|n|. |n| must be a power of two. Additionally, we must have
// 0 <= tna < n and 0 <= tnb < n, and |tna| and |tnb| must differ by at most
// one.
//
// TODO(davidben): Make this take |size_t| and perhaps the actual lengths of |a|
// and |b|.
static void bn_mul_part_recursive(BN_ULONG *r, const BN_ULONG *a,
const BN_ULONG *b, int n, int tna, int tnb,
BN_ULONG *t) {
// |n| is a power of two.
assert(n != 0 && (n & (n - 1)) == 0);
// Check |tna| and |tnb| are in range.
assert(0 <= tna && tna < n);
assert(0 <= tnb && tnb < n);
assert(-1 <= tna - tnb && tna - tnb <= 1);
int n2 = n * 2;
if (n < 8) {
bn_mul_normal(r, a, n + tna, b, n + tnb);
OPENSSL_memset(r + n2 + tna + tnb, 0, n2 - tna - tnb);
return;
}
// Split |a| and |b| into a0,a1 and b0,b1, where a0 and b0 have size |n|. |a1|
// and |b1| have size |tna| and |tnb|, respectively.
// Split |t| into t0,t1,t2,t3, each of size |n|, with the remaining 4*|n| used
// for recursive calls.
// Split |r| into r0,r1,r2,r3. We must contribute a0*b0 to r0,r1, a0*a1+b0*b1
// to r1,r2, and a1*b1 to r2,r3. The middle term we will compute as:
//
// a0*a1 + b0*b1 = (a0 - a1)*(b1 - b0) + a1*b1 + a0*b0
// t0 = a0 - a1 and t1 = b1 - b0. The result will be multiplied, so we XOR
// their sign masks, giving the sign of (a0 - a1)*(b1 - b0). t0 and t1
// themselves store the absolute value.
BN_ULONG neg = bn_abs_sub_part_words(t, a, &a[n], tna, n - tna, &t[n2]);
neg ^= bn_abs_sub_part_words(&t[n], &b[n], b, tnb, tnb - n, &t[n2]);
// Compute:
// t2,t3 = t0 * t1 = |(a0 - a1)*(b1 - b0)|
// r0,r1 = a0 * b0
// r2,r3 = a1 * b1
if (n == 8) {
bn_mul_comba8(&t[n2], t, &t[n]);
bn_mul_comba8(r, a, b);
bn_mul_normal(&r[n2], &a[n], tna, &b[n], tnb);
// |bn_mul_normal| only writes |tna| + |tna| words. Zero the rest.
OPENSSL_memset(&r[n2 + tna + tnb], 0, sizeof(BN_ULONG) * (n2 - tna - tnb));
} else {
BN_ULONG *p = &t[n2 * 2];
bn_mul_recursive(&t[n2], t, &t[n], n, 0, 0, p);
bn_mul_recursive(r, a, b, n, 0, 0, p);
OPENSSL_memset(&r[n2], 0, sizeof(BN_ULONG) * n2);
if (tna < BN_MUL_RECURSIVE_SIZE_NORMAL &&
tnb < BN_MUL_RECURSIVE_SIZE_NORMAL) {
bn_mul_normal(&r[n2], &a[n], tna, &b[n], tnb);
} else {
int i = n;
for (;;) {
i /= 2;
if (i < tna || i < tnb) {
// E.g., n == 16, i == 8 and tna == 11. |tna| and |tnb| are within one
// of each other, so if |tna| is larger and tna > i, then we know
// tnb >= i, and this call is valid.
bn_mul_part_recursive(&r[n2], &a[n], &b[n], i, tna - i, tnb - i, p);
break;
}
if (i == tna || i == tnb) {
// If there is only a bottom half to the number, just do it. We know
// the larger of |tna - i| and |tnb - i| is zero. The other is zero or
// -1 by because of |tna| and |tnb| differ by at most one.
bn_mul_recursive(&r[n2], &a[n], &b[n], i, tna - i, tnb - i, p);
break;
}
// This loop will eventually terminate when |i| falls below
// |BN_MUL_RECURSIVE_SIZE_NORMAL| because we know one of |tna| and |tnb|
// exceeds that.
