#include "cryptlib.h"
#include "bn_lcl.h"
+
/* The old slow way */
#if 0
-int BN_div(BIGNUM *dv, BIGNUM *rem, BIGNUM *m, BIGNUM *d, BN_CTX *ctx)
+int BN_div(BIGNUM *dv, BIGNUM *rem, const BIGNUM *m, const BIGNUM *d,
+ BN_CTX *ctx)
{
int i,nm,nd;
+ int ret = 0;
BIGNUM *D;
bn_check_top(m);
return(1);
}
- D= &(ctx->bn[ctx->tos]);
- if (dv == NULL) dv= &(ctx->bn[ctx->tos+1]);
- if (rem == NULL) rem= &(ctx->bn[ctx->tos+2]);
+ BN_CTX_start(ctx);
+ D = BN_CTX_get(ctx);
+ if (dv == NULL) dv = BN_CTX_get(ctx);
+ if (rem == NULL) rem = BN_CTX_get(ctx);
+ if (D == NULL || dv == NULL || rem == NULL)
+ goto end;
nd=BN_num_bits(d);
nm=BN_num_bits(m);
- if (BN_copy(D,d) == NULL) return(0);
- if (BN_copy(rem,m) == NULL) return(0);
+ if (BN_copy(D,d) == NULL) goto end;
+ if (BN_copy(rem,m) == NULL) goto end;
/* The next 2 are needed so we can do a dv->d[0]|=1 later
* since BN_lshift1 will only work once there is a value :-) */
bn_wexpand(dv,1);
dv->top=1;
- if (!BN_lshift(D,D,nm-nd)) return(0);
+ if (!BN_lshift(D,D,nm-nd)) goto end;
for (i=nm-nd; i>=0; i--)
{
- if (!BN_lshift1(dv,dv)) return(0);
+ if (!BN_lshift1(dv,dv)) goto end;
if (BN_ucmp(rem,D) >= 0)
{
dv->d[0]|=1;
- if (!BN_usub(rem,rem,D)) return(0);
+ if (!BN_usub(rem,rem,D)) goto end;
}
/* CAN IMPROVE (and have now :=) */
- if (!BN_rshift1(D,D)) return(0);
+ if (!BN_rshift1(D,D)) goto end;
}
rem->neg=BN_is_zero(rem)?0:m->neg;
dv->neg=m->neg^d->neg;
- return(1);
+ ret = 1;
+ end:
+ BN_CTX_end(ctx);
+ return(ret);
}
#else
+#if !defined(OPENSSL_NO_ASM) && !defined(OPENSSL_NO_INLINE_ASM) \
+ && !defined(PEDANTIC) && !defined(BN_DIV3W)
+# if defined(__GNUC__) && __GNUC__>=2
+# if defined(__i386) || defined (__i386__)
+ /*
+ * There were two reasons for implementing this template:
+ * - GNU C generates a call to a function (__udivdi3 to be exact)
+ * in reply to ((((BN_ULLONG)n0)<<BN_BITS2)|n1)/d0 (I fail to
+ * understand why...);
+ * - divl doesn't only calculate quotient, but also leaves
+ * remainder in %edx which we can definitely use here:-)
+ *
+ * <appro@fy.chalmers.se>
+ */
+# define bn_div_words(n0,n1,d0) \
+ ({ asm volatile ( \
+ "divl %4" \
+ : "=a"(q), "=d"(rem) \
+ : "a"(n1), "d"(n0), "g"(d0) \
+ : "cc"); \
+ q; \
+ })
+# define REMAINDER_IS_ALREADY_CALCULATED
+# elif defined(__x86_64) && defined(SIXTY_FOUR_BIT_LONG)
+ /*
+ * Same story here, but it's 128-bit by 64-bit division. Wow!
