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matty |
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/* crypto/bn/bn_mul.c */ |
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/* Copyright (C) 1995-1998 Eric Young (eay@cryptsoft.com) |
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* All rights reserved. |
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* |
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* This package is an SSL implementation written |
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* by Eric Young (eay@cryptsoft.com). |
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* The implementation was written so as to conform with Netscapes SSL. |
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* |
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* This library is free for commercial and non-commercial use as long as |
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* the following conditions are aheared to. The following conditions |
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* apply to all code found in this distribution, be it the RC4, RSA, |
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* lhash, DES, etc., code; not just the SSL code. The SSL documentation |
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* included with this distribution is covered by the same copyright terms |
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* except that the holder is Tim Hudson (tjh@cryptsoft.com). |
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* |
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* Copyright remains Eric Young's, and as such any Copyright notices in |
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* the code are not to be removed. |
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* If this package is used in a product, Eric Young should be given attribution |
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* as the author of the parts of the library used. |
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* This can be in the form of a textual message at program startup or |
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* in documentation (online or textual) provided with the package. |
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* |
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* Redistribution and use in source and binary forms, with or without |
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* modification, are permitted provided that the following conditions |
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* are met: |
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* 1. Redistributions of source code must retain the copyright |
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* notice, this list of conditions and the following disclaimer. |
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* 2. Redistributions in binary form must reproduce the above copyright |
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* notice, this list of conditions and the following disclaimer in the |
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* documentation and/or other materials provided with the distribution. |
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* 3. All advertising materials mentioning features or use of this software |
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* must display the following acknowledgement: |
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* "This product includes cryptographic software written by |
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* Eric Young (eay@cryptsoft.com)" |
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* The word 'cryptographic' can be left out if the rouines from the library |
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* being used are not cryptographic related :-). |
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* 4. If you include any Windows specific code (or a derivative thereof) from |
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* the apps directory (application code) you must include an acknowledgement: |
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* "This product includes software written by Tim Hudson (tjh@cryptsoft.com)" |
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* |
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* THIS SOFTWARE IS PROVIDED BY ERIC YOUNG ``AS IS'' AND |
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* ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE |
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* IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE |
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* ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE |
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* FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL |
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* DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS |
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* OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) |
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* HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT |
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* LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY |
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* OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF |
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* SUCH DAMAGE. |
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* |