}
}
}
// t0,t1,c = r0,r1 + r2,r3 = a0*b0 + a1*b1
BN_ULONG c = bn_add_words(t, r, &r[n2], n2);
// t2,t3,c = t0,t1,c + neg*t2,t3 = (a0 - a1)*(b1 - b0) + a1*b1 + a0*b0.
// The second term is stored as the absolute value, so we do this with a
// constant-time select.
BN_ULONG c_neg = c - bn_sub_words(&t[n2 * 2], t, &t[n2], n2);
BN_ULONG c_pos = c + bn_add_words(&t[n2], t, &t[n2], n2);
bn_select_words(&t[n2], neg, &t[n2 * 2], &t[n2], n2);
OPENSSL_STATIC_ASSERT(sizeof(BN_ULONG) <= sizeof(crypto_word_t),
"crypto_word_t is too small");
c = constant_time_select_w(neg, c_neg, c_pos);
// We now have our three components. Add them together.
// r1,r2,c = r1,r2 + t2,t3,c
c += bn_add_words(&r[n], &r[n], &t[n2], n2);
// Propagate the carry bit to the end.
for (int i = n + n2; i < n2 + n2; i++) {
BN_ULONG old = r[i];
r[i] = old + c;
c = r[i] < old;
}
// The product should fit without carries.
assert(c == 0);
}
// bn_mul_impl implements |BN_mul| and |bn_mul_consttime|. Note this function
// breaks |BIGNUM| invariants and may return a negative zero. This is handled by
// the callers.
static int bn_mul_impl(BIGNUM *r, const BIGNUM *a, const BIGNUM *b,
BN_CTX *ctx) {
int al = a->width;
int bl = b->width;
if (al == 0 || bl == 0) {
BN_zero(r);
return 1;
}
int ret = 0;
BIGNUM *rr;
BN_CTX_start(ctx);
if (r == a || r == b) {
rr = BN_CTX_get(ctx);
if (rr == NULL) {
goto err;
}
} else {
rr = r;
}
rr->neg = a->neg ^ b->neg;
int i = al - bl;
if (i == 0) {
if (al == 8) {
if (!bn_wexpand(rr, 16)) {
goto err;
}
rr->width = 16;
bn_mul_comba8(rr->d, a->d, b->d);
goto end;
}
}
int top = al + bl;
static const int kMulNormalSize = 16;
if (al >= kMulNormalSize && bl >= kMulNormalSize) {
if (-1 <= i && i <= 1) {
// Find the largest power of two less than or equal to the larger length.
int j;
if (i >= 0) {
j = BN_num_bits_word((BN_ULONG)al);
} else {
j = BN_num_bits_word((BN_ULONG)bl);
}
j = 1 << (j - 1);
assert(j <= al || j <= bl);
BIGNUM *t = BN_CTX_get(ctx);
if (t == NULL) {
goto err;
}
if (al > j || bl > j) {
// We know |al| and |bl| are at most one from each other, so if al > j,
// bl >= j, and vice versa. Thus we can use |bn_mul_part_recursive|.
//
// TODO(davidben): This codepath is almost unused in standard
// algorithms. Is this optimization necessary? See notes in
// https://boringssl-review.googlesource.com/q/I0bd604e2cd6a75c266f64476c23a730ca1721ea6
assert(al >= j && bl >= j);
if (!bn_wexpand(t, j * 8) ||
!bn_wexpand(rr, j * 4)) {
goto err;
}
bn_mul_part_recursive(rr->d, a->d, b->d, j, al - j, bl - j, t->d);
} else {
// al <= j && bl <= j. Additionally, we know j <= al or j <= bl, so one
// of al - j or bl - j is zero. The other, by the bound on |i| above, is
// zero or -1. Thus, we can use |bn_mul_recursive|.
