/* tmp must have 2*n words */
void bn_sqr_normal(BN_ULONG *r, BN_ULONG *a, int n, BN_ULONG *tmp)
{
int i,j,max;
BN_ULONG *ap,*rp;
max=n*2;
ap=a;
rp=r;
rp[0]=rp[max-1]=0;
rp++;
j=n;
if (--j > 0)
{
ap++;
rp[j]=bn_mul_words(rp,ap,j,ap[-1]);
rp+=2;
}
for (i=n-2; i>0; i--)
{
j--;
ap++;
rp[j]=bn_mul_add_words(rp,ap,j,ap[-1]);
rp+=2;
}
bn_add_words(r,r,r,max);
/* There will not be a carry */
bn_sqr_words(tmp,a,n);
bn_add_words(r,r,tmp,max);
}
void bn_mul_normal(BN_ULONG *r, BN_ULONG *a, int na, BN_ULONG *b, int nb)
{
BN_ULONG *rr;
#ifdef BN_COUNT
printf(" bn_mul_normal %d * %d\n",na,nb);
#endif
if (na < nb)
{
int itmp;
BN_ULONG *ltmp;
itmp=na; na=nb; nb=itmp;
ltmp=a; a=b; b=ltmp;
}
rr= &(r[na]);
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;
}
}
void bn_mul_normal(BN_ULONG *r, const BN_ULONG *a, int na, const BN_ULONG *b, int nb) /* const - pcg */
{
BN_ULONG *rr;
#ifdef BN_COUNT
fprintf(stderr, " bn_mul_normal %d * %d\n", na, nb);
#endif
if (na < nb) {
int itmp;
const BN_ULONG *ltmp; /* const - pcg */
itmp = na;
na = nb;
nb = itmp;
ltmp = a;
a = b;
b = ltmp;
}
rr = &(r[na]);
if (nb <= 0) {
(void)bn_mul_words(r, a, na, 0);
return;
} else
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;
}
}
static void bn_mul_normal(BN_ULONG *r, BN_ULONG *a, int na, BN_ULONG *b,
int nb) {
BN_ULONG *rr;
if (na < nb) {
int itmp;
BN_ULONG *ltmp;
itmp = na;
na = nb;
nb = itmp;
ltmp = a;
a = b;
b = ltmp;
}
rr = &(r[na]);
if (nb <= 0) {
(void)bn_mul_words(r, a, na, 0);
return;
} else {
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;
}
}
int BN_mul_word(BIGNUM *a, BN_ULONG w)
{
BN_ULONG ll;
w&=BN_MASK2;
if (a->top)
{
ll=bn_mul_words(a->d,a->d,a->top,w);
if (ll)
{
if (bn_wexpand(a,a->top+1) == NULL) return(0);
a->d[a->top++]=ll;
}
}
return(1);
}
void bn_mul_low_normal(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, int n)
{
bn_mul_words(r,a,n,b[0]);
for (;;)
{
if (--n <= 0) return;
bn_mul_add_words(&(r[1]),a,n,b[1]);
if (--n <= 0) return;
bn_mul_add_words(&(r[2]),a,n,b[2]);
if (--n <= 0) return;
bn_mul_add_words(&(r[3]),a,n,b[3]);
if (--n <= 0) return;
bn_mul_add_words(&(r[4]),a,n,b[4]);
r+=4;
b+=4;
}
}
int BN_mul_word(BIGNUM *bn, BN_ULONG w) {
if (!bn->top) {
return 1;
}
if (w == 0) {
BN_zero(bn);
return 1;
}
BN_ULONG ll = bn_mul_words(bn->d, bn->d, bn->top, w);
if (ll) {
if (!bn_wexpand(bn, bn->top + 1)) {
return 0;
}
bn->d[bn->top++] = ll;
}
return 1;
}
void bn_mul_low_normal(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, int n)
{
#ifdef BN_COUNT
fprintf(stderr," bn_mul_low_normal %d * %d\n",n,n);
#endif
bn_mul_words(r,a,n,b[0]);
for (;;)
{
if (--n <= 0) return;
bn_mul_add_words(&(r[1]),a,n,b[1]);
if (--n <= 0) return;
bn_mul_add_words(&(r[2]),a,n,b[2]);
if (--n <= 0) return;
bn_mul_add_words(&(r[3]),a,n,b[3]);
if (--n <= 0) return;
bn_mul_add_words(&(r[4]),a,n,b[4]);
r+=4;
b+=4;
}
}
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;
}
}
int BN_mul_word(BIGNUM *a, BN_ULONG w)
{
BN_ULONG ll;
bn_check_top(a);
w&=BN_MASK2;
if (a->top)
{
if (w == 0)
BN_zero(a);
else
{
ll=bn_mul_words(a->d,a->d,a->top,w);
if (ll)
{
if (bn_wexpand(a,a->top+1) == NULL) return(0);
a->d[a->top++]=ll;
}
}
}
bn_check_top(a);
return(1);
}
// 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_div_no_branch is a special version of BN_div. It does not contain
* branches that may leak sensitive information.