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* The licence and distribution terms for any publically available version or |
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* derivative of this code cannot be changed. i.e. this code cannot simply be |
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* copied and put under another distribution licence |
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* [including the GNU Public Licence.] |
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*/ |
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#include <stdio.h> |
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#include "bn_lcl.h" |
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#ifdef BN_RECURSION |
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/* Karatsuba recursive multiplication algorithm |
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* (cf. Knuth, The Art of Computer Programming, Vol. 2) */ |
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/* r is 2*n2 words in size, |
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* a and b are both n2 words in size. |
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* n2 must be a power of 2. |
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* We multiply and return the result. |
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* t must be 2*n2 words in size |
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* We calculate |
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* a[0]*b[0] |
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* a[0]*b[0]+a[1]*b[1]+(a[0]-a[1])*(b[1]-b[0]) |
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* a[1]*b[1] |
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*/ |
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void bn_mul_recursive(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, int n2, |
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BN_ULONG *t) |
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{ |
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int n=n2/2,c1,c2; |
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unsigned int neg,zero; |
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BN_ULONG ln,lo,*p; |
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# ifdef BN_COUNT |
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printf(" bn_mul_recursive %d * %d\n",n2,n2); |
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# endif |
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# ifdef BN_MUL_COMBA |
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# if 0 |
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if (n2 == 4) |
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{ |
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bn_mul_comba4(r,a,b); |
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return; |
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} |
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# endif |
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if (n2 == 8) |
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{ |
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bn_mul_comba8(r,a,b); |
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return; |
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} |
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# endif /* BN_MUL_COMBA */ |
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if (n2 < BN_MUL_RECURSIVE_SIZE_NORMAL) |
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{ |
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/* This should not happen */ |
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bn_mul_normal(r,a,n2,b,n2); |
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return; |
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} |
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/* r=(a[0]-a[1])*(b[1]-b[0]) */ |
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c1=bn_cmp_words(a,&(a[n]),n); |
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c2=bn_cmp_words(&(b[n]),b,n); |
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zero=neg=0; |
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switch (c1*3+c2) |
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{ |
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case -4: |
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bn_sub_words(t, &(a[n]),a, n); /* - */ |
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bn_sub_words(&(t[n]),b, &(b[n]),n); /* - */ |
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break; |
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case -3: |
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zero=1; |
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break; |
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case -2: |
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bn_sub_words(t, &(a[n]),a, n); /* - */ |
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bn_sub_words(&(t[n]),&(b[n]),b, n); /* + */ |
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neg=1; |
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break; |
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case -1: |
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case 0: |
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case 1: |
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zero=1; |
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break; |
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case 2: |