if (!bn_wexpand(t, j * 4) ||
!bn_wexpand(rr, j * 2)) {
goto err;
}
bn_mul_recursive(rr->d, a->d, b->d, j, al - j, bl - j, t->d);
}
rr->width = top;
goto end;
}
}
if (!bn_wexpand(rr, top)) {
goto err;
}
rr->width = top;
bn_mul_normal(rr->d, a->d, al, b->d, bl);
end:
if (r != rr && !BN_copy(r, rr)) {
goto err;
}
ret = 1;
err:
BN_CTX_end(ctx);
return ret;
}
int BN_mul(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx) {
if (!bn_mul_impl(r, a, b, ctx)) {
return 0;
}
// This additionally fixes any negative zeros created by |bn_mul_impl|.
bn_set_minimal_width(r);
return 1;
}
int bn_mul_consttime(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx) {
// Prevent negative zeros.
if (a->neg || b->neg) {
OPENSSL_PUT_ERROR(BN, BN_R_NEGATIVE_NUMBER);
return 0;
}
return bn_mul_impl(r, a, b, ctx);
}
void bn_mul_small(BN_ULONG *r, size_t num_r, const BN_ULONG *a, size_t num_a,
const BN_ULONG *b, size_t num_b) {
if (num_r != num_a + num_b) {
abort();
}
// TODO(davidben): Should this call |bn_mul_comba4| too? |BN_mul| does not
// hit that code.
if (num_a == 8 && num_b == 8) {
bn_mul_comba8(r, a, b);
} else {
bn_mul_normal(r, a, num_a, b, num_b);
}
}
// tmp must have 2*n words
static void bn_sqr_normal(BN_ULONG *r, const BN_ULONG *a, size_t n,
BN_ULONG *tmp) {
if (n == 0) {
return;
}
size_t max = n * 2;
const BN_ULONG *ap = a;
BN_ULONG *rp = r;
rp[0] = rp[max - 1] = 0;
rp++;
// Compute the contribution of a[i] * a[j] for all i < j.
if (n > 1) {
ap++;
rp[n - 1] = bn_mul_words(rp, ap, n - 1, ap[-1]);
rp += 2;
}
if (n > 2) {
for (size_t i = n - 2; i > 0; i--) {
ap++;
rp[i] = bn_mul_add_words(rp, ap, i, ap[-1]);
rp += 2;
}
}
// The final result fits in |max| words, so none of the following operations
// will overflow.
// Double |r|, giving the contribution of a[i] * a[j] for all i != j.
bn_add_words(r, r, r, max);
// Add in the contribution of a[i] * a[i] for all i.
bn_sqr_words(tmp, a, n);
bn_add_words(r, r, tmp, max);
}
// bn_sqr_recursive sets |r| to |a|^2, using |t| as scratch space. |r| has
// length 2*|n2|, |a| has length |n2|, and |t| has length 4*|n2|. |n2| must be
// a power of two.
static void bn_sqr_recursive(BN_ULONG *r, const BN_ULONG *a, size_t n2,
BN_ULONG *t) {
// |n2| is a power of two.
assert(n2 != 0 && (n2 & (n2 - 1)) == 0);
if (n2 == 4) {
bn_sqr_comba4(r, a);
return;
}
if (n2 == 8) {
bn_sqr_comba8(r, a);
return;
}
if (n2 < BN_SQR_RECURSIVE_SIZE_NORMAL) {
bn_sqr_normal(r, a, n2, t);
return;
}
// Split |a| into a0,a1, each of size |n|.
// Split |t| into t0,t1,t2,t3, each of size |n|, with the remaining 4*|n| used
// for recursive calls.
