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);
}
}
int 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) {
OPENSSL_PUT_ERROR(BN, ERR_R_SHOULD_NOT_HAVE_BEEN_CALLED);
return 0;
}
// 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);
}
return 1;
}
/* dnX may not be positive, but n2/2+dnX has to be */
void bn_mul_recursive(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, int n2,
int dna, int dnb, BN_ULONG *t)
{
int n = n2 / 2, c1, c2;
int tna = n + dna, tnb = n + dnb;
unsigned int neg, zero;
BN_ULONG ln, lo, *p;
# ifdef BN_MUL_COMBA
# if 0
if (n2 == 4) {
bn_mul_comba4(r, a, b);
return;
}
# endif
/*
* 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;
}
# endif /* BN_MUL_COMBA */
/* 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)
memset(&r[2 * n2 + dna + dnb], 0,
sizeof(BN_ULONG) * -(dna + dnb));
return;
}
/* r=(a[0]-a[1])*(b[1]-b[0]) */
c1 = bn_cmp_part_words(a, &(a[n]), tna, n - tna);
c2 = bn_cmp_part_words(&(b[n]), b, tnb, tnb - n);
zero = neg = 0;
switch (c1 * 3 + c2) {
case -4:
bn_sub_part_words(t, &(a[n]), a, tna, tna - n); /* - */
bn_sub_part_words(&(t[n]), b, &(b[n]), tnb, n - tnb); /* - */
break;
case -3:
zero = 1;
break;
case -2:
bn_sub_part_words(t, &(a[n]), a, tna, tna - n); /* - */
bn_sub_part_words(&(t[n]), &(b[n]), b, tnb, tnb - n); /* + */
neg = 1;
break;
case -1:
case 0:
case 1:
zero = 1;
break;
case 2:
bn_sub_part_words(t, a, &(a[n]), tna, n - tna); /* + */
bn_sub_part_words(&(t[n]), b, &(b[n]), tnb, n - tnb); /* - */
neg = 1;
break;
case 3:
zero = 1;
break;
case 4:
bn_sub_part_words(t, a, &(a[n]), tna, n - tna);
bn_sub_part_words(&(t[n]), &(b[n]), b, tnb, tnb - n);
break;
}
# ifdef BN_MUL_COMBA
if (n == 4 && dna == 0 && dnb == 0) { /* XXX: bn_mul_comba4 could take
* extra args to do this well */
if (!zero)
bn_mul_comba4(&(t[n2]), t, &(t[n]));
else
memset(&t[n2], 0, sizeof(*t) * 8);
bn_mul_comba4(r, a, b);
bn_mul_comba4(&(r[n2]), &(a[n]), &(b[n]));
} else if (n == 8 && dna == 0 && dnb == 0) { /* XXX: bn_mul_comba8 could
* take extra args to do
* this well */
if (!zero)
bn_mul_comba8(&(t[n2]), t, &(t[n]));
else
memset(&t[n2], 0, sizeof(*t) * 16);
bn_mul_comba8(r, a, b);
bn_mul_comba8(&(r[n2]), &(a[n]), &(b[n]));
} else
# endif /* BN_MUL_COMBA */
{
p = &(t[n2 * 2]);
if (!zero)
bn_mul_recursive(&(t[n2]), t, &(t[n]), n, 0, 0, p);
else
memset(&t[n2], 0, sizeof(*t) * n2);
bn_mul_recursive(r, a, b, n, 0, 0, p);
bn_mul_recursive(&(r[n2]), &(a[n]), &(b[n]), n, dna, dnb, p);
}
/*-
* t[32] holds (a[0]-a[1])*(b[1]-b[0]), c1 is the sign
* r[10] holds (a[0]*b[0])
* r[32] holds (b[1]*b[1])
*/
c1 = (int)(bn_add_words(t, r, &(r[n2]), n2));
if (neg) { /* if t[32] is negative */
c1 -= (int)(bn_sub_words(&(t[n2]), t, &(t[n2]), n2));
} else {
/* Might have a carry */
c1 += (int)(bn_add_words(&(t[n2]), &(t[n2]), t, n2));
}
/*-
* t[32] holds (a[0]-a[1])*(b[1]-b[0])+(a[0]*b[0])+(a[1]*b[1])
* r[10] holds (a[0]*b[0])
* r[32] holds (b[1]*b[1])
* c1 holds the carry bits
*/
c1 += (int)(bn_add_words(&(r[n]), &(r[n]), &(t[n2]), n2));
if (c1) {
p = &(r[n + n2]);
lo = *p;
ln = (lo + c1) & BN_MASK2;
*p = ln;
/*
* The overflow will stop before we over write words we should not
* overwrite
*/
if (ln < (BN_ULONG)c1) {
do {
p++;
lo = *p;
ln = (lo + 1) & BN_MASK2;
*p = ln;
} while (ln == 0);
}
}
}
int BN_mul(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx) {
int ret = 0;
int top, al, bl;
BIGNUM *rr;
int i;
BIGNUM *t = NULL;
int j = 0, k;
al = a->top;
bl = b->top;
if ((al == 0) || (bl == 0)) {
BN_zero(r);
return 1;
}
top = al + bl;
BN_CTX_start(ctx);
if ((r == a) || (r == b)) {
if ((rr = BN_CTX_get(ctx)) == NULL) {
goto err;
}
} else {
rr = r;
}
rr->neg = a->neg ^ b->neg;
i = al - bl;
if (i == 0) {
if (al == 8) {
if (bn_wexpand(rr, 16) == NULL) {
goto err;
}
rr->top = 16;
bn_mul_comba8(rr->d, a->d, b->d);
goto end;
}
}
if ((al >= BN_MULL_SIZE_NORMAL) && (bl >= BN_MULL_SIZE_NORMAL)) {
if (i >= -1 && i <= 1) {
/* Find out the power of two lower or equal