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bn_sub_words(t, a, &(a[n]),n); /* + */ |
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bn_sub_words(&(t[n]),b, &(b[n]),n); /* - */ |
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neg=1; |
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break; |
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case 3: |
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zero=1; |
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break; |
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case 4: |
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bn_sub_words(t, a, &(a[n]),n); |
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bn_sub_words(&(t[n]),&(b[n]),b, n); |
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break; |
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} |
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# ifdef BN_MUL_COMBA |
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if (n == 4) |
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{ |
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if (!zero) |
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bn_mul_comba4(&(t[n2]),t,&(t[n])); |
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else |
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memset(&(t[n2]),0,8*sizeof(BN_ULONG)); |
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bn_mul_comba4(r,a,b); |
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bn_mul_comba4(&(r[n2]),&(a[n]),&(b[n])); |
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} |
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else if (n == 8) |
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{ |
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if (!zero) |
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bn_mul_comba8(&(t[n2]),t,&(t[n])); |
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else |
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memset(&(t[n2]),0,16*sizeof(BN_ULONG)); |
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bn_mul_comba8(r,a,b); |
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bn_mul_comba8(&(r[n2]),&(a[n]),&(b[n])); |
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} |
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else |
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# endif /* BN_MUL_COMBA */ |
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{ |
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p= &(t[n2*2]); |
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if (!zero) |
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bn_mul_recursive(&(t[n2]),t,&(t[n]),n,p); |
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else |
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memset(&(t[n2]),0,n2*sizeof(BN_ULONG)); |
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bn_mul_recursive(r,a,b,n,p); |
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bn_mul_recursive(&(r[n2]),&(a[n]),&(b[n]),n,p); |
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} |
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/* t[32] holds (a[0]-a[1])*(b[1]-b[0]), c1 is the sign |
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* r[10] holds (a[0]*b[0]) |
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* r[32] holds (b[1]*b[1]) |
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*/ |
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c1=(int)(bn_add_words(t,r,&(r[n2]),n2)); |
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if (neg) /* if t[32] is negative */ |
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{ |
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c1-=(int)(bn_sub_words(&(t[n2]),t,&(t[n2]),n2)); |
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} |
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else |
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{ |
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/* Might have a carry */ |
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c1+=(int)(bn_add_words(&(t[n2]),&(t[n2]),t,n2)); |
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} |
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/* t[32] holds (a[0]-a[1])*(b[1]-b[0])+(a[0]*b[0])+(a[1]*b[1]) |
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* r[10] holds (a[0]*b[0]) |
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* r[32] holds (b[1]*b[1]) |
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* c1 holds the carry bits |
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*/ |
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c1+=(int)(bn_add_words(&(r[n]),&(r[n]),&(t[n2]),n2)); |
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if (c1) |
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{ |
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p= &(r[n+n2]); |
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lo= *p; |
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ln=(lo+c1)&BN_MASK2; |
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*p=ln; |
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/* The overflow will stop before we over write |
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* words we should not overwrite */ |
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if (ln < (BN_ULONG)c1) |
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{ |
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do { |
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p++; |
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lo= *p; |