*/
static int BN_div_no_branch(BIGNUM *dv, BIGNUM *rm, const BIGNUM *num,
const BIGNUM *divisor, BN_CTX *ctx)
{
int norm_shift,i,loop;
BIGNUM *tmp,wnum,*snum,*sdiv,*res;
BN_ULONG *resp,*wnump;
BN_ULONG d0,d1;
int num_n,div_n;
bn_check_top(dv);
bn_check_top(rm);
/* bn_check_top(num); */ /* 'num' has been checked in BN_div() */
bn_check_top(divisor);
if (BN_is_zero(divisor))
{
BNerr(BN_F_BN_DIV_NO_BRANCH,BN_R_DIV_BY_ZERO);
return(0);
}
BN_CTX_start(ctx);
tmp=BN_CTX_get(ctx);
snum=BN_CTX_get(ctx);
sdiv=BN_CTX_get(ctx);
if (dv == NULL)
res=BN_CTX_get(ctx);
else res=dv;
if (sdiv == NULL || res == NULL) goto err;
/* First we normalise the numbers */
norm_shift=BN_BITS2-((BN_num_bits(divisor))%BN_BITS2);
if (!(BN_lshift(sdiv,divisor,norm_shift))) goto err;
sdiv->neg=0;
norm_shift+=BN_BITS2;
if (!(BN_lshift(snum,num,norm_shift))) goto err;
snum->neg=0;
/* Since we don't know whether snum is larger than sdiv,
* we pad snum with enough zeroes without changing its
* value.
*/
if (snum->top <= sdiv->top+1)
{
if (bn_wexpand(snum, sdiv->top + 2) == NULL) goto err;
for (i = snum->top; i < sdiv->top + 2; i++) snum->d[i] = 0;
snum->top = sdiv->top + 2;
}
else
{
if (bn_wexpand(snum, snum->top + 1) == NULL) goto err;
snum->d[snum->top] = 0;
snum->top ++;
}
div_n=sdiv->top;
num_n=snum->top;
loop=num_n-div_n;
/* Lets setup a 'window' into snum
* This is the part that corresponds to the current
* 'area' being divided */
wnum.neg = 0;
wnum.d = &(snum->d[loop]);
wnum.top = div_n;
/* only needed when BN_ucmp messes up the values between top and max */
wnum.dmax = snum->dmax - loop; /* so we don't step out of bounds */
/* Get the top 2 words of sdiv */
/* div_n=sdiv->top; */
d0=sdiv->d[div_n-1];
d1=(div_n == 1)?0:sdiv->d[div_n-2];
/* pointer to the 'top' of snum */
wnump= &(snum->d[num_n-1]);
/* Setup to 'res' */
res->neg= (num->neg^divisor->neg);
if (!bn_wexpand(res,(loop+1))) goto err;
res->top=loop-1;
resp= &(res->d[loop-1]);
/* space for temp */
if (!bn_wexpand(tmp,(div_n+1))) goto err;
/* if res->top == 0 then clear the neg value otherwise decrease
* the resp pointer */
if (res->top == 0)
res->neg = 0;
else
resp--;
for (i=0; i<loop-1; i++, wnump--, resp--)
{
BN_ULONG q,l0;
/* the first part of the loop uses the top two words of
* snum and sdiv to calculate a BN_ULONG q such that
* | wnum - sdiv * q | < sdiv */
#if defined(BN_DIV3W) && !defined(OPENSSL_NO_ASM)
BN_ULONG bn_div_3_words(BN_ULONG*,BN_ULONG,BN_ULONG);
q=bn_div_3_words(wnump,d1,d0);
#else
BN_ULONG n0,n1,rem=0;
n0=wnump[0];
n1=wnump[-1];
if (n0 == d0)
q=BN_MASK2;
else /* n0 < d0 */
{
#ifdef BN_LLONG
BN_ULLONG t2;
#if defined(BN_LLONG) && defined(BN_DIV2W) && !defined(bn_div_words)
q=(BN_ULONG)(((((BN_ULLONG)n0)<<BN_BITS2)|n1)/d0);
#else
q=bn_div_words(n0,n1,d0);
#ifdef BN_DEBUG_LEVITTE
TINYCLR_SSL_FPRINTF(OPENSSL_TYPE__FILE_STDERR,"DEBUG: bn_div_words(0x%08X,0x%08X,0x%08\
X) -> 0x%08X\n",
n0, n1, d0, q);
#endif
#endif
#ifndef REMAINDER_IS_ALREADY_CALCULATED
/*
* rem doesn't have to be BN_ULLONG. The least we
* know it's less that d0, isn't it?
