/* crypto/bn/bn_mul.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.] */ #ifndef BN_DEBUG # undef NDEBUG /* avoid conflicting definitions */ # define NDEBUG #endif #include <stdio.h> #include <assert.h> #include "cryptlib.h" #include "bn_lcl.h" #if defined(OPENSSL_NO_ASM) || !defined(OPENSSL_BN_ASM_PART_WORDS) /* Here follows specialised variants of bn_add_words() and bn_sub_words(). They have the property performing operations on arrays of different sizes. The sizes of those arrays is expressed through cl, which is the common length ( basicall, min(len(a),len(b)) ), and dl, which is the delta between the two lengths, calculated as len(a)-len(b). All lengths are the number of BN_ULONGs... For the operations that require a result array as parameter, it must have the length cl+abs(dl). These functions should probably end up in bn_asm.c as soon as there are assembler counterparts for the systems that use assembler files. */ BN_ULONG bn_sub_part_words(BN_ULONG *r, const BN_ULONG *a, const BN_ULONG *b, int cl, int dl) { BN_ULONG c, t; assert(cl >= 0); c = bn_sub_words(r, a, b, cl); if (dl == 0) return c; r += cl; a += cl; b += cl; if (dl < 0) { #ifdef BN_COUNT fprintf(stderr, " bn_sub_part_words %d + %d (dl < 0, c = %d)\n", cl, dl, c); #endif for (;;) { t = b[0]; r[0] = (0-t-c)&BN_MASK2; if (t != 0) c=1; if (++dl >= 0) break; t = b[1]; r[1] = (0-t-c)&BN_MASK2; if (t != 0) c=1; if (++dl >= 0) break; t = b[2]; r[2] = (0-t-c)&BN_MASK2; if (t != 0) c=1; if (++dl >= 0) break; t = b[3]; r[3] = (0-t-c)&BN_MASK2; if (t != 0) c=1; if (++dl >= 0) break; b += 4; r += 4; } } else { int save_dl = dl; #ifdef BN_COUNT fprintf(stderr, " bn_sub_part_words %d + %d (dl > 0, c = %d)\n", cl, dl, c); #endif while(c) { t = a[0]; r[0] = (t-c)&BN_MASK2; if (t != 0) c=0; if (--dl <= 0) break; t = a[1]; r[1] = (t-c)&BN_MASK2; if (t != 0) c=0; if (--dl <= 0) break; t = a[2]; r[2] = (t-c)&BN_MASK2; if (t != 0) c=0; if (--dl <= 0) break; t = a[3]; r[3] = (t-c)&BN_MASK2; if (t != 0) c=0; if (--dl <= 0) break; save_dl = dl; a += 4; r += 4; } if (dl > 0) { #ifdef BN_COUNT fprintf(stderr, " bn_sub_part_words %d + %d (dl > 0, c == 0)\n", cl, dl); #endif if (save_dl > dl) { switch (save_dl - dl) { case 1: r[1] = a[1]; if (--dl <= 0) break; case 2: r[2] = a[2]; if (--dl <= 0) break; case 3: r[3] = a[3]; if (--dl <= 0) break; } a += 4; r += 4; } } if (dl > 0) { #ifdef BN_COUNT fprintf(stderr, " bn_sub_part_words %d + %d (dl > 0, copy)\n", cl, dl); #endif for(;;) { r[0] = a[0]; if (--dl <= 0) break; r[1] = a[1]; if (--dl <= 0) break; r[2] = a[2]; if (--dl <= 0) break; r[3] = a[3]; if (--dl <= 0) break; a += 4; r += 4; } } } return c; } #endif BN_ULONG bn_add_part_words(BN_ULONG *r, const BN_ULONG *a, const BN_ULONG *b, int cl, int dl) { BN_ULONG c, l, t; assert(cl >= 0); c = bn_add_words(r, a, b, cl); if (dl == 0) return c; r += cl; a += cl; b += cl; if (dl < 0) { int save_dl = dl; #ifdef BN_COUNT fprintf(stderr, " bn_add_part_words %d + %d (dl < 0, c = %d)\n", cl, dl, c); #endif while (c) { l=(c+b[0])&BN_MASK2; c=(l < c); r[0]=l; if (++dl >= 0) break; l=(c+b[1])&BN_MASK2; c=(l < c); r[1]=l; if (++dl >= 0) break; l=(c+b[2])&BN_MASK2; c=(l < c); r[2]=l; if (++dl >= 0) break; l=(c+b[3])&BN_MASK2; c=(l < c); r[3]=l; if (++dl >= 0) break; save_dl = dl; b+=4; r+=4; } if (dl < 0) { #ifdef BN_COUNT fprintf(stderr, " bn_add_part_words %d + %d (dl < 0, c == 0)\n", cl, dl); #endif if (save_dl < dl) { switch (dl - save_dl) { case 1: r[1] = b[1]; if (++dl >= 0) break; case 2: r[2] = b[2]; if (++dl >= 0) break; case 3: r[3] = b[3]; if (++dl >= 0) break; } b += 4; r += 4; } } if (dl < 0) { #ifdef BN_COUNT fprintf(stderr, " bn_add_part_words %d + %d (dl < 0, copy)\n", cl, dl); #endif for(;;) { r[0] = b[0]; if (++dl >= 0) break; r[1] = b[1]; if (++dl >= 0) break; r[2] = b[2]; if (++dl >= 0) break; r[3] = b[3]; if (++dl >= 0) break; b += 4; r += 4; } } } else { int save_dl = dl; #ifdef BN_COUNT fprintf(stderr, " bn_add_part_words %d + %d (dl > 0)\n", cl, dl); #endif while (c) { t=(a[0]+c)&BN_MASK2; c=(t < c); r[0]=t; if (--dl <= 0) break; t=(a[1]+c)&BN_MASK2; c=(t < c); r[1]=t; if (--dl <= 0) break; t=(a[2]+c)&BN_MASK2; c=(t < c); r[2]=t; if (--dl <= 0) break; t=(a[3]+c)&BN_MASK2; c=(t < c); r[3]=t; if (--dl <= 0) break; save_dl = dl; a+=4; r+=4; } #ifdef BN_COUNT fprintf(stderr, " bn_add_part_words %d + %d (dl > 0, c == 0)\n", cl, dl); #endif if (dl > 0) { if (save_dl > dl) { switch (save_dl - dl) { case 1: r[1] = a[1]; if (--dl <= 0) break; case 2: r[2] = a[2]; if (--dl <= 0) break; case 3: r[3] = a[3]; if (--dl <= 0) break; } a += 4; r += 4; } } if (dl > 0) { #ifdef BN_COUNT fprintf(stderr, " bn_add_part_words %d + %d (dl > 0, copy)\n", cl, dl); #endif for(;;) { r[0] = a[0]; if (--dl <= 0) break; r[1] = a[1]; if (--dl <= 0) break; r[2] = a[2]; if (--dl <= 0) break; r[3] = a[3]; if (--dl <= 0) break; a += 4; r += 4; } } } return c; } #ifdef BN_RECURSION /* Karatsuba recursive multiplication algorithm * (cf. Knuth, The Art of Computer Programming, Vol. 2) */ /* 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 */ 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_COUNT fprintf(stderr," bn_mul_recursive %d%+d * %d%+d\n",n2,dna,n2,dnb); # endif # 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]),0,8*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 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,0,0,p); else 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)&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); } } } /* 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 */ 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,zero; BN_ULONG ln,lo,*p; # ifdef BN_COUNT fprintf(stderr," bn_mul_part_recursive (%d%+d) * (%d%+d)\n", n, tna, n, tnb); # endif 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); 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; } /* 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]),tna,&(b[n]),tnb); 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); 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); 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(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)&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); } } } /* a and b must be the same size, which is n2. * r needs to be n2 words and t needs to be n2*2 */ void bn_mul_low_recursive(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, int n2, BN_ULONG *t) { int n=n2/2; # ifdef BN_COUNT fprintf(stderr," bn_mul_low_recursive %d * %d\n",n2,n2); # endif bn_mul_recursive(r,a,b,n,0,0,&(t[0])); if (n >= BN_MUL_LOW_RECURSIVE_SIZE_NORMAL) { bn_mul_low_recursive(&(t[0]),&(a[0]),&(b[n]),n,&(t[n2])); bn_add_words(&(r[n]),&(r[n]),&(t[0]),n); bn_mul_low_recursive(&(t[0]),&(a[n]),&(b[0]),n,&(t[n2])); bn_add_words(&(r[n]),&(r[n]),&(t[0]),n); } else { bn_mul_low_normal(&(t[0]),&(a[0]),&(b[n]),n); bn_mul_low_normal(&(t[n]),&(a[n]),&(b[0]),n); bn_add_words(&(r[n]),&(r[n]),&(t[0]),n); bn_add_words(&(r[n]),&(r[n]),&(t[n]),n); } } /* a and b must be the same size, which is n2. * r needs to be n2 words and t needs to be n2*2 * l is the low words of the output. * t needs to be n2*3 */ void bn_mul_high(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, BN_ULONG *l, int n2, BN_ULONG *t) { int i,n; int c1,c2; int neg,oneg,zero; BN_ULONG