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ln=(lo+1)&BN_MASK2; |
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*p=ln; |
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} while (ln == 0); |
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} |
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} |
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} |
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/* n+tn is the word length |
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* t needs to be n*4 is size, as does r */ |
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void bn_mul_part_recursive(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, int tn, |
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int n, BN_ULONG *t) |
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{ |
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int i,j,n2=n*2; |
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unsigned int c1,c2,neg,zero; |
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BN_ULONG ln,lo,*p; |
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# ifdef BN_COUNT |
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printf(" bn_mul_part_recursive %d * %d\n",tn+n,tn+n); |
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# endif |
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if (n < 8) |
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{ |
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i=tn+n; |
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bn_mul_normal(r,a,i,b,i); |
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return; |
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} |
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/* r=(a[0]-a[1])*(b[1]-b[0]) */ |
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c1=bn_cmp_words(a,&(a[n]),n); |
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c2=bn_cmp_words(&(b[n]),b,n); |
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zero=neg=0; |
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switch (c1*3+c2) |
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{ |
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case -4: |
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bn_sub_words(t, &(a[n]),a, n); /* - */ |
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bn_sub_words(&(t[n]),b, &(b[n]),n); /* - */ |
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break; |
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case -3: |
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zero=1; |
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/* break; */ |
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case -2: |
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bn_sub_words(t, &(a[n]),a, n); /* - */ |
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bn_sub_words(&(t[n]),&(b[n]),b, n); /* + */ |
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neg=1; |
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break; |
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case -1: |
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case 0: |
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case 1: |
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zero=1; |
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/* break; */ |
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case 2: |
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bn_sub_words(t, a, &(a[n]),n); /* + */ |
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bn_sub_words(&(t[n]),b, &(b[n]),n); /* - */ |
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neg=1; |
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break; |
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case 3: |
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zero=1; |
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/* break; */ |
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case 4: |
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bn_sub_words(t, a, &(a[n]),n); |
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bn_sub_words(&(t[n]),&(b[n]),b, n); |
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break; |
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} |
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/* The zero case isn't yet implemented here. The speedup |
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would probably be negligible. */ |
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# if 0 |
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if (n == 4) |
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{ |
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bn_mul_comba4(&(t[n2]),t,&(t[n])); |
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bn_mul_comba4(r,a,b); |
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bn_mul_normal(&(r[n2]),&(a[n]),tn,&(b[n]),tn); |
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memset(&(r[n2+tn*2]),0,sizeof(BN_ULONG)*(n2-tn*2)); |
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} |
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else |
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# endif |
287 |
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if (n == 8) |
288 |
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{ |
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bn_mul_comba8(&(t[n2]),t,&(t[n])); |
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bn_mul_comba8(r,a,b); |
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bn_mul_normal(&(r[n2]),&(a[n]),tn,&(b[n]),tn); |
