// 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_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;
}
/* I've just gone over this and it is now %20 faster on x86 - eay - 27 Jun 96 */
int BN_sqr(BIGNUM *r, BIGNUM *a, BN_CTX *ctx)
{
int max,al;
int ret = 0;
BIGNUM *tmp,*rr;
#ifdef BN_COUNT
printf("BN_sqr %d * %d\n",a->top,a->top);
#endif
bn_check_top(a);
al=a->top;
if (al <= 0)
{
r->top=0;
return(1);
}
BN_CTX_start(ctx);
rr=(a != r) ? r : BN_CTX_get(ctx);
tmp=BN_CTX_get(ctx);
if (tmp == NULL) goto err;
max=(al+al);
if (bn_wexpand(rr,max+1) == NULL) goto err;
r->neg=0;
if (al == 4)
{
#ifndef BN_SQR_COMBA
BN_ULONG t[8];
bn_sqr_normal(rr->d,a->d,4,t);
#else
bn_sqr_comba4(rr->d,a->d);
#endif
}
else if (al == 8)
{
#ifndef BN_SQR_COMBA
BN_ULONG t[16];
bn_sqr_normal(rr->d,a->d,8,t);
#else
bn_sqr_comba8(rr->d,a->d);
#endif
}
else
{
#if defined(BN_RECURSION)
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
{
int j,k;
j=BN_num_bits_word((BN_ULONG)al);
j=1<<(j-1);
k=j+j;
if (al == j)
{
if (bn_wexpand(a,k*2) == NULL) goto err;
if (bn_wexpand(tmp,k*2) == NULL) goto err;
bn_sqr_recursive(rr->d,a->d,al,tmp->d);
}
else
{
if (bn_wexpand(tmp,max) == NULL) goto err;
bn_sqr_normal(rr->d,a->d,al,tmp->d);
}
}
#else
if (bn_wexpand(tmp,max) == NULL) goto err;
bn_sqr_normal(rr->d,a->d,al,tmp->d);
#endif
}
rr->top=max;
if ((max > 0) && (rr->d[max-1] == 0)) rr->top--;
if (rr != r) BN_copy(r,rr);
ret = 1;
err:
BN_CTX_end(ctx);
return(ret);
}
/* r is 2*n words in size,
* a and b are both n words in size.
* n must be a power of 2.
* We multiply and return the result.
* t must be 2*n 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_sqr_recursive(BN_ULONG *r, BN_ULONG *a, int n2, BN_ULONG *t)
{
int n=n2/2;
int zero,c1;
BN_ULONG ln,lo,*p;
#ifdef BN_COUNT
printf(" bn_sqr_recursive %d * %d\n",n2,n2);
#endif
if (n2 == 4)
{
#ifndef BN_SQR_COMBA
bn_sqr_normal(r,a,4,t);
#else
bn_sqr_comba4(r,a);
#endif
return;
}
else if (n2 == 8)
{
#ifndef BN_SQR_COMBA
bn_sqr_normal(r,a,8,t);
#else
bn_sqr_comba8(r,a);
#endif
return;
}
if (n2 < BN_SQR_RECURSIVE_SIZE_NORMAL)
{
bn_sqr_normal(r,a,n2,t);
return;
}
/* r=(a[0]-a[1])*(a[1]-a[0]) */
c1=bn_cmp_words(a,&(a[n]),n);
zero=0;
if (c1 > 0)
bn_sub_words(t,a,&(a[n]),n);
else if (c1 < 0)
bn_sub_words(t,&(a[n]),a,n);
else
zero=1;
/* The result will always be negative unless it is zero */
p= &(t[n2*2]);
if (!zero)
bn_sqr_recursive(&(t[n2]),t,n,p);
else
memset(&(t[n2]),0,n*sizeof(BN_ULONG));
bn_sqr_recursive(r,a,n,p);
bn_sqr_recursive(&(r[n2]),&(a[n]),n,p);
/* t[32] holds (a[0]-a[1])*(a[1]-a[0]), it is negative or zero
* r[10] holds (a[0]*b[0])
* r[32] holds (b[1]*b[1])
*/
c1=(int)(bn_add_words(t,r,&(r[n2]),n2));
/* t[32] is negative */
c1-=(int)(bn_sub_words(&(t[n2]),t,&(t[n2]),n2));