ll,lc,*lp,*mp; # ifdef BN_COUNT fprintf(stderr," bn_mul_high %d * %d\n",n2,n2); # endif n=n2/2; /* Calculate (al-ah)*(bh-bl) */ neg=zero=0; c1=bn_cmp_words(&(a[0]),&(a[n]),n); c2=bn_cmp_words(&(b[n]),&(b[0]),n); switch (c1*3+c2) { case -4: bn_sub_words(&(r[0]),&(a[n]),&(a[0]),n); bn_sub_words(&(r[n]),&(b[0]),&(b[n]),n); break; case -3: zero=1; break; case -2: bn_sub_words(&(r[0]),&(a[n]),&(a[0]),n); bn_sub_words(&(r[n]),&(b[n]),&(b[0]),n); neg=1; break; case -1: case 0: case 1: zero=1; break; case 2: bn_sub_words(&(r[0]),&(a[0]),&(a[n]),n); bn_sub_words(&(r[n]),&(b[0]),&(b[n]),n); neg=1; break; case 3: zero=1; break; case 4: bn_sub_words(&(r[0]),&(a[0]),&(a[n]),n); bn_sub_words(&(r[n]),&(b[n]),&(b[0]),n); break; } oneg=neg; /* t[10] = (a[0]-a[1])*(b[1]-b[0]) */ /* r[10] = (a[1]*b[1]) */ # ifdef BN_MUL_COMBA if (n == 8) { bn_mul_comba8(&(t[0]),&(r[0]),&(r[n])); bn_mul_comba8(r,&(a[n]),&(b[n])); } else # endif { bn_mul_recursive(&(t[0]),&(r[0]),&(r[n]),n,0,0,&(t[n2])); bn_mul_recursive(r,&(a[n]),&(b[n]),n,0,0,&(t[n2])); } /* s0 == low(al*bl) * s1 == low(ah*bh)+low((al-ah)*(bh-bl))+low(al*bl)+high(al*bl) * We know s0 and s1 so the only unknown is high(al*bl) * high(al*bl) == s1 - low(ah*bh+s0+(al-ah)*(bh-bl)) * high(al*bl) == s1 - (r[0]+l[0]+t[0]) */ if (l != NULL) { lp= &(t[n2+n]); c1=(int)(bn_add_words(lp,&(r[0]),&(l[0]),n)); } else { c1=0; lp= &(r[0]); } if (neg) neg=(int)(bn_sub_words(&(t[n2]),lp,&(t[0]),n)); else { bn_add_words(&(t[n2]),lp,&(t[0]),n); neg=0; } if (l != NULL) { bn_sub_words(&(t[n2+n]),&(l[n]),&(t[n2]),n); } else { lp= &(t[n2+n]); mp= &(t[n2]); for (i=0; i<n; i++) lp[i]=((~mp[i])+1)&BN_MASK2; } /* s[0] = low(al*bl) * t[3] = high(al*bl) * t[10] = (a[0]-a[1])*(b[1]-b[0]) neg is the sign * r[10] = (a[1]*b[1]) */ /* R[10] = al*bl * R[21] = al*bl + ah*bh + (a[0]-a[1])*(b[1]-b[0]) * R[32] = ah*bh */ /* R[1]=t[3]+l[0]+r[0](+-)t[0] (have carry/borrow) * R[2]=r[0]+t[3]+r[1](+-)t[1] (have carry/borrow) * R[3]=r[1]+(carry/borrow) */ if (l != NULL) { lp= &(t[n2]); c1= (int)(bn_add_words(lp,&(t[n2+n]),&(l[0]),n)); } else { lp= &(t[n2+n]); c1=0; } c1+=(int)(bn_add_words(&(t[n2]),lp, &(r[0]),n)); if (oneg) c1-=(int)(bn_sub_words(&(t[n2]),&(t[n2]),&(t[0]),n)); else c1+=(int)(bn_add_words(&(t[n2]),&(t[n2]),&(t[0]),n)); c2 =(int)(bn_add_words(&(r[0]),&(r[0]),&(t[n2+n]),n)); c2+=(int)(bn_add_words(&(r[0]),&(r[0]),&(r[n]),n)); if (oneg) c2-=(int)(bn_sub_words(&(r[0]),&(r[0]),&(t[n]),n)); else c2+=(int)(bn_add_words(&(r[0]),&(r[0]),&(t[n]),n)); if (c1 != 0) /* Add starting at r[0], could be +ve or -ve */ { i=0; if (c1 > 0) { lc=c1; do { ll=(r[i]+lc)&BN_MASK2; r[i++]=ll; lc=(lc > ll); } while (lc); } else { lc= -c1; do { ll=r[i]; r[i++]=(ll-lc)&BN_MASK2; lc=(lc > ll); } while (lc); } } if (c2 != 0) /* Add starting at r[1] */ { i=n; if (c2 > 0) { lc=c2; do { ll=(r[i]+lc)&BN_MASK2; r[i++]=ll; lc=(lc > ll); } while (lc); } else { lc= -c2; do { ll=r[i]; r[i++]=(ll-lc)&BN_MASK2; lc=(lc > ll); } while (lc); } } } #endif /* BN_RECURSION */ 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 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 && i <= 1) { int sav_j =0; /* 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); } sav_j = j; 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 bn_correct_top(rr); if (r != rr) BN_copy(r,rr); ret=1; err: bn_check_top(r); BN_CTX_end(ctx); return(ret); } void bn_mul_normal(BN_ULONG *r, BN_ULONG *a, int na, BN_ULONG *b, int nb) { BN_ULONG *rr; #ifdef BN_COUNT fprintf(stderr," 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]); 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; } } 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; } }