*/
rem=(n1-q*d0)&BN_MASK2;
#endif
t2=(BN_ULLONG)d1*q;
for (;;)
{
if (t2 <= ((((BN_ULLONG)rem)<<BN_BITS2)|wnump[-2]))
break;
q--;
rem += d0;
if (rem < d0) break; /* don't let rem overflow */
t2 -= d1;
}
#else /* !BN_LLONG */
BN_ULONG t2l,t2h;
q=bn_div_words(n0,n1,d0);
#ifdef BN_DEBUG_LEVITTE
TINYCLR_SSL_FPRINTF(OPENSSL_TYPE__FILE_STDERR,"DEBUG: bn_div_words(0x%08X,0x%08X,0x%08\
X) -> 0x%08X\n",
n0, n1, d0, q);
#endif
#ifndef REMAINDER_IS_ALREADY_CALCULATED
rem=(n1-q*d0)&BN_MASK2;
#endif
#if defined(BN_UMULT_LOHI)
BN_UMULT_LOHI(t2l,t2h,d1,q);
#elif defined(BN_UMULT_HIGH)
t2l = d1 * q;
t2h = BN_UMULT_HIGH(d1,q);
#else
{
BN_ULONG ql, qh;
t2l=LBITS(d1); t2h=HBITS(d1);
ql =LBITS(q); qh =HBITS(q);
mul64(t2l,t2h,ql,qh); /* t2=(BN_ULLONG)d1*q; */
}
#endif
for (;;)
{
if ((t2h < rem) ||
((t2h == rem) && (t2l <= wnump[-2])))
break;
q--;
rem += d0;
if (rem < d0) break; /* don't let rem overflow */
if (t2l < d1) t2h--; t2l -= d1;
}
#endif /* !BN_LLONG */
}
#endif /* !BN_DIV3W */
l0=bn_mul_words(tmp->d,sdiv->d,div_n,q);
tmp->d[div_n]=l0;
wnum.d--;
/* ingore top values of the bignums just sub the two
* BN_ULONG arrays with bn_sub_words */
if (bn_sub_words(wnum.d, wnum.d, tmp->d, div_n+1))
{
/* Note: As we have considered only the leading
* two BN_ULONGs in the calculation of q, sdiv * q
* might be greater than wnum (but then (q-1) * sdiv
* is less or equal than wnum)
*/
q--;
if (bn_add_words(wnum.d, wnum.d, sdiv->d, div_n))
/* we can't have an overflow here (assuming
* that q != 0, but if q == 0 then tmp is
* zero anyway) */
(*wnump)++;
}
/* store part of the result */
*resp = q;
}
bn_correct_top(snum);
if (rm != NULL)
{
/* Keep a copy of the neg flag in num because if rm==num
* BN_rshift() will overwrite it.
*/
int neg = num->neg;
BN_rshift(rm,snum,norm_shift);
if (!BN_is_zero(rm))
rm->neg = neg;
bn_check_top(rm);
}
bn_correct_top(res);
BN_CTX_end(ctx);
return(1);
err:
bn_check_top(rm);
BN_CTX_end(ctx);
return(0);
}
int BN_div(BIGNUM *dv, BIGNUM *rm, const BIGNUM *num, const BIGNUM *divisor,
BN_CTX *ctx)
{
int norm_shift, i, j, loop;
BIGNUM *tmp, wnum, *snum, *sdiv, *res;
BN_ULONG *resp, *wnump;
BN_ULONG d0, d1;
int num_n, div_n;
bn_check_top(num);
bn_check_top(divisor);
if(BN_is_zero(divisor))
{
return (0);
}
if(BN_ucmp(num, divisor) < 0)
{
if(rm != NULL)
{
if(BN_copy(rm, num) == NULL) { return (0); }
}
if(dv != NULL) { BN_zero(dv); }
return (1);
}
BN_CTX_start(ctx);
tmp = BN_CTX_get(ctx);
snum = BN_CTX_get(ctx);
sdiv = BN_CTX_get(ctx);
if(dv == NULL)
{ res = BN_CTX_get(ctx); }
else { res = dv; }
if(sdiv == NULL || res == NULL) { goto err; }
tmp->neg = 0;
/* First we normalise the numbers */
norm_shift = BN_BITS2 - ((BN_num_bits(divisor)) % BN_BITS2);
BN_lshift(sdiv, divisor, norm_shift);
sdiv->neg = 0;
norm_shift += BN_BITS2;
BN_lshift(snum, num, norm_shift);
snum->neg = 0;
div_n = sdiv->top;
num_n = snum->top;
loop = num_n - div_n;
/* Lets setup a 'window' into snum
* This is the part that corresponds to the current
* 'area' being divided */
BN_init(&wnum);
wnum.d = &(snum->d[loop]);
wnum.top = div_n;
wnum.dmax = snum->dmax + 1; /* a bit of a lie */
/* Get the top 2 words of sdiv */
/* i=sdiv->top; */
d0 = sdiv->d[div_n - 1];
d1 = (div_n == 1) ? 0 : sdiv->d[div_n - 2];
/* pointer to the 'top' of snum */
wnump = &(snum->d[num_n - 1]);
/* Setup to 'res' */
res->neg = (num->neg ^ divisor->neg);
if(!bn_wexpand(res, (loop + 1))) { goto err; }
res->top = loop;
resp = &(res->d[loop - 1]);
/* space for temp */
if(!bn_wexpand(tmp, (div_n + 1))) { goto err; }
if(BN_ucmp(&wnum, sdiv) >= 0)
{
if(!BN_usub(&wnum, &wnum, sdiv)) { goto err; }
*resp = 1;
res->d[res->top - 1] = 1;
}
else
{ res->top--; }
resp--;
for(i = 0; i < loop - 1; i++)
{
BN_ULONG q, l0;
#if defined(BN_DIV3W) && !defined(NO_ASM)
BN_ULONG bn_div_3_words(BN_ULONG *, BN_ULONG, BN_ULONG);
q = bn_div_3_words(wnump, d1, d0);
#else
BN_ULONG n0, n1, rem = 0;
n0 = wnump[0];
n1 = wnump[-1];
if(n0 == d0)
{ q = BN_MASK2; }
else /* n0 < d0 */
{
#ifdef BN_LLONG
BN_ULLONG t2;
#if defined(BN_LLONG) && defined(BN_DIV2W) && !defined(bn_div_words)
q = (BN_ULONG)(((((BN_ULLONG)n0) << BN_BITS2) | n1) / d0);
#else
q = bn_div_words(n0, n1, d0);
#endif
#ifndef REMAINDER_IS_ALREADY_CALCULATED
/*
* rem doesn't have to be BN_ULLONG. The least we
* know it's less that d0, isn't it?