// Split |r| into r0,r1,r2,r3. We must contribute a0^2 to r0,r1, 2*a0*a1 to
// r1,r2, and a1^2 to r2,r3.
size_t n = n2 / 2;
BN_ULONG *t_recursive = &t[n2 * 2];
// t0 = |a0 - a1|.
bn_abs_sub_words(t, a, &a[n], n, &t[n]);
// t2,t3 = t0^2 = |a0 - a1|^2 = a0^2 - 2*a0*a1 + a1^2
bn_sqr_recursive(&t[n2], t, n, t_recursive);
// r0,r1 = a0^2
bn_sqr_recursive(r, a, n, t_recursive);
// r2,r3 = a1^2
bn_sqr_recursive(&r[n2], &a[n], n, t_recursive);
// t0,t1,c = r0,r1 + r2,r3 = a0^2 + a1^2
BN_ULONG c = bn_add_words(t, r, &r[n2], n2);
// t2,t3,c = t0,t1,c - t2,t3 = 2*a0*a1
c -= bn_sub_words(&t[n2], t, &t[n2], n2);
// We now have our three components. Add them together.
// r1,r2,c = r1,r2 + t2,t3,c
c += bn_add_words(&r[n], &r[n], &t[n2], n2);
// Propagate the carry bit to the end.
for (size_t i = n + n2; i < n2 + n2; i++) {
BN_ULONG old = r[i];
r[i] = old + c;
c = r[i] < old;
}
// The square should fit without carries.
assert(c == 0);
}
int BN_mul_word(BIGNUM *bn, BN_ULONG w) {
if (!bn->width) {
return 1;
}
if (w == 0) {
BN_zero(bn);
return 1;
}
BN_ULONG ll = bn_mul_words(bn->d, bn->d, bn->width, w);
if (ll) {
if (!bn_wexpand(bn, bn->width + 1)) {
return 0;
}
bn->d[bn->width++] = ll;
}
return 1;
}
int bn_sqr_consttime(BIGNUM *r, const BIGNUM *a, BN_CTX *ctx) {
int al = a->width;
if (al <= 0) {
r->width = 0;
r->neg = 0;
return 1;
}
int ret = 0;
BN_CTX_start(ctx);
BIGNUM *rr = (a != r) ? r : BN_CTX_get(ctx);
BIGNUM *tmp = BN_CTX_get(ctx);
if (!rr || !tmp) {
goto err;
}
int max = 2 * al; // Non-zero (from above)
if (!bn_wexpand(rr, max)) {
goto err;
}
if (al == 4) {
bn_sqr_comba4(rr->d, a->d);
} else if (al == 8) {
bn_sqr_comba8(rr->d, a->d);
} else {
if (al < BN_SQR_RECURSIVE_SIZE_NORMAL) {
BN_ULONG t[BN_SQR_RECURSIVE_SIZE_NORMAL * 2];
bn_sqr_normal(rr->d, a->d, al, t);
} else {
// If |al| is a power of two, we can use |bn_sqr_recursive|.
if (al != 0 && (al & (al - 1)) == 0) {
if (!bn_wexpand(tmp, al * 4)) {
goto err;
}
bn_sqr_recursive(rr->d, a->d, al, tmp->d);
} else {
if (!bn_wexpand(tmp, max)) {
goto err;
}
bn_sqr_normal(rr->d, a->d, al, tmp->d);
}
}
}
rr->neg = 0;
rr->width = max;
if (rr != r && !BN_copy(r, rr)) {
goto err;
}
ret = 1;
err:
BN_CTX_end(ctx);
return ret;
}
int BN_sqr(BIGNUM *r, const BIGNUM *a, BN_CTX *ctx) {
if (!bn_sqr_consttime(r, a, ctx)) {
return 0;
}
bn_set_minimal_width(r);
return 1;
}
void bn_sqr_small(BN_ULONG *r, size_t num_r, const BN_ULONG *a, size_t num_a) {
if (num_r != 2 * num_a || num_a > BN_SMALL_MAX_WORDS) {
abort();
}
if (num_a == 4) {
bn_sqr_comba4(r, a);
} else if (num_a == 8) {
bn_sqr_comba8(r, a);
} else {
BN_ULONG tmp[2 * BN_SMALL_MAX_WORDS];
bn_sqr_normal(r, a, num_a, tmp);
OPENSSL_cleanse(tmp, 2 * num_a * sizeof(BN_ULONG));
}
}