to the longest of the two numbers */
if (i >= 0) {
j = BN_num_bits_word((BN_ULONG)al);
}
if (i == -1) {
j = BN_num_bits_word((BN_ULONG)bl);
}
j = 1 << (j - 1);
assert(j <= al || j <= bl);
k = j + j;
t = BN_CTX_get(ctx);
if (t == NULL) {
goto err;
}
if (al > j || bl > j) {
if (bn_wexpand(t, k * 4) == NULL) {
goto err;
}
if (bn_wexpand(rr, k * 4) == NULL) {
goto err;
}
bn_mul_part_recursive(rr->d, a->d, b->d, j, al - j, bl - j, t->d);
} else {
/* al <= j || bl <= j */
if (bn_wexpand(t, k * 2) == NULL) {
goto err;
}
if (bn_wexpand(rr, k * 2) == NULL) {
goto err;
}
bn_mul_recursive(rr->d, a->d, b->d, j, al - j, bl - j, t->d);
}
rr->top = top;
goto end;
}
}
if (bn_wexpand(rr, top) == NULL) {
goto err;
}
rr->top = top;
bn_mul_normal(rr->d, a->d, al, b->d, bl);
end:
bn_correct_top(rr);
if (r != rr) {
BN_copy(r, rr);
}
ret = 1;
err:
BN_CTX_end(ctx);
return ret;
}
// n+tn is the word length
// t needs to be n*4 is size, as does r
// tnX may not be negative but less than n
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) {
int i, j, n2 = n * 2;
int c1, c2, neg;
BN_ULONG ln, lo, *p;
if (n < 8) {
bn_mul_normal(r, a, n + tna, b, n + tnb);
return;
}
// r=(a[0]-a[1])*(b[1]-b[0])
c1 = bn_cmp_part_words(a, &(a[n]), tna, n - tna);
c2 = bn_cmp_part_words(&(b[n]), b, tnb, tnb - n);
neg = 0;
switch (c1 * 3 + c2) {
case -4:
bn_sub_part_words(t, &(a[n]), a, tna, tna - n); // -
bn_sub_part_words(&(t[n]), b, &(b[n]), tnb, n - tnb); // -
break;
case -3:
// break;
case -2:
bn_sub_part_words(t, &(a[n]), a, tna, tna - n); // -
bn_sub_part_words(&(t[n]), &(b[n]), b, tnb, tnb - n); // +
neg = 1;
break;
case -1:
case 0:
case 1:
// break;
case 2:
bn_sub_part_words(t, a, &(a[n]), tna, n - tna); // +
bn_sub_part_words(&(t[n]), b, &(b[n]), tnb, n - tnb); // -
neg = 1;
break;
case 3:
// break;
case 4:
bn_sub_part_words(t, a, &(a[n]), tna, n - tna);
bn_sub_part_words(&(t[n]), &(b[n]), b, tnb, tnb - n);
break;
}
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);
OPENSSL_memset(&(r[n2 + tna + tnb]), 0, sizeof(BN_ULONG) * (n2 - tna - tnb));
} else {
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);
i = n / 2;
// If there is only a bottom half to the number,
// just do it
if (tna > tnb) {
j = tna - i;
} else {
j = tnb - i;
}
if (j == 0) {
bn_mul_recursive(&(r[n2]), &(a[n]), &(b[n]), i, tna - i, tnb - i, p);
OPENSSL_memset(&(r[n2 + i * 2]), 0, sizeof(BN_ULONG) * (n2 - i * 2));
} else if (j > 0) {
// eg, n == 16, i == 8 and tn == 11
bn_mul_part_recursive(&(r[n2]), &(a[n]), &(b[n]), i, tna - i, tnb - i, p);
OPENSSL_memset(&(r[n2 + tna + tnb]), 0,
sizeof(BN_ULONG) * (n2 - tna - tnb));
} else {
// (j < 0) eg, n == 16, i == 8 and tn == 5
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 {
for (;;) {
i /= 2;
// these simplified conditions work
// exclusively because difference
// between tna and tnb is 1 or 0
if (i < tna || i < tnb) {
bn_mul_part_recursive(&(r[n2]), &(a[n]), &(b[n]), i, tna - i,
tnb - i, p);
break;
} else if (i == tna || i == tnb) {
bn_mul_recursive(&(r[n2]), &(a[n]), &(b[n]), i, tna - i, tnb - i,
p);
break;
}
}
}
}
}
// t[32] holds (a[0]-a[1])*(b[1]-b[0]), c1 is the sign
// r[10] holds (a[0]*b[0])
// r[32] holds (b[1]*b[1])
c1 = (int)(bn_add_words(t, r, &(r[n2]), n2));
if (neg) {
// if t[32] is negative
c1 -= (int)(bn_sub_words(&(t[n2]), t, &(t[n2]), n2));
} else {
// Might have a carry
c1 += (int)(bn_add_words(&(t[n2]), &(t[n2]), t, n2));
}
// t[32] holds (a[0]-a[1])*(b[1]-b[0])+(a[0]*b[0])+(a[1]*b[1])
// r[10] holds (a[0]*b[0])
// r[32] holds (b[1]*b[1])
// c1 holds the carry bits
c1 += (int)(bn_add_words(&(r[n]), &(r[n]), &(t[n2]), n2));
if (c1) {
p = &(r[n + n2]);
lo = *p;
ln = lo + c1;
*p = ln;
// The overflow will stop before we over write
// words we should not overwrite
if (ln < (BN_ULONG)c1) {
do {
p++;
lo = *p;
ln = lo + 1;
*p = ln;
} while (ln == 0);
}
}
}
// r is 2*n2 words in size,
// a and b are both n2 words in size.
// n2 must be a power of 2.
// We multiply and return the result.
