/* crypto/bn/bn_div.c */ /* Copyright (C) 1995-1998 Eric Young (eay@cryptsoft.com) * All rights reserved. * * This package is an SSL implementation written * by Eric Young (eay@cryptsoft.com). * The implementation was written so as to conform with Netscapes SSL. * * This library is free for commercial and non-commercial use as long as * the following conditions are aheared to. The following conditions * apply to all code found in this distribution, be it the RC4, RSA, * lhash, DES, etc., code; not just the SSL code. The SSL documentation * included with this distribution is covered by the same copyright terms * except that the holder is Tim Hudson (tjh@cryptsoft.com). * * Copyright remains Eric Young's, and as such any Copyright notices in * the code are not to be removed. * If this package is used in a product, Eric Young should be given attribution * as the author of the parts of the library used. * This can be in the form of a textual message at program startup or * in documentation (online or textual) provided with the package. * * Redistribution and use in source and binary forms, with or without * modification, are permitted provided that the following conditions * are met: * 1. Redistributions of source code must retain the copyright * notice, this list of conditions and the following disclaimer. * 2. Redistributions in binary form must reproduce the above copyright * notice, this list of conditions and the following disclaimer in the * documentation and/or other materials provided with the distribution. * 3. All advertising materials mentioning features or use of this software * must display the following acknowledgement: * "This product includes cryptographic software written by * Eric Young (eay@cryptsoft.com)" * The word 'cryptographic' can be left out if the rouines from the library * being used are not cryptographic related :-). * 4. If you include any Windows specific code (or a derivative thereof) from * the apps directory (application code) you must include an acknowledgement: * "This product includes software written by Tim Hudson (tjh@cryptsoft.com)" * * THIS SOFTWARE IS PROVIDED BY ERIC YOUNG ``AS IS'' AND * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF * SUCH DAMAGE. * * The licence and distribution terms for any publically available version or * derivative of this code cannot be changed. i.e. this code cannot simply be * copied and put under another distribution licence * [including the GNU Public Licence.] */ #include #include #include "cryptlib.h" #include "bn_lcl.h" /* The old slow way */ #if 0 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); bn_check_top(d); if (BN_is_zero(d)) { BNerr(BN_F_BN_DIV,BN_R_DIV_BY_ZERO); return(0); } if (BN_ucmp(m,d) < 0) { if (rem != NULL) { if (BN_copy(rem,m) == NULL) return(0); } if (dv != NULL) BN_zero(dv); return(1); } 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) 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_zero(dv); bn_wexpand(dv,1); dv->top=1; if (!BN_lshift(D,D,nm-nd)) goto end; for (i=nm-nd; i>=0; i--) { if (!BN_lshift1(dv,dv)) goto end; if (BN_ucmp(rem,D) >= 0) { dv->d[0]|=1; if (!BN_usub(rem,rem,D)) goto end; } /* CAN IMPROVE (and have now :=) */ if (!BN_rshift1(D,D)) goto end; } rem->neg=BN_is_zero(rem)?0:m->neg; dv->neg=m->neg^d->neg; 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)< */ # 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! * */ # 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 /* __ */ # 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,loop; BIGNUM *tmp,wnum,*snum,*sdiv,*res; BN_ULONG *resp,*wnump; BN_ULONG d0,d1; int num_n,div_n; if (BN_get_flags(num, 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); 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(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; 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; 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_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 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)< 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 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(ctx); return(1); err: bn_check_top(rm); BN_CTX_end(ctx); return(0); } /* BN_div_no_branch is a special version of BN_div. It does not contain * branches that may leak sensitive information. */ 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); bn_check_top(divisor); if (BN_is_zero(divisor)) { BNerr(BN_F_BN_DIV,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 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)< 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 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(ctx); return(1); err: bn_check_top(rm); BN_CTX_end(ctx); return(0); } #endif