*/
rem = (n1 - q * d0)&BN_MASK2;
#endif
t2 = (BN_ULLONG)d1 * q;
for(;;)
{
if(t2 <= ((((BN_ULLONG)rem) << BN_BITS2) | wnump[-2]))
{ break; }
q--;
rem += d0;
if(rem < d0) { break; } /* don't let rem overflow */
t2 -= d1;
}
#else /* !BN_LLONG */
BN_ULONG t2l, t2h, ql, qh;
q = bn_div_words(n0, n1, d0);
#ifndef REMAINDER_IS_ALREADY_CALCULATED
rem = (n1 - q * d0)&BN_MASK2;
#endif
#ifdef BN_UMULT_HIGH
t2l = d1 * q;
t2h = BN_UMULT_HIGH(d1, q);
#else
t2l = LBITS(d1);
t2h = HBITS(d1);
ql = LBITS(q);
qh = HBITS(q);
mul64(t2l, t2h, ql, qh); /* t2=(BN_ULLONG)d1*q; */
#endif
for(;;)
{
if((t2h < rem) ||
((t2h == rem) && (t2l <= wnump[-2])))
{ break; }
q--;
rem += d0;
if(rem < d0) { break; } /* don't let rem overflow */
if(t2l < d1) { t2h--; }
t2l -= d1;
}
#endif /* !BN_LLONG */
}
#endif /* !BN_DIV3W */
l0 = bn_mul_words(tmp->d, sdiv->d, div_n, q);
wnum.d--;
wnum.top++;
tmp->d[div_n] = l0;
for(j = div_n + 1; j > 0; j--)
if(tmp->d[j - 1]) { break; }
tmp->top = j;
j = wnum.top;
BN_sub(&wnum, &wnum, tmp);
snum->top = snum->top + wnum.top - j;
if(wnum.neg)
{
q--;
j = wnum.top;
BN_add(&wnum, &wnum, sdiv);
snum->top += wnum.top - j;
}
*(resp--) = q;
wnump--;
}
if(rm != NULL)
{
BN_rshift(rm, snum, norm_shift);
rm->neg = num->neg;
}
BN_CTX_end(ctx);
return (1);
err:
BN_CTX_end(ctx);
return (0);
}
int BN_div(BIGNUM *dv, BIGNUM *rm, const BIGNUM *num, const BIGNUM *divisor,
BN_CTX *ctx)
{
int norm_shift,i,loop;
BIGNUM *tmp,*snum,*sdiv,*res;
#ifdef BN_ALLOC /* pcg */
BIGNUM wnum;
#else
BN_ULONG *wnum_d;
#endif /* !BN_ALLOC */
BN_ULONG *resp,*wnump;
BN_ULONG d0,d1;
int num_n,div_n;
/* Invalid zero-padding would have particularly bad consequences
* in the case of 'num', so don't just rely on bn_check_top() for this one
* (bn_check_top() works only for BN_DEBUG builds) */
if (num->top > 0 && num->d[num->top - 1] == 0)
{
BNerr(BN_F_BN_DIV,BN_R_NOT_INITIALIZED);
return 0;
}
bn_check_top(num);
if ((BN_get_flags(num, BN_FLG_CONSTTIME) != 0) || (BN_get_flags(divisor, BN_FLG_CONSTTIME) != 0))
{
return BN_div_no_branch(dv, rm, num, divisor, ctx);
}
bn_check_top(dv);
bn_check_top(rm);
/* bn_check_top(num); */ /* 'num' has been checked already */
bn_check_top(divisor);
if (BN_is_zero(divisor))
{
BNerr(BN_F_BN_DIV,BN_R_DIV_BY_ZERO);
return(0);
}
if (BN_ucmp(num,divisor) < 0)
{
if (rm != NULL)
{ if (BN_copy(rm,num) == NULL) return(0); }
if (dv != NULL) BN_zero(dv);
return(1);
}
BN_CTX_start(ctx);
tmp=BN_CTX_get(ctx);
snum=BN_CTX_get_ext( ctx, BIGNUM_EXT_MUL1 ); /* pcg */
sdiv=BN_CTX_get(ctx);