// t must be 2*n2 words in size
// We calculate
// a[0]*b[0]
// a[0]*b[0]+a[1]*b[1]+(a[0]-a[1])*(b[1]-b[0])
// a[1]*b[1]
// dnX may not be positive, but n2/2+dnX has to be
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) {
int n = n2 / 2, c1, c2;
int tna = n + dna, tnb = n + dnb;
unsigned int neg, zero;
BN_ULONG ln, lo, *p;
// 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;
}
// r=(a[0]-a[1])*(b[1]-b[0])
c1 = bn_cmp_part_words(a, &(a[n]), tna, n - tna);
c2 = bn_cmp_part_words(&(b[n]), b, tnb, tnb - n);
zero = neg = 0;
switch (c1 * 3 + c2) {
case -4:
bn_sub_part_words(t, &(a[n]), a, tna, tna - n); // -
bn_sub_part_words(&(t[n]), b, &(b[n]), tnb, n - tnb); // -
break;
case -3:
zero = 1;
break;
case -2:
bn_sub_part_words(t, &(a[n]), a, tna, tna - n); // -
bn_sub_part_words(&(t[n]), &(b[n]), b, tnb, tnb - n); // +
neg = 1;
break;
case -1:
case 0:
case 1:
zero = 1;
break;
case 2:
bn_sub_part_words(t, a, &(a[n]), tna, n - tna); // +
bn_sub_part_words(&(t[n]), b, &(b[n]), tnb, n - tnb); // -
neg = 1;
break;
case 3:
zero = 1;
break;
case 4:
bn_sub_part_words(t, a, &(a[n]), tna, n - tna);
bn_sub_part_words(&(t[n]), &(b[n]), b, tnb, tnb - n);
break;
}
if (n == 4 && dna == 0 && dnb == 0) {
// XXX: bn_mul_comba4 could take extra args to do this well
if (!zero) {
bn_mul_comba4(&(t[n2]), t, &(t[n]));
} else {
OPENSSL_memset(&(t[n2]), 0, 8 * sizeof(BN_ULONG));
}
bn_mul_comba4(r, a, b);
bn_mul_comba4(&(r[n2]), &(a[n]), &(b[n]));
} else if (n == 8 && dna == 0 && dnb == 0) {
// XXX: bn_mul_comba8 could take extra args to do this well
if (!zero) {
bn_mul_comba8(&(t[n2]), t, &(t[n]));
} else {
OPENSSL_memset(&(t[n2]), 0, 16 * sizeof(BN_ULONG));
}
bn_mul_comba8(r, a, b);
bn_mul_comba8(&(r[n2]), &(a[n]), &(b[n]));
} else {
p = &(t[n2 * 2]);
if (!zero) {
bn_mul_recursive(&(t[n2]), t, &(t[n]), n, 0, 0, p);
} else {
OPENSSL_memset(&(t[n2]), 0, n2 * sizeof(BN_ULONG));
}
bn_mul_recursive(r, a, b, n, 0, 0, p);
bn_mul_recursive(&(r[n2]), &(a[n]), &(b[n]), n, dna, dnb, p);
}
// t[32] holds (a[0]-a[1])*(b[1]-b[0]), c1 is the sign
// r[10] holds (a[0]*b[0])
// r[32] holds (b[1]*b[1])
c1 = (int)(bn_add_words(t, r, &(r[n2]), n2));
if (neg) {
// if t[32] is negative
c1 -= (int)(bn_sub_words(&(t[n2]), t, &(t[n2]), n2));
} else {
// Might have a carry
c1 += (int)(bn_add_words(&(t[n2]), &(t[n2]), t, n2));
}
// t[32] holds (a[0]-a[1])*(b[1]-b[0])+(a[0]*b[0])+(a[1]*b[1])
// r[10] holds (a[0]*b[0])
// r[32] holds (b[1]*b[1])
// c1 holds the carry bits
c1 += (int)(bn_add_words(&(r[n]), &(r[n]), &(t[n2]), n2));
if (c1) {
p = &(r[n + n2]);
lo = *p;
ln = lo + c1;
*p = ln;
// The overflow will stop before we over write
// words we should not overwrite
if (ln < (BN_ULONG)c1) {
do {
p++;
lo = *p;
ln = lo + 1;
*p = ln;
} while (ln == 0);
}
}
}
int BN_mul(BIGNUM *r, BIGNUM *a, BIGNUM *b, BN_CTX *ctx)
{
int top,al,bl;
BIGNUM *rr;
int ret = 0;
#if defined(BN_MUL_COMBA) || defined(BN_RECURSION)
int i;
#endif
#ifdef BN_COUNT
printf("BN_mul %d * %d\n",a->top,b->top);
#endif
bn_check_top(a);
bn_check_top(b);
bn_check_top(r);
al=a->top;
bl=b->top;
if ((al == 0) || (bl == 0))
{
BN_zero(r);
return(1);
}
top=al+bl;
BN_CTX_start(ctx);
if ((r == a) || (r == b))
{
if ((rr = BN_CTX_get(ctx)) == NULL) goto err;
}
else
rr = r;
rr->neg=a->neg^b->neg;
#if defined(BN_MUL_COMBA) || defined(BN_RECURSION)
i = al-bl;
#endif
#ifdef BN_MUL_COMBA
if (i == 0)
{
# if 0
if (al == 4)
{
if (bn_wexpand(rr,8) == NULL) goto err;
rr->top=8;
bn_mul_comba4(rr->d,a->d,b->d);
goto end;
}
# endif
if (al == 8)
{
if (bn_wexpand(rr,16) == NULL) goto err;
rr->top=16;
bn_mul_comba8(rr->d,a->d,b->d);
goto end;
}
}
#endif /* BN_MUL_COMBA */
if (bn_wexpand(rr,top) == NULL) goto err;
rr->top=top;
bn_mul_normal(rr->d,a->d,al,b->d,bl);
#if defined(BN_MUL_COMBA) || defined(BN_RECURSION)
end:
#endif
bn_fix_top(rr);
if (r != rr) BN_copy(r,rr);
ret=1;
err:
BN_CTX_end(ctx);
return(ret);
}
// 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_COMPILE_ASSERT(sizeof(BN_ULONG) <= sizeof(crypto_word_t),
crypto_word_t_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);
}
/* r is 2*n2 words in size,
* a and b are both n2 words in size.
* n2 must be a power of 2.
* We multiply and return the result.