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memset(&(r[n2+tn*2]),0,sizeof(BN_ULONG)*(n2-tn*2)); |
293 |
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} |
294 |
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else |
295 |
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{ |
296 |
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p= &(t[n2*2]); |
297 |
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bn_mul_recursive(&(t[n2]),t,&(t[n]),n,p); |
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bn_mul_recursive(r,a,b,n,p); |
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i=n/2; |
300 |
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/* If there is only a bottom half to the number, |
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* just do it */ |
302 |
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j=tn-i; |
303 |
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if (j == 0) |
304 |
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{ |
305 |
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bn_mul_recursive(&(r[n2]),&(a[n]),&(b[n]),i,p); |
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memset(&(r[n2+i*2]),0,sizeof(BN_ULONG)*(n2-i*2)); |
307 |
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} |
308 |
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else if (j > 0) /* eg, n == 16, i == 8 and tn == 11 */ |
309 |
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{ |
310 |
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bn_mul_part_recursive(&(r[n2]),&(a[n]),&(b[n]), |
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j,i,p); |
312 |
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memset(&(r[n2+tn*2]),0, |
313 |
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sizeof(BN_ULONG)*(n2-tn*2)); |
314 |
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} |
315 |
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else /* (j < 0) eg, n == 16, i == 8 and tn == 5 */ |
316 |
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{ |
317 |
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memset(&(r[n2]),0,sizeof(BN_ULONG)*n2); |
318 |
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if (tn < BN_MUL_RECURSIVE_SIZE_NORMAL) |
319 |
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{ |
320 |
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bn_mul_normal(&(r[n2]),&(a[n]),tn,&(b[n]),tn); |
321 |
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} |
322 |
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else |
323 |
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{ |
324 |
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for (;;) |
325 |
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{ |
326 |
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i/=2; |
327 |
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if (i < tn) |
328 |
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{ |
329 |
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bn_mul_part_recursive(&(r[n2]), |
330 |
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&(a[n]),&(b[n]), |
331 |
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tn-i,i,p); |
332 |
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break; |
333 |
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} |
334 |
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else if (i == tn) |
335 |
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{ |
336 |
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bn_mul_recursive(&(r[n2]), |
337 |
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&(a[n]),&(b[n]), |
338 |
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i,p); |
339 |
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break; |
340 |
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} |
341 |
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} |
342 |
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} |
343 |
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} |
344 |
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} |
345 |
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|
346 |
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/* t[32] holds (a[0]-a[1])*(b[1]-b[0]), c1 is the sign |
347 |
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* r[10] holds (a[0]*b[0]) |
348 |
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* r[32] holds (b[1]*b[1]) |
349 |
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*/ |
350 |
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351 |
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c1=(int)(bn_add_words(t,r,&(r[n2]),n2)); |
352 |
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353 |
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if (neg) /* if t[32] is negative */ |
354 |
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{ |
355 |
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c1-=(int)(bn_sub_words(&(t[n2]),t,&(t[n2]),n2)); |
356 |
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} |
357 |
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else |
358 |
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{ |
359 |
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/* Might have a carry */ |
360 |
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c1+=(int)(bn_add_words(&(t[n2]),&(t[n2]),t,n2)); |
361 |
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} |
362 |
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|
363 |