if (dv == NULL)
res=BN_CTX_get(ctx);
else res=dv;
if (sdiv == NULL || res == NULL || tmp == NULL || snum == NULL)
goto err;
/* First we normalise the numbers */
norm_shift=BN_BITS2-((BN_num_bits(divisor))%BN_BITS2);
if (!(BN_lshift(sdiv,divisor,norm_shift))) goto err;
sdiv->neg=0;
norm_shift+=BN_BITS2;
if (!(BN_lshift(snum,num,norm_shift))) goto err;
snum->neg=0;
div_n=sdiv->top;
num_n=snum->top;
loop=num_n-div_n;
/* Lets setup a 'window' into snum
* This is the part that corresponds to the current
* 'area' being divided */
#ifdef BN_ALLOC /* pcg */
wnum.neg = 0;
wnum.d = &(snum->d[loop]);
wnum.top = div_n;
/* only needed when BN_ucmp messes up the values between top and max */
wnum.dmax = snum->dmax - loop; /* so we don't step out of bounds */
#else
wnum_d = &(snum->d[loop]);
#endif /* BN_ALLOC */
/* Get the top 2 words of sdiv */
/* div_n=sdiv->top; */
d0=sdiv->d[div_n-1];
d1=(div_n == 1)?0:sdiv->d[div_n-2];
/* pointer to the 'top' of snum */
wnump= &(snum->d[num_n-1]);
/* Setup to 'res' */
res->neg= (num->neg^divisor->neg);
if (!bn_wexpand(res,(loop+1))) goto err;
res->top=loop;
resp= &(res->d[loop-1]);
/* space for temp */
if( div_n+1 > BIGNUM_ALLOC_WORDS ) { assert( 0 ); goto err; }
if (BN_ucmp_word(wnum_d,div_n,sdiv) >= 0)
{
/* If BN_DEBUG_RAND is defined BN_ucmp changes (via
* bn_pollute) the const bignum arguments =>
* clean the values between top and max again */
bn_clear_top2max(&wnum);
bn_sub_words(wnum_d, wnum_d, sdiv->d, div_n);
*resp=1;
}
else
res->top--;
/* if res->top == 0 then clear the neg value otherwise decrease
* the resp pointer */
if (res->top == 0)
res->neg = 0;
else
resp--;
for (i=0; i<loop-1; i++, wnump--, resp--)
{
BN_ULONG q,l0;
/* the first part of the loop uses the top two words of
* snum and sdiv to calculate a BN_ULONG q such that
* | wnum - sdiv * q | < sdiv */
#if defined(BN_DIV3W) && !defined(OPENSSL_NO_ASM)
BN_ULONG bn_div_3_words(BN_ULONG*,BN_ULONG,BN_ULONG);
q=bn_div_3_words(wnump,d1,d0);
#else
BN_ULONG n0,n1,rem=0;
n0=wnump[0];
n1=wnump[-1];
if (n0 == d0)
q=BN_MASK2;
else /* n0 < d0 */
{
#ifdef BN_LLONG
BN_ULLONG t2;
#if defined(BN_LLONG) && defined(BN_DIV2W) && !defined(bn_div_words)
q=(BN_ULONG)(((((BN_ULLONG)n0)<<BN_BITS2)|n1)/d0);
#else
q=bn_div_words(n0,n1,d0);
#ifdef BN_DEBUG_LEVITTE
fprintf(stderr,"DEBUG: bn_div_words(0x%08X,0x%08X,0x%08\
X) -> 0x%08X\n",
n0, n1, d0, q);
#endif
#endif
#ifndef REMAINDER_IS_ALREADY_CALCULATED
/*
* rem doesn't have to be BN_ULLONG. The least we
* know it's less that d0, isn't it?