/* t[32] holds (a[0]-a[1])*(a[1]-a[0])+(a[0]*a[0])+(a[1]*a[1])
* r[10] holds (a[0]*a[0])
* r[32] holds (a[1]*a[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);
}
}
}
/* I've just gone over this and it is now %20 faster on x86 - eay - 27 Jun 96 */
int BN_sqr(BIGNUM *r, const BIGNUM *a, BN_CTX *ctx)
{
int max,al;
int ret = 0;
BIGNUM *tmp,*rr;
#ifdef BN_COUNT
fprintf(stderr,"BN_sqr %d * %d\n",a->top,a->top);
#endif
bn_check_top(a);
al=a->top;
if (al <= 0)
{
r->top=0;
return 1;
}
BN_CTX_start(ctx);
rr=(a != r) ? r : BN_CTX_get(ctx);
tmp=BN_CTX_get(ctx);
if (!rr || !tmp) goto err;
max = 2 * al; /* Non-zero (from above) */
if (bn_wexpand(rr,max) == NULL) goto err;
if (al == 4)
{
#ifndef BN_SQR_COMBA
BN_ULONG t[8];
bn_sqr_normal(rr->d,a->d,4,t);
#else
bn_sqr_comba4(rr->d,a->d);
#endif
}
else if (al == 8)
{
#ifndef BN_SQR_COMBA
BN_ULONG t[16];
bn_sqr_normal(rr->d,a->d,8,t);
#else
bn_sqr_comba8(rr->d,a->d);
#endif
}
else
{
#if defined(BN_RECURSION)
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
{
int j,k;
j=BN_num_bits_word((BN_ULONG)al);
j=1<<(j-1);
k=j+j;
if (al == j)
{
if (bn_wexpand(tmp,k*2) == NULL) goto err;
bn_sqr_recursive(rr->d,a->d,al,tmp->d);
}
else
{
if (bn_wexpand(tmp,max) == NULL) goto err;
bn_sqr_normal(rr->d,a->d,al,tmp->d);
}
}
#else
if (bn_wexpand(tmp,max) == NULL) goto err;
bn_sqr_normal(rr->d,a->d,al,tmp->d);
#endif
}
rr->neg=0;
/* If the most-significant half of the top word of 'a' is zero, then
* the square of 'a' will max-1 words. */
if(a->d[al - 1] == (a->d[al - 1] & BN_MASK2l))
rr->top = max - 1;
else
rr->top = max;
if (rr != r) BN_copy(r,rr);
ret = 1;
err:
bn_check_top(rr);
bn_check_top(tmp);
BN_CTX_end(ctx);
return(ret);
}
int BN_sqr(BIGNUM *r, const BIGNUM *a, BN_CTX *ctx) {
int max, al;
int ret = 0;
BIGNUM *tmp, *rr;
al = a->top;
if (al <= 0) {
r->top = 0;
r->neg = 0;
return 1;
}
BN_CTX_start(ctx);
rr = (a != r) ? r : BN_CTX_get(ctx);
tmp = BN_CTX_get(ctx);
if (!rr || !tmp) {
goto err;
}
max = 2 * al; /* Non-zero (from above) */
if (bn_wexpand(rr, max) == NULL) {
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 {
int j, k;
j = BN_num_bits_word((BN_ULONG)al);
j = 1 << (j - 1);
k = j + j;
if (al == j) {
if (bn_wexpand(tmp, k * 2) == NULL) {
goto err;
}
bn_sqr_recursive(rr->d, a->d, al, tmp->d);
} else {
if (bn_wexpand(tmp, max) == NULL) {
goto err;
}
bn_sqr_normal(rr->d, a->d, al, tmp->d);
}
}
}
rr->neg = 0;
/* If the most-significant half of the top word of 'a' is zero, then
* the square of 'a' will max-1 words. */
if (a->d[al - 1] == (a->d[al - 1] & BN_MASK2l)) {
rr->top = max - 1;
} else {
rr->top = max;
}
if (rr != r) {
BN_copy(r, rr);
}
ret = 1;
err:
BN_CTX_end(ctx);
return ret;
}
// r is 2*n words in size,
// a and b are both n words in size. (There's not actually a 'b' here ...)