* t must be 2*n2 words in size
* We calculate
* a[0]*b[0]
* a[0]*b[0]+a[1]*b[1]+(a[0]-a[1])*(b[1]-b[0])
* a[1]*b[1]
*/
void bn_mul_recursive(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, int n2,
BN_ULONG *t)
{
int n=n2/2,c1,c2;
unsigned int neg,zero;
BN_ULONG ln,lo,*p;
# ifdef BN_COUNT
printf(" bn_mul_recursive %d * %d\n",n2,n2);
# endif
# ifdef BN_MUL_COMBA
# if 0
if (n2 == 4)
{
bn_mul_comba4(r,a,b);
return;
}
# endif
if (n2 == 8)
{
bn_mul_comba8(r,a,b);
return;
}
# endif /* BN_MUL_COMBA */
if (n2 < BN_MUL_RECURSIVE_SIZE_NORMAL)
{
/* This should not happen */
bn_mul_normal(r,a,n2,b,n2);
return;
}
/* r=(a[0]-a[1])*(b[1]-b[0]) */
c1=bn_cmp_words(a,&(a[n]),n);
c2=bn_cmp_words(&(b[n]),b,n);
zero=neg=0;
switch (c1*3+c2)
{
case -4:
bn_sub_words(t, &(a[n]),a, n); /* - */
bn_sub_words(&(t[n]),b, &(b[n]),n); /* - */
break;
case -3:
zero=1;
break;
case -2:
bn_sub_words(t, &(a[n]),a, n); /* - */
bn_sub_words(&(t[n]),&(b[n]),b, n); /* + */
neg=1;
break;
case -1:
case 0:
case 1:
zero=1;
break;
case 2:
bn_sub_words(t, a, &(a[n]),n); /* + */
bn_sub_words(&(t[n]),b, &(b[n]),n); /* - */
neg=1;
break;
case 3:
zero=1;
break;
case 4:
bn_sub_words(t, a, &(a[n]),n);
bn_sub_words(&(t[n]),&(b[n]),b, n);
break;
}
# ifdef BN_MUL_COMBA
if (n == 4)
{
if (!zero)
bn_mul_comba4(&(t[n2]),t,&(t[n]));
else
memset(&(t[n2]),0,8*sizeof(BN_ULONG));
bn_mul_comba4(r,a,b);
bn_mul_comba4(&(r[n2]),&(a[n]),&(b[n]));
}
else if (n == 8)
{
if (!zero)
bn_mul_comba8(&(t[n2]),t,&(t[n]));
else
memset(&(t[n2]),0,16*sizeof(BN_ULONG));
bn_mul_comba8(r,a,b);
bn_mul_comba8(&(r[n2]),&(a[n]),&(b[n]));
}
else
# endif /* BN_MUL_COMBA */
{
p= &(t[n2*2]);
if (!zero)
bn_mul_recursive(&(t[n2]),t,&(t[n]),n,p);
else
memset(&(t[n2]),0,n2*sizeof(BN_ULONG));
bn_mul_recursive(r,a,b,n,p);
bn_mul_recursive(&(r[n2]),&(a[n]),&(b[n]),n,p);
}
/* t[32] holds (a[0]-a[1])*(b[1]-b[0]), c1 is the sign
* r[10] holds (a[0]*b[0])
* r[32] holds (b[1]*b[1])
*/
c1=(int)(bn_add_words(t,r,&(r[n2]),n2));
if (neg) /* if t[32] is negative */
{
c1-=(int)(bn_sub_words(&(t[n2]),t,&(t[n2]),n2));
}
else
{
/* Might have a carry */
c1+=(int)(bn_add_words(&(t[n2]),&(t[n2]),t,n2));
}
/* t[32] holds (a[0]-a[1])*(b[1]-b[0])+(a[0]*b[0])+(a[1]*b[1])
* r[10] holds (a[0]*b[0])
* r[32] holds (b[1]*b[1])
* c1 holds the carry bits
*/
c1+=(int)(bn_add_words(&(r[n]),&(r[n]),&(t[n2]),n2));
if (c1)
{
p= &(r[n+n2]);
lo= *p;
ln=(lo+c1)&BN_MASK2;
*p=ln;
/* The overflow will stop before we over write
* words we should not overwrite */
if (ln < (BN_ULONG)c1)
{
do {
p++;
lo= *p;
ln=(lo+1)&BN_MASK2;
*p=ln;
} while (ln == 0);
}
}
}
int BN_mul(BIGNUM *r, BIGNUM *a, BIGNUM *b, BN_CTX *ctx)
{
int top,al,bl;
BIGNUM *rr;
int ret = 0;
#if defined(BN_MUL_COMBA) || defined(BN_RECURSION)
int i;
#endif
#ifdef BN_RECURSION
BIGNUM *t;
int j,k;
#endif
#ifdef BN_COUNT
printf("BN_mul %d * %d\n",a->top,b->top);
#endif
bn_check_top(a);
bn_check_top(b);
bn_check_top(r);
al=a->top;
bl=b->top;
if ((al == 0) || (bl == 0))
{
BN_zero(r);
return(1);
}
top=al+bl;
BN_CTX_start(ctx);
if ((r == a) || (r == b))
{
if ((rr = BN_CTX_get(ctx)) == NULL) goto err;
}
else
rr = r;
rr->neg=a->neg^b->neg;
#if defined(BN_MUL_COMBA) || defined(BN_RECURSION)
i = al-bl;
#endif
#ifdef BN_MUL_COMBA
if (i == 0)
{
# if 0
if (al == 4)
{
if (bn_wexpand(rr,8) == NULL) goto err;
rr->top=8;
bn_mul_comba4(rr->d,a->d,b->d);
goto end;
}
# endif
if (al == 8)
{
if (bn_wexpand(rr,16) == NULL) goto err;
rr->top=16;
bn_mul_comba8(rr->d,a->d,b->d);
goto end;
}
}
#endif /* BN_MUL_COMBA */
#ifdef BN_RECURSION
if ((al >= BN_MULL_SIZE_NORMAL) && (bl >= BN_MULL_SIZE_NORMAL))
{
if (i == 1 && !BN_get_flags(b,BN_FLG_STATIC_DATA))
{
if (bn_wexpand(b,al) == NULL) goto err;
b->d[bl]=0;
bl++;
i--;
}
else if (i == -1 && !BN_get_flags(a,BN_FLG_STATIC_DATA))
{
if (bn_wexpand(a,bl) == NULL) goto err;
a->d[al]=0;
al++;
i++;
}
if (i == 0)
{
/* symmetric and > 4 */
/* 16 or larger */