*/
rem=(n1-q*d0)&BN_MASK2;
#endif
t2=(BN_ULLONG)d1*q;
for (;;)
{
if (t2 <= ((((BN_ULLONG)rem)<<BN_BITS2)|wnump[-2]))
break;
q--;
rem += d0;
if (rem < d0) break; /* don't let rem overflow */
t2 -= d1;
}
#else /* !BN_LLONG */
BN_ULONG t2l,t2h;
#if !defined( BN_UMULT_LOHI ) && !defined( BN_UMULT_HIGH ) /* pcg */
BN_ULONG ql,qh;
#endif
q=bn_div_words(n0,n1,d0);
#ifdef BN_DEBUG_LEVITTE
fprintf(stderr,"DEBUG: bn_div_words(0x%08X,0x%08X,0x%08\
X) -> 0x%08X\n",
n0, n1, d0, q);
#endif
#ifndef REMAINDER_IS_ALREADY_CALCULATED
rem=(n1-q*d0)&BN_MASK2;
#endif
#if defined(BN_UMULT_LOHI)
BN_UMULT_LOHI(t2l,t2h,d1,q);
#elif defined(BN_UMULT_HIGH)
t2l = d1 * q;
t2h = BN_UMULT_HIGH(d1,q);
#else
{
BN_ULONG ql, qh;
t2l=LBITS(d1); t2h=HBITS(d1);
ql =LBITS(q); qh =HBITS(q);
mul64(t2l,t2h,ql,qh); /* t2=(BN_ULLONG)d1*q; */
}
#endif
for (;;)
{
if ((t2h < rem) ||
((t2h == rem) && (t2l <= wnump[-2])))
break;
q--;
rem += d0;
if (rem < d0) break; /* don't let rem overflow */
if (t2l < d1) t2h--; t2l -= d1;
}
#endif /* !BN_LLONG */
}
#endif /* !BN_DIV3W */
l0=bn_mul_words(tmp->d,sdiv->d,div_n,q);
tmp->d[div_n]=l0;
wnum_d--;
/* ingore top values of the bignums just sub the two
* BN_ULONG arrays with bn_sub_words */
if (bn_sub_words(wnum_d, wnum_d, tmp->d, div_n+1))
{
/* Note: As we have considered only the leading
* two BN_ULONGs in the calculation of q, sdiv * q
* might be greater than wnum (but then (q-1) * sdiv
* is less or equal than wnum)
*/
q--;
if (bn_add_words(wnum_d, wnum_d, sdiv->d, div_n))
/* we can't have an overflow here (assuming
* that q != 0, but if q == 0 then tmp is
* zero anyway) */
(*wnump)++;
}
/* store part of the result */
*resp = q;
}
bn_correct_top(snum);
if (rm != NULL)
{
/* Keep a copy of the neg flag in num because if rm==num
* BN_rshift() will overwrite it.
*/
int neg = num->neg;
BN_rshift(rm,snum,norm_shift);
if (!BN_is_zero(rm))
rm->neg = neg;
bn_check_top(rm);
}
BN_CTX_end_ext( ctx, BIGNUM_EXT_MUL1 ); /* pcg */
return(1);
err:
bn_check_top(rm);
BN_CTX_end_ext( ctx, BIGNUM_EXT_MUL1 ); /* pcg */
return(0);
}
int BN_div(BIGNUM *dv, BIGNUM *rm, const BIGNUM *num, const BIGNUM *divisor,
BN_CTX *ctx)
{
int norm_shift,i,j,loop;
BIGNUM *tmp,wnum,*snum,*sdiv,*res;
BN_ULONG *resp,*wnump;
BN_ULONG d0,d1;
int num_n,div_n;
bn_check_top(num);
bn_check_top(divisor);
if (BN_is_zero(divisor))
return(0);
if (BN_ucmp(num,divisor) < 0)
{
if (rm != NULL)
{ if (BN_copy(rm,num) == NULL) return(0); }
if (dv != NULL) BN_zero(dv);
return(1);
}
BN_CTX_start(ctx);
tmp=BN_CTX_get(ctx);
snum=BN_CTX_get(ctx);
sdiv=BN_CTX_get(ctx);
if (dv == NULL)
res=BN_CTX_get(ctx);
else res=dv;
if (sdiv==NULL || res == NULL) goto err;
tmp->neg=0;
/* First we normalise the numbers */
norm_shift=BN_BITS2-((BN_num_bits(divisor))%BN_BITS2);
if (!(BN_lshift(sdiv,divisor,norm_shift))) goto err;
sdiv->neg=0;
norm_shift+=BN_BITS2;
if (!(BN_lshift(snum,num,norm_shift))) goto err;
snum->neg=0;
div_n=sdiv->top;
num_n=snum->top;
loop=num_n-div_n;
/* Lets setup a 'window' into snum
* This is the part that corresponds to the current
* 'area' being divided */
BN_init(&wnum);
wnum.d= &(snum->d[loop]);
wnum.top= div_n;
wnum.dmax= snum->dmax+1; /* a bit of a lie */
/* Get the top 2 words of sdiv */
/* i=sdiv->top; */
d0=sdiv->d[div_n-1];
d1=(div_n == 1)?0:sdiv->d[div_n-2];
/* pointer to the 'top' of snum */
wnump= &(snum->d[num_n-1]);
/* Setup to 'res' */
res->neg= (num->neg^divisor->neg);
if (!bn_wexpand(res,(loop+1))) goto err;
res->top=loop;
resp= &(res->d[loop-1]);
/* space for temp */
if (!bn_wexpand(tmp,(div_n+1))) goto err;
if (BN_ucmp(&wnum,sdiv) >= 0)
{
if (!BN_usub(&wnum,&wnum,sdiv)) goto err;
*resp=1;
res->d[res->top-1]=1;
}
else
res->top--;
resp--;
for (i=0; i<loop-1; i++)
{
BN_ULONG q,l0;
BN_ULONG n0,n1,rem=0;
n0=wnump[0];
n1=wnump[-1];
if (n0 == d0)
q=BN_MASK2;
else /* n0 < d0 */
{
BN_ULONG t2l,t2h,ql,qh;
q=bn_div_words(n0,n1,d0);
rem=(n1-q*d0)&BN_MASK2;
t2l=LBITS(d1); t2h=HBITS(d1);
ql =LBITS(q); qh =HBITS(q);
mul64(t2l,t2h,ql,qh); /* t2=(BN_ULLONG)d1*q; */
for (;;)
{
if ((t2h < rem) ||
((t2h == rem) && (t2l <= wnump[-2])))
break;
q--;
rem += d0;
if (rem < d0) break; /* don't let rem overflow */
if (t2l < d1) t2h--; t2l -= d1;
}
}
l0=bn_mul_words(tmp->d,sdiv->d,div_n,q);
wnum.d--; wnum.top++;
tmp->d[div_n]=l0;
for (j=div_n+1; j>0; j--)
if (tmp->d[j-1]) break;
tmp->top=j;
j=wnum.top;
if (!BN_sub(&wnum,&wnum,tmp)) goto err;
snum->top=snum->top+wnum.top-j;
if (wnum.neg)
{
q--;
j=wnum.top;
if (!BN_add(&wnum,&wnum,sdiv)) goto err;
snum->top+=wnum.top-j;
}
*(resp--)=q;
wnump--;
}
if (rm != NULL)
{
BN_rshift(rm,snum,norm_shift);
rm->neg=num->neg;
}
BN_CTX_end(ctx);
return(1);
err:
BN_CTX_end(ctx);
return(0);
}
/*-
* BN_div computes dv := num / divisor, rounding towards
* zero, and sets up rm such that dv*divisor + rm = num holds.