// n must be a power of 2.
// We multiply and return the result.
// t must be 2*n 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]
static void bn_sqr_recursive(BN_ULONG *r, const BN_ULONG *a, int n2,
BN_ULONG *t) {
int n = n2 / 2;
int zero, c1;
BN_ULONG ln, lo, *p;
if (n2 == 4) {
bn_sqr_comba4(r, a);
return;
} else if (n2 == 8) {
bn_sqr_comba8(r, a);
return;
}
if (n2 < BN_SQR_RECURSIVE_SIZE_NORMAL) {
bn_sqr_normal(r, a, n2, t);
return;
}
// r=(a[0]-a[1])*(a[1]-a[0])
c1 = bn_cmp_words(a, &(a[n]), n);
zero = 0;
if (c1 > 0) {
bn_sub_words(t, a, &(a[n]), n);
} else if (c1 < 0) {
bn_sub_words(t, &(a[n]), a, n);
} else {
zero = 1;
}
// The result will always be negative unless it is zero
p = &(t[n2 * 2]);
if (!zero) {
bn_sqr_recursive(&(t[n2]), t, n, p);
} else {
OPENSSL_memset(&(t[n2]), 0, n2 * sizeof(BN_ULONG));
}
bn_sqr_recursive(r, a, n, p);
bn_sqr_recursive(&(r[n2]), &(a[n]), n, p);
// t[32] holds (a[0]-a[1])*(a[1]-a[0]), it is negative or zero
// r[10] holds (a[0]*b[0])
// r[32] holds (b[1]*b[1])
c1 = (int)(bn_add_words(t, r, &(r[n2]), n2));
// t[32] is negative
c1 -= (int)(bn_sub_words(&(t[n2]), t, &(t[n2]), n2));
// t[32] holds (a[0]-a[1])*(a[1]-a[0])+(a[0]*a[0])+(a[1]*a[1])
// r[10] holds (a[0]*a[0])
// r[32] holds (a[1]*a[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_sqr_fixed_top(BIGNUM *r, const BIGNUM *a, BN_CTX *ctx)
{
int max, al;
int ret = 0;
BIGNUM *tmp, *rr;
bn_check_top(a);
al = a->top;
if (al <= 0) {
r->top = 0;
r->neg = 0;
return 1;
}
BN_CTX_start(ctx);
rr = (a != r) ? r : BN_CTX_get(ctx);
tmp = BN_CTX_get(ctx);
if (rr == NULL || tmp == NULL)
goto err;
max = 2 * al; /* Non-zero (from above) */
if (bn_wexpand(rr, max) == NULL)
goto err;
if (al == 4) {
#ifndef BN_SQR_COMBA
BN_ULONG t[8];
bn_sqr_normal(rr->d, a->d, 4, t);
#else
bn_sqr_comba4(rr->d, a->d);
#endif
} else if (al == 8) {
#ifndef BN_SQR_COMBA
BN_ULONG t[16];
bn_sqr_normal(rr->d, a->d, 8, t);
#else
bn_sqr_comba8(rr->d, a->d);
#endif
} else {
#if defined(BN_RECURSION)
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 {
int j, k;
j = BN_num_bits_word((BN_ULONG)al);
j = 1 << (j - 1);
k = j + j;
if (al == j) {
if (bn_wexpand(tmp, k * 2) == NULL)
goto err;
bn_sqr_recursive(rr->d, a->d, al, tmp->d);
} else {
if (bn_wexpand(tmp, max) == NULL)
goto err;
bn_sqr_normal(rr->d, a->d, al, tmp->d);
}
}
#else
if (bn_wexpand(tmp, max) == NULL)
goto err;
bn_sqr_normal(rr->d, a->d, al, tmp->d);
#endif
}
rr->neg = 0;
rr->top = max;
rr->flags |= BN_FLG_FIXED_TOP;
if (r != rr && BN_copy(r, rr) == NULL)
goto err;
ret = 1;
err:
bn_check_top(rr);
bn_check_top(tmp);
BN_CTX_end(ctx);
return ret;
}