j=BN_num_bits_word((BN_ULONG)al);
j=1<<(j-1);
k=j+j;
t = BN_CTX_get(ctx);
if (al == j) /* exact multiple */
{
if (bn_wexpand(t,k*2) == NULL) goto err;
if (bn_wexpand(rr,k*2) == NULL) goto err;
bn_mul_recursive(rr->d,a->d,b->d,al,t->d);
}
else
{
if (bn_wexpand(a,k) == NULL) goto err;
if (bn_wexpand(b,k) == NULL) goto err;
if (bn_wexpand(t,k*4) == NULL) goto err;
if (bn_wexpand(rr,k*4) == NULL) goto err;
for (i=a->top; i<k; i++)
a->d[i]=0;
for (i=b->top; i<k; i++)
b->d[i]=0;
bn_mul_part_recursive(rr->d,a->d,b->d,al-j,j,t->d);
}
rr->top=top;
goto end;
}
}
#endif /* BN_RECURSION */
if (bn_wexpand(rr,top) == NULL) goto err;
rr->top=top;
bn_mul_normal(rr->d,a->d,al,b->d,bl);
#if defined(BN_MUL_COMBA) || defined(BN_RECURSION)
end:
#endif
bn_fix_top(rr);
if (r != rr) BN_copy(r,rr);
ret=1;
err:
BN_CTX_end(ctx);
return(ret);
}
/* n+tn is the word length
* t needs to be n*4 is size, as does r */
void bn_mul_part_recursive(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, int tn,
int n, BN_ULONG *t)
{
int c1,c2,i,j,n2=n*2;
unsigned int neg;
BN_ULONG ln,lo,*p;
# ifdef BN_COUNT
printf(" bn_mul_part_recursive %d * %d\n",tn+n,tn+n);
# endif
if (n < 8)
{
i=tn+n;
bn_mul_normal(r,a,i,b,i);
return;
}
/* r=(a[0]-a[1])*(b[1]-b[0]) */
c1=bn_cmp_words(a,&(a[n]),n);
c2=bn_cmp_words(&(b[n]),b,n);
neg=0;
switch (c1*3+c2)
{
case -4:
bn_sub_words(t, &(a[n]),a, n); /* - */
bn_sub_words(&(t[n]),b, &(b[n]),n); /* - */
break;
case -3:
case -2:
bn_sub_words(t, &(a[n]),a, n); /* - */
bn_sub_words(&(t[n]),&(b[n]),b, n); /* + */
neg=1;
break;
case -1:
case 0:
case 1:
case 2:
bn_sub_words(t, a, &(a[n]),n); /* + */
bn_sub_words(&(t[n]),b, &(b[n]),n); /* - */
neg=1;
break;
case 3:
case 4:
bn_sub_words(t, a, &(a[n]),n);
bn_sub_words(&(t[n]),&(b[n]),b, n);
break;
}
/* The zero case isn't yet implemented here. The speedup
would probably be negligible. */
# if 0
if (n == 4)
{
bn_mul_comba4(&(t[n2]),t,&(t[n]));
bn_mul_comba4(r,a,b);
bn_mul_normal(&(r[n2]),&(a[n]),tn,&(b[n]),tn);
memset(&(r[n2+tn*2]),0,sizeof(BN_ULONG)*(n2-tn*2));
}
else
# endif
if (n == 8)
{
bn_mul_comba8(&(t[n2]),t,&(t[n]));
bn_mul_comba8(r,a,b);
bn_mul_normal(&(r[n2]),&(a[n]),tn,&(b[n]),tn);
memset(&(r[n2+tn*2]),0,sizeof(BN_ULONG)*(n2-tn*2));
}
else
{
p= &(t[n2*2]);
bn_mul_recursive(&(t[n2]),t,&(t[n]),n,p);
bn_mul_recursive(r,a,b,n,p);
i=n/2;
/* If there is only a bottom half to the number,
* just do it */
j=tn-i;
if (j == 0)
{
bn_mul_recursive(&(r[n2]),&(a[n]),&(b[n]),i,p);
memset(&(r[n2+i*2]),0,sizeof(BN_ULONG)*(n2-i*2));
}
else if (j > 0) /* eg, n == 16, i == 8 and tn == 11 */
{
bn_mul_part_recursive(&(r[n2]),&(a[n]),&(b[n]),
j,i,p);
memset(&(r[n2+tn*2]),0,
sizeof(BN_ULONG)*(n2-tn*2));
}
else /* (j < 0) eg, n == 16, i == 8 and tn == 5 */
{
memset(&(r[n2]),0,sizeof(BN_ULONG)*n2);
if (tn < BN_MUL_RECURSIVE_SIZE_NORMAL)
{
bn_mul_normal(&(r[n2]),&(a[n]),tn,&(b[n]),tn);
}
else
{
for (;;)
{
i/=2;
if (i < tn)
{
bn_mul_part_recursive(&(r[n2]),
&(a[n]),&(b[n]),
tn-i,i,p);
break;
}
else if (i == tn)
{
bn_mul_recursive(&(r[n2]),
&(a[n]),&(b[n]),
i,p);
break;
}
}
}
}
}
/* t[32] holds (a[0]-a[1])*(b[1]-b[0]), c1 is the sign
* r[10] holds (a[0]*b[0])
* r[32] holds (b[1]*b[1])
*/
c1=(int)(bn_add_words(t,r,&(r[n2]),n2));
if (neg) /* if t[32] is negative */
{
c1-=(int)(bn_sub_words(&(t[n2]),t,&(t[n2]),n2));
}
else
{
/* Might have a carry */
c1+=(int)(bn_add_words(&(t[n2]),&(t[n2]),t,n2));
}
/* t[32] holds (a[0]-a[1])*(b[1]-b[0])+(a[0]*b[0])+(a[1]*b[1])
* r[10] holds (a[0]*b[0])
* r[32] holds (b[1]*b[1])
* c1 holds the carry bits
*/
c1+=(int)(bn_add_words(&(r[n]),&(r[n]),&(t[n2]),n2));
if (c1)
{
p= &(r[n+n2]);
lo= *p;
ln=(lo+c1)&BN_MASK2;
*p=ln;
/* The overflow will stop before we over write
* words we should not overwrite */
if (ln < (BN_ULONG)c1)
{
do {
p++;
lo= *p;
ln=(lo+1)&BN_MASK2;
*p=ln;
} while (ln == 0);
}
}
}
int BN_mul(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx)