+ * <appro@fy.chalmers.se>
+ */
+# define bn_div_words(n0,n1,d0) \
+ ({ asm volatile ( \
+ "divq %4" \
+ : "=a"(q), "=d"(rem) \
+ : "a"(n1), "d"(n0), "g"(d0) \
+ : "cc"); \
+ q; \
+ })
+# define REMAINDER_IS_ALREADY_CALCULATED
+# endif /* __<cpu> */
+# endif /* __GNUC__ */
+#endif /* OPENSSL_NO_ASM */
+
+
+/* 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,j,loop;
+ int norm_shift,i,loop;
BIGNUM *tmp,wnum,*snum,*sdiv,*res;
BN_ULONG *resp,*wnump;
BN_ULONG d0,d1;
int num_n,div_n;
+ if (dv)
+ bn_check_top(dv);
+ if (rm)
+ bn_check_top(rm);
bn_check_top(num);
bn_check_top(divisor);
return(1);
}
- tmp= &(ctx->bn[ctx->tos]);
- tmp->neg=0;
- snum= &(ctx->bn[ctx->tos+1]);
- sdiv= &(ctx->bn[ctx->tos+2]);
+ BN_CTX_start(ctx);
+ tmp=BN_CTX_get(ctx);
+ snum=BN_CTX_get(ctx);
+ sdiv=BN_CTX_get(ctx);
if (dv == NULL)
- res= &(ctx->bn[ctx->tos+3]);
+ 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);
+ if (!(BN_lshift(sdiv,divisor,norm_shift))) goto err;
sdiv->neg=0;
norm_shift+=BN_BITS2;
- BN_lshift(snum,num,norm_shift);
+ 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.max= snum->max+1; /* a bit of a lie */
+ 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 */
- /* i=sdiv->top; */
+ /* div_n=sdiv->top; */
d0=sdiv->d[div_n-1];
d1=(div_n == 1)?0:sdiv->d[div_n-2];
if (BN_ucmp(&wnum,sdiv) >= 0)
{
- if (!BN_usub(&wnum,&wnum,sdiv)) goto err;
+ /* 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;
- res->d[res->top-1]=1;
}
else
res->top--;
- 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++)
+ for (i=0; i<loop-1; i++, wnump--, resp--)
{
BN_ULONG q,l0;
-#ifdef BN_DIV3W
- q=bn_div_3_words(wnump,d0,d1);
+ /* 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
-
-#if !defined(NO_ASM) && !defined(PEDANTIC)
-# if defined(__GNUC__) && __GNUC__>=2
-# if defined(__i386)
- /*
- * There were two reasons for implementing this template:
- * - GNU C generates a call to a function (__udivdi3 to be exact)
- * in reply to ((((BN_ULLONG)n0)<<BN_BITS2)|n1)/d0 (I fail to
- * understand why...);
- * - divl doesn't only calculate quotient, but also leaves
- * remainder in %edx which we can definitely use here:-)
- *
- * <appro@fy.chalmers.se>
- */
-# define bn_div_words(n0,n1,d0) \
- ({ asm volatile ( \
- "divl %4" \
- : "=a"(q), "=d"(rem) \
- : "a"(n1), "d"(n0), "g"(d0) \
- : "cc"); \
- q; \
- })
-# define REMINDER_IS_ALREADY_CALCULATED
-# endif /* __<cpu> */
-# endif /* __GNUC__ */
-#endif /* NO_ASM */
BN_ULONG n0,n1,rem=0;
n0=wnump[0];
n1=wnump[-1];
if (n0 == d0)
q=BN_MASK2;
- else
+ else /* n0 < d0 */
+ {
+#ifdef BN_LLONG
+ BN_ULLONG t2;
+
#if defined(BN_LLONG) && defined(BN_DIV2W) && !defined(bn_div_words)
- q=((((BN_ULLONG)n0)<<BN_BITS2)|n1)/d0;
+ 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
- {
-#ifdef BN_LLONG
- BN_ULLONG t2;
-#ifndef REMINDER_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;
+#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;
+ 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;
- 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_ULONG t2l,t2h,ql,qh;
+ 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
-#ifndef REMINDER_IS_ALREADY_CALCULATED
- /*
- * It's more than enough with the only multiplication.
- * See the comment above in BN_LLONG section...
- */
- rem=(n1-q*d0)&BN_MASK2;
+#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
+ t2l=LBITS(d1); t2h=HBITS(d1);
+ ql =LBITS(q); qh =HBITS(q);
+ mul64(t2l,t2h,ql,qh); /* t2=(BN_ULLONG)d1*q; */
#endif
- 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;
+ 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
- }
#endif /* !BN_DIV3W */
- wnum.d--; wnum.top++;
+
l0=bn_mul_words(tmp->d,sdiv->d,div_n,q);
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)
+ 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--;
- j=wnum.top;
- BN_add(&wnum,&wnum,sdiv);
- snum->top+=wnum.top-j;
+ 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)++;
}
- *(resp--)=q;
- 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);
- rm->neg=num->neg;
+ if (!BN_is_zero(rm))
+ rm->neg = neg;
+ bn_check_top(rm);
}
+ BN_CTX_end(ctx);
return(1);
err:
+ if (rm)
+ bn_check_top(rm);
+ BN_CTX_end(ctx);
return(0);
}
#endif
-
-/* rem != m */
-int BN_mod(BIGNUM *rem, const BIGNUM *m, const BIGNUM *d, BN_CTX *ctx)
- {
-#if 0 /* The old slow way */
- int i,nm,nd;
- BIGNUM *dv;
-
- if (BN_ucmp(m,d) < 0)
- return((BN_copy(rem,m) == NULL)?0:1);
-
- dv= &(ctx->bn[ctx->tos]);
-
- if (!BN_copy(rem,m)) return(0);
-
- nm=BN_num_bits(rem);
- nd=BN_num_bits(d);
- if (!BN_lshift(dv,d,nm-nd)) return(0);
- for (i=nm-nd; i>=0; i--)
- {
- if (BN_cmp(rem,dv) >= 0)
- {
- if (!BN_sub(rem,rem,dv)) return(0);
- }
- if (!BN_rshift1(dv,dv)) return(0);
- }
- return(1);
-#else
- return(BN_div(NULL,rem,m,d,ctx));
-#endif
- }
-
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