* Thus:
* dv->neg == num->neg ^ divisor->neg (unless the result is zero)
* rm->neg == num->neg (unless the remainder is zero)
* If 'dv' or 'rm' is NULL, the respective value is not returned.
*/
int BN_div(BIGNUM *dv, BIGNUM *rm, const BIGNUM *num, const BIGNUM *divisor,
BN_CTX *ctx)
{
int norm_shift, i, loop;
BIGNUM *tmp, wnum, *snum, *sdiv, *res;
BN_ULONG *resp, *wnump;
BN_ULONG d0, d1;
int num_n, div_n;
int no_branch = 0;
/*
* Invalid zero-padding would have particularly bad consequences so don't
* just rely on bn_check_top() here (bn_check_top() works only for
* BN_DEBUG builds)
*/
if ((num->top > 0 && num->d[num->top - 1] == 0) ||
(divisor->top > 0 && divisor->d[divisor->top - 1] == 0)) {
BNerr(BN_F_BN_DIV, BN_R_NOT_INITIALIZED);
return 0;
}
bn_check_top(num);
bn_check_top(divisor);
if ((BN_get_flags(num, BN_FLG_CONSTTIME) != 0)
|| (BN_get_flags(divisor, BN_FLG_CONSTTIME) != 0)) {
no_branch = 1;
}
bn_check_top(dv);
bn_check_top(rm);
/*- bn_check_top(num); *//*
* 'num' has been checked already
*/
/*- bn_check_top(divisor); *//*
* 'divisor' has been checked already
*/
if (BN_is_zero(divisor)) {
BNerr(BN_F_BN_DIV, BN_R_DIV_BY_ZERO);
return 0;
}
if (!no_branch && BN_ucmp(num, divisor) < 0) {
if (rm != NULL) {
if (BN_copy(rm, num) == NULL)
return 0;
}
if (dv != NULL)
BN_zero(dv);
return 1;
}
BN_CTX_start(ctx);
res = (dv == NULL) ? BN_CTX_get(ctx) : dv;
tmp = BN_CTX_get(ctx);
snum = BN_CTX_get(ctx);
sdiv = BN_CTX_get(ctx);
if (sdiv == NULL)
goto err;
/* First we normalise the numbers */
norm_shift = BN_BITS2 - ((BN_num_bits(divisor)) % BN_BITS2);
if (!(BN_lshift(sdiv, divisor, norm_shift)))
goto err;
sdiv->neg = 0;
norm_shift += BN_BITS2;
if (!(BN_lshift(snum, num, norm_shift)))
goto err;
snum->neg = 0;
if (no_branch) {
/*
* Since we don't know whether snum is larger than sdiv, we pad snum
* with enough zeroes without changing its value.