{
int ret = 0;
int top, al, bl;
BIGNUM *rr;
#if defined(BN_MUL_COMBA) || defined(BN_RECURSION)
int i;
#endif
#ifdef BN_RECURSION
BIGNUM *t = NULL;
int j = 0, k;
#endif
#ifdef BN_COUNT
fprintf(stderr, "BN_mul %d * %d\n", a->top, b->top);
#endif
bn_check_top(a);
bn_check_top(b);
bn_check_top(r);
al = a->top;
bl = b->top;
if ((al == 0) || (bl == 0)) {
BN_zero(r);
return (1);
}
top = al + bl;
BN_CTX_start(ctx);
if ((r == a) || (r == b)) {
if ((rr = BN_CTX_get(ctx)) == NULL)
goto err;
} else
/* Changes for cryptlib - pcg */
{
/* Usually we can set:
rr = r;
but in the cases where t gets large (see the check further down
for overflow due to k * 2 / k * 4) the value of rr needs to be
large as well. We can't predict in advance when this will occur
so we have to use an extended-size bignum for rr in all cases */
rr = ( BIGNUM * ) BN_CTX_get_ext( ctx, BIGNUM_EXT_MUL1 );
if( rr == NULL )
goto err;
}
/* End changes for cryptlib - pcg */
rr->neg = a->neg ^ b->neg;
#if defined(BN_MUL_COMBA) || defined(BN_RECURSION)
i = al - bl;
#endif
#ifdef BN_MUL_COMBA
if (i == 0) {
# if 0
if (al == 4) {
if (bn_wexpand(rr, 8) == NULL)
goto err;
rr->top = 8;
bn_mul_comba4(rr->d, a->d, b->d);
goto end;
}
# endif
if (al == 8) {
if (bn_wexpand(rr, 16) == NULL)
goto err;
rr->top = 16;
bn_mul_comba8(rr->d, a->d, b->d);
goto end;
}
}
#endif /* BN_MUL_COMBA */
#ifdef BN_RECURSION
if ((al >= BN_MULL_SIZE_NORMAL) && (bl >= BN_MULL_SIZE_NORMAL)) {
if (i >= -1 && i <= 1) {
/*
* Find out the power of two lower or equal to the longest of the
* two numbers
*/
if (i >= 0) {
j = BN_num_bits_word((BN_ULONG)al);
}
if (i == -1) {
j = BN_num_bits_word((BN_ULONG)bl);
}
j = 1 << (j - 1);
assert(j <= al || j <= bl);
k = j + j;
/* Changes for cryptlib - pcg */
if( ( k * 2 > BIGNUM_ALLOC_WORDS ) || \
( ( al > j || bl > j ) && ( k * 4 > BIGNUM_ALLOC_WORDS ) ) )
{
/* We're about to expand the temporary bignum that we're
using to an enormous size, get a special extended-size
bignum that won't result in a storage size-check error
when used */
t = BN_CTX_get_ext( ctx, BIGNUM_EXT_MUL2 );
}
else
t = BN_CTX_get(ctx);
/* End changes for cryptlib - pcg */
if (t == NULL)
goto err;
if (al > j || bl > j) {
if (bn_wexpand(t, k * 4) == NULL)
goto err;
if (bn_wexpand(rr, k * 4) == NULL)
goto err;
bn_mul_part_recursive(rr->d, a->d, b->d,
j, al - j, bl - j, t->d);
} else { /* al <= j || bl <= j */
if (bn_wexpand(t, k * 2) == NULL)
goto err;
if (bn_wexpand(rr, k * 2) == NULL)
goto err;
bn_mul_recursive(rr->d, a->d, b->d, j, al - j, bl - j, t->d);
}
rr->top = top;
goto end;
}
# if 0
if (i == 1 && !BN_get_flags(b, BN_FLG_STATIC_DATA)) {
BIGNUM *tmp_bn = (BIGNUM *)b;
if (bn_wexpand(tmp_bn, al) == NULL)
goto err;
tmp_bn->d[bl] = 0;
bl++;
i--;
} else if (i == -1 && !BN_get_flags(a, BN_FLG_STATIC_DATA)) {
BIGNUM *tmp_bn = (BIGNUM *)a;
if (bn_wexpand(tmp_bn, bl) == NULL)
goto err;
tmp_bn->d[al] = 0;
al++;
i++;
}
if (i == 0) {
/* symmetric and > 4 */
/* 16 or larger */
j = BN_num_bits_word((BN_ULONG)al);
j = 1 << (j - 1);
k = j + j;
t = BN_CTX_get(ctx);
if (al == j) { /* exact multiple */
if (bn_wexpand(t, k * 2) == NULL)
goto err;
if (bn_wexpand(rr, k * 2) == NULL)
goto err;
bn_mul_recursive(rr->d, a->d, b->d, al, t->d);
} else {
if (bn_wexpand(t, k * 4) == NULL)
goto err;
if (bn_wexpand(rr, k * 4) == NULL)
goto err;
bn_mul_part_recursive(rr->d, a->d, b->d, al - j, j, t->d);
}
rr->top = top;
goto end;
}
# endif
}
#endif /* BN_RECURSION */
if (bn_wexpand(rr, top) == NULL)
goto err;
rr->top = top;
bn_mul_normal(rr->d, a->d, al, b->d, bl);
#if defined(BN_MUL_COMBA) || defined(BN_RECURSION)
end:
#endif
bn_correct_top(rr);
if (r != rr)
BN_copy(r, rr);
ret = 1;
err:
bn_check_top(r);
BN_CTX_end_ext( ctx, BIGNUM_EXT_MUL1 ); /* pcg */
return (ret);
}
// 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 larger 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|.
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;
}
/* tnX may not be negative but less than n */
void bn_mul_part_recursive(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, int n,
int tna, int tnb, BN_ULONG *t)
{
int i, j, n2 = n * 2;
int c1, c2, neg;
BN_ULONG ln, lo, *p;
if (n < 8) {
bn_mul_normal(r, a, n + tna, b, n + tnb);
return;
}
/* r=(a[0]-a[1])*(b[1]-b[0]) */
c1 = bn_cmp_part_words(a, &(a[n]), tna, n - tna);
c2 = bn_cmp_part_words(&(b[n]), b, tnb, tnb - n);
neg = 0;
switch (c1 * 3 + c2) {
case -4:
bn_sub_part_words(t, &(a[n]), a, tna, tna - n); /* - */
bn_sub_part_words(&(t[n]), b, &(b[n]), tnb, n - tnb); /* - */
break;
case -3:
case -2:
bn_sub_part_words(t, &(a[n]), a, tna, tna - n); /* - */
bn_sub_part_words(&(t[n]), &(b[n]), b, tnb, tnb - n); /* + */
neg = 1;
break;
case -1:
case 0:
case 1:
case 2:
bn_sub_part_words(t, a, &(a[n]), tna, n - tna); /* + */
bn_sub_part_words(&(t[n]), b, &(b[n]), tnb, n - tnb); /* - */
neg = 1;
break;
case 3:
case 4:
bn_sub_part_words(t, a, &(a[n]), tna, n - tna);
bn_sub_part_words(&(t[n]), &(b[n]), b, tnb, tnb - n);
break;
}
/*
* The zero case isn't yet implemented here. The speedup would probably
* be negligible.
*/
# if 0
if (n == 4) {
bn_mul_comba4(&(t[n2]), t, &(t[n]));
bn_mul_comba4(r, a, b);
bn_mul_normal(&(r[n2]), &(a[n]), tn, &(b[n]), tn);
memset(&r[n2 + tn * 2], 0, sizeof(*r) * (n2 - tn * 2));
} else
# endif
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);
memset(&r[n2 + tna + tnb], 0, sizeof(*r) * (n2 - tna - tnb));
} else {
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);
i = n / 2;
/*
* If there is only a bottom half to the number, just do it
*/
if (tna > tnb)
j = tna - i;
else
j = tnb - i;
if (j == 0) {
bn_mul_recursive(&(r[n2]), &(a[n]), &(b[n]),
i, tna - i, tnb - i, p);
memset(&r[n2 + i * 2], 0, sizeof(*r) * (n2 - i * 2));
} else if (j > 0) { /* eg, n == 16, i == 8 and tn == 11 */
bn_mul_part_recursive(&(r[n2]), &(a[n]), &(b[n]),
i, tna - i, tnb - i, p);
memset(&(r[n2 + tna + tnb]), 0,
sizeof(BN_ULONG) * (n2 - tna - tnb));
} else { /* (j < 0) eg, n == 16, i == 8 and tn == 5 */
memset(&r[n2], 0, sizeof(*r) * 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 {
for (;;) {
i /= 2;
/*
* these simplified conditions work exclusively because
* difference between tna and tnb is 1 or 0
*/
if (i < tna || i < tnb) {
bn_mul_part_recursive(&(r[n2]),
&(a[n]), &(b[n]),
i, tna - i, tnb - i, p);
break;
} else if (i == tna || i == tnb) {
bn_mul_recursive(&(r[n2]),
&(a[n]), &(b[n]),
i, tna - i, tnb - i, p);
break;
}
}
}
}
}
/*-
* t[32] holds (a[0]-a[1])*(b[1]-b[0]), c1 is the sign
* r[10] holds (a[0]*b[0])
* r[32] holds (b[1]*b[1])
*/
c1 = (int)(bn_add_words(t, r, &(r[n2]), n2));
if (neg) { /* if t[32] is negative */
c1 -= (int)(bn_sub_words(&(t[n2]), t, &(t[n2]), n2));
} else {
/* Might have a carry */
c1 += (int)(bn_add_words(&(t[n2]), &(t[n2]), t, n2));
}
/*-
* t[32] holds (a[0]-a[1])*(b[1]-b[0])+(a[0]*b[0])+(a[1]*b[1])
* r[10] holds (a[0]*b[0])
* r[32] holds (b[1]*b[1])
* c1 holds the carry bits
*/
c1 += (int)(bn_add_words(&(r[n]), &(r[n]), &(t[n2]), n2));
if (c1) {
p = &(r[n + n2]);
lo = *p;
ln = (lo + c1) & BN_MASK2;
*p = ln;
/*
* The overflow will stop before we over write words we should not
* overwrite
*/
if (ln < (BN_ULONG)c1) {
do {
p++;
lo = *p;
ln = (lo + 1) & BN_MASK2;
*p = ln;
} while (ln == 0);
}
}
}
int bn_mul_fixed_top(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx)
{
int ret = 0;
int top, al, bl;
BIGNUM *rr;
#if defined(BN_MUL_COMBA) || defined(BN_RECURSION)
int i;
#endif
#ifdef BN_RECURSION
BIGNUM *t = NULL;
int j = 0, k;
#endif
bn_check_top(a);
bn_check_top(b);
bn_check_top(r);
al = a->top;
bl = b->top;
if ((al == 0) || (bl == 0)) {
BN_zero(r);
return 1;
}
top = al + bl;
BN_CTX_start(ctx);
if ((r == a) || (r == b)) {
if ((rr = BN_CTX_get(ctx)) == NULL)
goto err;
} else
rr = r;
#if defined(BN_MUL_COMBA) || defined(BN_RECURSION)
i = al - bl;
#endif
#ifdef BN_MUL_COMBA
if (i == 0) {
# if 0
if (al == 4) {
if (bn_wexpand(rr, 8) == NULL)
goto err;
rr->top = 8;
bn_mul_comba4(rr->d, a->d, b->d);
goto end;
}
# endif
if (al == 8) {
if (bn_wexpand(rr, 16) == NULL)
goto err;
rr->top = 16;
bn_mul_comba8(rr->d, a->d, b->d);
goto end;
}
}
#endif /* BN_MUL_COMBA */