*/
if (snum->top <= sdiv->top + 1) {
if (bn_wexpand(snum, sdiv->top + 2) == NULL)
goto err;
for (i = snum->top; i < sdiv->top + 2; i++)
snum->d[i] = 0;
snum->top = sdiv->top + 2;
} else {
if (bn_wexpand(snum, snum->top + 1) == NULL)
goto err;
snum->d[snum->top] = 0;
snum->top++;
}
}
div_n = sdiv->top;
num_n = snum->top;
loop = num_n - div_n;
/*
* Lets setup a 'window' into snum This is the part that corresponds to
* the current 'area' being divided
*/
wnum.neg = 0;
wnum.d = &(snum->d[loop]);
wnum.top = div_n;
wnum.flags = BN_FLG_STATIC_DATA;
/*
* only needed when BN_ucmp messes up the values between top and max
*/
wnum.dmax = snum->dmax - loop; /* so we don't step out of bounds */
/* Get the top 2 words of sdiv */
/* div_n=sdiv->top; */
d0 = sdiv->d[div_n - 1];
d1 = (div_n == 1) ? 0 : sdiv->d[div_n - 2];
/* pointer to the 'top' of snum */
wnump = &(snum->d[num_n - 1]);
/* Setup to 'res' */
if (!bn_wexpand(res, (loop + 1)))
goto err;
res->neg = (num->neg ^ divisor->neg);
res->top = loop - no_branch;
resp = &(res->d[loop - 1]);
/* space for temp */
if (!bn_wexpand(tmp, (div_n + 1)))
goto err;
if (!no_branch) {
if (BN_ucmp(&wnum, sdiv) >= 0) {
/*
* If BN_DEBUG_RAND is defined BN_ucmp changes (via bn_pollute)
* the const bignum arguments => clean the values between top and
* max again
*/
bn_clear_top2max(&wnum);
bn_sub_words(wnum.d, wnum.d, sdiv->d, div_n);
*resp = 1;
} else
res->top--;
}
/* Increase the resp pointer so that we never create an invalid pointer. */
resp++;
/*
* if res->top == 0 then clear the neg value otherwise decrease the resp
* pointer
*/
if (res->top == 0)
res->neg = 0;
else
resp--;
for (i = 0; i < loop - 1; i++, wnump--) {
BN_ULONG q, l0;
/*
* the first part of the loop uses the top two words of snum and sdiv
* to calculate a BN_ULONG q such that | wnum - sdiv * q | < sdiv
*/
# if defined(BN_DIV3W) && !defined(OPENSSL_NO_ASM)
BN_ULONG bn_div_3_words(BN_ULONG *, BN_ULONG, BN_ULONG);
q = bn_div_3_words(wnump, d1, d0);
# else
BN_ULONG n0, n1, rem = 0;
n0 = wnump[0];
n1 = wnump[-1];
if (n0 == d0)
q = BN_MASK2;
else { /* n0 < d0 */
# ifdef BN_LLONG
BN_ULLONG t2;
# if defined(BN_LLONG) && defined(BN_DIV2W) && !defined(bn_div_words)
q = (BN_ULONG)(((((BN_ULLONG) n0) << BN_BITS2) | n1) / d0);
# else
q = bn_div_words(n0, n1, d0);
# endif
# ifndef REMAINDER_IS_ALREADY_CALCULATED
/*
* rem doesn't have to be BN_ULLONG. The least we
* know it's less that d0, isn't it?
*/
rem = (n1 - q * d0) & BN_MASK2;
# endif
t2 = (BN_ULLONG) d1 *q;
for (;;) {
if (t2 <= ((((BN_ULLONG) rem) << BN_BITS2) | wnump[-2]))
break;
q--;
rem += d0;
if (rem < d0)
break; /* don't let rem overflow */
t2 -= d1;
}
# else /* !BN_LLONG */
BN_ULONG t2l, t2h;
q = bn_div_words(n0, n1, d0);
# ifndef REMAINDER_IS_ALREADY_CALCULATED
rem = (n1 - q * d0) & BN_MASK2;
# endif
# if defined(BN_UMULT_LOHI)
BN_UMULT_LOHI(t2l, t2h, d1, q);
# elif defined(BN_UMULT_HIGH)
t2l = d1 * q;
t2h = BN_UMULT_HIGH(d1, q);
# else
{
BN_ULONG ql, qh;
t2l = LBITS(d1);
t2h = HBITS(d1);
ql = LBITS(q);
qh = HBITS(q);
mul64(t2l, t2h, ql, qh); /* t2=(BN_ULLONG)d1*q; */
}
# endif
for (;;) {
if ((t2h < rem) || ((t2h == rem) && (t2l <= wnump[-2])))
break;
q--;
rem += d0;
if (rem < d0)
break; /* don't let rem overflow */
if (t2l < d1)
t2h--;
t2l -= d1;
}
# endif /* !BN_LLONG */
}
# endif /* !BN_DIV3W */
l0 = bn_mul_words(tmp->d, sdiv->d, div_n, q);
tmp->d[div_n] = l0;
wnum.d--;
/*
* ingore top values of the bignums just sub the two BN_ULONG arrays
* with bn_sub_words
*/
if (bn_sub_words(wnum.d, wnum.d, tmp->d, div_n + 1)) {
/*
* Note: As we have considered only the leading two BN_ULONGs in
* the calculation of q, sdiv * q might be greater than wnum (but
* then (q-1) * sdiv is less or equal than wnum)
*/
q--;
if (bn_add_words(wnum.d, wnum.d, sdiv->d, div_n))
/*
* we can't have an overflow here (assuming that q != 0, but
* if q == 0 then tmp is zero anyway)
*/
(*wnump)++;
}
/* store part of the result */
resp--;
*resp = q;
}
bn_correct_top(snum);
if (rm != NULL) {
/*
* Keep a copy of the neg flag in num because if rm==num BN_rshift()
* will overwrite it.
*/
int neg = num->neg;
BN_rshift(rm, snum, norm_shift);
if (!BN_is_zero(rm))
rm->neg = neg;
bn_check_top(rm);
}
if (no_branch)
bn_correct_top(res);
BN_CTX_end(ctx);
return 1;
err:
bn_check_top(rm);
BN_CTX_end(ctx);
return 0;
}