#ifdef BN_RECURSION
if ((al >= BN_MULL_SIZE_NORMAL) && (bl >= BN_MULL_SIZE_NORMAL)) {
if (i >= -1 && i <= 1) {
/*
* Find out the power of two lower or equal to the longest of the
* two numbers
*/
if (i >= 0) {
j = BN_num_bits_word((BN_ULONG)al);
}
if (i == -1) {
j = BN_num_bits_word((BN_ULONG)bl);
}
j = 1 << (j - 1);
assert(j <= al || j <= bl);
k = j + j;
t = BN_CTX_get(ctx);
if (t == NULL)
goto err;
if (al > j || bl > j) {
if (bn_wexpand(t, k * 4) == NULL)
goto err;
if (bn_wexpand(rr, k * 4) == NULL)
goto err;
bn_mul_part_recursive(rr->d, a->d, b->d,
j, al - j, bl - j, t->d);
} else { /* al <= j || bl <= j */
if (bn_wexpand(t, k * 2) == NULL)
goto err;
if (bn_wexpand(rr, k * 2) == NULL)
goto err;
bn_mul_recursive(rr->d, a->d, b->d, j, al - j, bl - j, t->d);
}
rr->top = top;
goto end;
}
}
#endif /* BN_RECURSION */
if (bn_wexpand(rr, top) == NULL)
goto err;
rr->top = top;
bn_mul_normal(rr->d, a->d, al, b->d, bl);
#if defined(BN_MUL_COMBA) || defined(BN_RECURSION)
end:
#endif
rr->neg = a->neg ^ b->neg;
rr->flags |= BN_FLG_FIXED_TOP;
if (r != rr && BN_copy(r, rr) == NULL)
goto err;
ret = 1;
err:
bn_check_top(r);
BN_CTX_end(ctx);
return ret;
}
int BN_mul(BIGNUM *r, const BIGNUM *a, const BIGNUM *b, BN_CTX *ctx)
{
int ret = 0;
int top, al, bl;
BIGNUM *rr;
#if defined(BN_MUL_COMBA) || defined(BN_RECURSION)
int i;
#endif
#ifdef BN_RECURSION
BIGNUM *t = NULL;
int j = 0, k;
#endif
bn_check_top(a);
bn_check_top(b);
bn_check_top(r);
al = a->top;
bl = b->top;
if ((al == 0) || (bl == 0)) {
BN_zero(r);
return (1);
}
top = al + bl;
BN_CTX_start(ctx);
if ((r == a) || (r == b)) {
if ((rr = BN_CTX_get(ctx)) == NULL)
goto err;
} else
rr = r;
#if defined(BN_MUL_COMBA) || defined(BN_RECURSION)
i = al - bl;
#endif
#ifdef BN_MUL_COMBA
if (i == 0) {
# if 0
if (al == 4) {
if (bn_wexpand(rr, 8) == NULL)
goto err;
rr->top = 8;
bn_mul_comba4(rr->d, a->d, b->d);
goto end;
}
# endif
if (al == 8) {
if (bn_wexpand(rr, 16) == NULL)
goto err;
rr->top = 16;
bn_mul_comba8(rr->d, a->d, b->d);
goto end;
}
}
#endif /* BN_MUL_COMBA */
#ifdef BN_RECURSION
if ((al >= BN_MULL_SIZE_NORMAL) && (bl >= BN_MULL_SIZE_NORMAL)) {
if (i >= -1 && i <= 1) {
/*
* Find out the power of two lower or equal to the longest of the
* two numbers
*/
if (i >= 0) {
j = BN_num_bits_word((BN_ULONG)al);
}
if (i == -1) {
j = BN_num_bits_word((BN_ULONG)bl);
}
j = 1 << (j - 1);
assert(j <= al || j <= bl);
k = j + j;
t = BN_CTX_get(ctx);
if (t == NULL)
goto err;
if (al > j || bl > j) {
if (bn_wexpand(t, k * 4) == NULL)
goto err;
if (bn_wexpand(rr, k * 4) == NULL)
goto err;
bn_mul_part_recursive(rr->d, a->d, b->d,
j, al - j, bl - j, t->d);
} else { /* al <= j || bl <= j */
if (bn_wexpand(t, k * 2) == NULL)
goto err;
if (bn_wexpand(rr, k * 2) == NULL)
goto err;
bn_mul_recursive(rr->d, a->d, b->d, j, al - j, bl - j, t->d);
}
rr->top = top;
goto end;
}
# if 0
if (i == 1 && !BN_get_flags(b, BN_FLG_STATIC_DATA)) {
BIGNUM *tmp_bn = (BIGNUM *)b;
if (bn_wexpand(tmp_bn, al) == NULL)
goto err;
tmp_bn->d[bl] = 0;
bl++;
i--;
} else if (i == -1 && !BN_get_flags(a, BN_FLG_STATIC_DATA)) {
BIGNUM *tmp_bn = (BIGNUM *)a;
if (bn_wexpand(tmp_bn, bl) == NULL)
goto err;
tmp_bn->d[al] = 0;
al++;
i++;
}
if (i == 0) {
/* symmetric and > 4 */
/* 16 or larger */
j = BN_num_bits_word((BN_ULONG)al);
j = 1 << (j - 1);
k = j + j;
t = BN_CTX_get(ctx);
if (al == j) { /* exact multiple */
if (bn_wexpand(t, k * 2) == NULL)
goto err;
if (bn_wexpand(rr, k * 2) == NULL)
goto err;
bn_mul_recursive(rr->d, a->d, b->d, al, t->d);
} else {
if (bn_wexpand(t, k * 4) == NULL)
goto err;
if (bn_wexpand(rr, k * 4) == NULL)
goto err;
bn_mul_part_recursive(rr->d, a->d, b->d, al - j, j, t->d);
}
rr->top = top;
goto end;
}
# endif
}
#endif /* BN_RECURSION */
if (bn_wexpand(rr, top) == NULL)
goto err;
rr->top = top;
bn_mul_normal(rr->d, a->d, al, b->d, bl);
#if defined(BN_MUL_COMBA) || defined(BN_RECURSION)
end:
#endif
rr->neg = a->neg ^ b->neg;
bn_correct_top(rr);
if (r != rr && BN_copy(r, rr) == NULL)
goto err;
ret = 1;
err:
bn_check_top(r);
BN_CTX_end(ctx);
return (ret);
}
// 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_COMPILE_ASSERT(sizeof(BN_ULONG) <= sizeof(crypto_word_t),
crypto_word_t_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);
}