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/* t[32] holds (a[0]-a[1])*(b[1]-b[0])+(a[0]*b[0])+(a[1]*b[1]) |
364 |
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* r[10] holds (a[0]*b[0]) |
365 |
|
|
* r[32] holds (b[1]*b[1]) |
366 |
|
|
* c1 holds the carry bits |
367 |
|
|
*/ |
368 |
|
|
c1+=(int)(bn_add_words(&(r[n]),&(r[n]),&(t[n2]),n2)); |
369 |
|
|
if (c1) |
370 |
|
|
{ |
371 |
|
|
p= &(r[n+n2]); |
372 |
|
|
lo= *p; |
373 |
|
|
ln=(lo+c1)&BN_MASK2; |
374 |
|
|
*p=ln; |
375 |
|
|
|
376 |
|
|
/* The overflow will stop before we over write |
377 |
|
|
* words we should not overwrite */ |
378 |
|
|
if (ln < c1) |
379 |
|
|
{ |
380 |
|
|
do { |
381 |
|
|
p++; |
382 |
|
|
lo= *p; |
383 |
|
|
ln=(lo+1)&BN_MASK2; |
384 |
|
|
*p=ln; |
385 |
|
|
} while (ln == 0); |
386 |
|
|
} |
387 |
|
|
} |
388 |
|
|
} |
389 |
|
|
|
390 |
|
|
/* a and b must be the same size, which is n2. |
391 |
|
|
* r needs to be n2 words and t needs to be n2*2 |
392 |
|
|
*/ |
393 |
|
|
void bn_mul_low_recursive(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, int n2, |
394 |
|
|
BN_ULONG *t) |
395 |
|
|
{ |
396 |
|
|
int n=n2/2; |
397 |
|
|
|
398 |
|
|
# ifdef BN_COUNT |
399 |
|
|
printf(" bn_mul_low_recursive %d * %d\n",n2,n2); |
400 |
|
|
# endif |
401 |
|
|
|
402 |
|
|
bn_mul_recursive(r,a,b,n,&(t[0])); |
403 |
|
|
if (n >= BN_MUL_LOW_RECURSIVE_SIZE_NORMAL) |
404 |
|
|
{ |
405 |
|
|
bn_mul_low_recursive(&(t[0]),&(a[0]),&(b[n]),n,&(t[n2])); |
406 |
|
|
bn_add_words(&(r[n]),&(r[n]),&(t[0]),n); |
407 |
|
|
bn_mul_low_recursive(&(t[0]),&(a[n]),&(b[0]),n,&(t[n2])); |
408 |
|
|
bn_add_words(&(r[n]),&(r[n]),&(t[0]),n); |
409 |
|
|
} |
410 |
|
|
else |
411 |
|
|
{ |
412 |
|
|
bn_mul_low_normal(&(t[0]),&(a[0]),&(b[n]),n); |
413 |
|
|
bn_mul_low_normal(&(t[n]),&(a[n]),&(b[0]),n); |
414 |
|
|
bn_add_words(&(r[n]),&(r[n]),&(t[0]),n); |
415 |
|
|
bn_add_words(&(r[n]),&(r[n]),&(t[n]),n); |
416 |
|
|
} |
417 |
|
|
} |
418 |
|
|
|
419 |
|
|
/* a and b must be the same size, which is n2. |
420 |
|
|
* r needs to be n2 words and t needs to be n2*2 |
421 |
|
|
* l is the low words of the output. |
422 |
|
|
* t needs to be n2*3 |
423 |
|
|
*/ |
424 |
|
|
void bn_mul_high(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, BN_ULONG *l, int n2, |
425 |
|
|
BN_ULONG *t) |
426 |
|
|
{ |
427 |
|
|
int i,n; |
428 |
|
|
int c1,c2; |
429 |
|
|
int neg,oneg,zero; |
430 |
|
|
BN_ULONG ll,lc,*lp,*mp; |
431 |
|
|
|
432 |
|
|
# ifdef BN_COUNT |
433 |
|
|
printf(" bn_mul_high %d * %d\n",n2,n2); |
434 |
|
|
# endif |
435 |
|
|
n=n2/2; |
436 |
|
|
|
437 |
|
|
/* Calculate (al-ah)*(bh-bl) */ |
438 |
|
|
neg=zero=0; |
439 |
|
|
c1=bn_cmp_words(&(a[0]),&(a[n]),n); |
440 |
|
|
c2=bn_cmp_words(&(b[n]),&(b[0]),n); |
441 |
|
|
switch (c1*3+c2) |
442 |
|
|
{ |
443 |
|
|
case -4: |
444 |
|
|
bn_sub_words(&(r[0]),&(a[n]),&(a[0]),n); |
445 |
|
|
bn_sub_words(&(r[n]),&(b[0]),&(b[n]),n); |
446 |
|
|
break; |
447 |
|
|
case -3: |
448 |
|
|
zero=1; |
449 |
|
|
break; |
450 |
|
|
case -2: |
451 |
|
|
bn_sub_words(&(r[0]),&(a[n]),&(a[0]),n); |
452 |
|
|
bn_sub_words(&(r[n]),&(b[n]),&(b[0]),n); |
453 |
|
|
neg=1; |
454 |
|
|
break; |
455 |
|
|
case -1: |
456 |
|
|
case 0: |
457 |
|
|
case 1: |
458 |
|
|
zero=1; |
459 |
|
|
break; |
460 |
|
|
case 2: |
461 |
|
|
bn_sub_words(&(r[0]),&(a[0]),&(a[n]),n); |
462 |
|
|
bn_sub_words(&(r[n]),&(b[0]),&(b[n]),n); |
463 |
|
|
neg=1; |
464 |
|
|
break; |
465 |
|
|
case 3: |
466 |
|
|
zero=1; |
467 |
|
|
break; |
468 |
|
|
case 4: |
469 |
|
|
bn_sub_words(&(r[0]),&(a[0]),&(a[n]),n); |
470 |
|
|
bn_sub_words(&(r[n]),&(b[n]),&(b[0]),n); |
471 |
|
|
break; |
472 |
|
|
} |
473 |
|
|
|
474 |
|
|
oneg=neg; |
475 |
|
|
/* t[10] = (a[0]-a[1])*(b[1]-b[0]) */ |
476 |
|
|
/* r[10] = (a[1]*b[1]) */ |
477 |
|
|
# ifdef BN_MUL_COMBA |
478 |
|
|
if (n == 8) |
479 |
|
|
{ |
480 |
|
|
bn_mul_comba8(&(t[0]),&(r[0]),&(r[n])); |
481 |
|
|
bn_mul_comba8(r,&(a[n]),&(b[n])); |
482 |
|
|
} |
483 |
|
|
else |
484 |
|
|
# endif |
485 |
|
|
{ |
486 |
|
|
bn_mul_recursive(&(t[0]),&(r[0]),&(r[n]),n,&(t[n2])); |
487 |
|
|
bn_mul_recursive(r,&(a[n]),&(b[n]),n,&(t[n2])); |
488 |
|
|
} |
489 |
|
|
|
490 |
|
|
/* s0 == low(al*bl) |
491 |
|
|
* s1 == low(ah*bh)+low((al-ah)*(bh-bl))+low(al*bl)+high(al*bl) |
492 |
|
|
* We know s0 and s1 so the only unknown is high(al*bl) |
493 |
|
|
* high(al*bl) == s1 - low(ah*bh+s0+(al-ah)*(bh-bl)) |
494 |
|
|
* high(al*bl) == s1 - (r[0]+l[0]+t[0]) |
495 |
|
|
*/ |
496 |
|
|
if (l != NULL) |
497 |
|
|
{ |
498 |
|
|
lp= &(t[n2+n]); |
499 |
|
|
c1=(int)(bn_add_words(lp,&(r[0]),&(l[0]),n)); |
500 |
|
|
} |
501 |
|
|
else |
502 |
|
|
{ |
503 |
|
|
c1=0; |
504 |
|
|
lp= &(r[0]); |
505 |
|
|
} |
506 |
|
|
|
507 |
|
|
if (neg) |
508 |
|
|
neg=(int)(bn_sub_words(&(t[n2]),lp,&(t[0]),n)); |
509 |
|
|
else |
510 |
|
|
{ |
511 |
|
|
bn_add_words(&(t[n2]),lp,&(t[0]),n); |
512 |
|
|
neg=0; |
513 |
|
|
} |
514 |
|
|
|
515 |
|
|
if (l != NULL) |
516 |
|
|
{ |
517 |
|
|
bn_sub_words(&(t[n2+n]),&(l[n]),&(t[n2]),n); |
518 |
|
|
} |
519 |
|
|
else |
520 |
|
|
{ |
521 |
|
|
lp= &(t[n2+n]); |
522 |
|
|
mp= &(t[n2]); |
523 |
|
|
for (i=0; i<n; i++) |
524 |
|
|
lp[i]=((~mp[i])+1)&BN_MASK2; |
525 |
|
|
} |
526 |
|
|
|
527 |
|
|
/* s[0] = low(al*bl) |
528 |
|
|
* t[3] = high(al*bl) |
529 |
|
|
* t[10] = (a[0]-a[1])*(b[1]-b[0]) neg is the sign |
530 |
|
|
* r[10] = (a[1]*b[1]) |
531 |
|
|
*/ |
532 |
|
|
/* R[10] = al*bl |
533 |
|
|
* R[21] = al*bl + ah*bh + (a[0]-a[1])*(b[1]-b[0]) |
534 |
|
|
* R[32] = ah*bh |
535 |
|
|
*/ |
536 |
|
|
/* R[1]=t[3]+l[0]+r[0](+-)t[0] (have carry/borrow) |
537 |
|
|
* R[2]=r[0]+t[3]+r[1](+-)t[1] (have carry/borrow) |
538 |
|
|
* R[3]=r[1]+(carry/borrow) |
539 |
|
|
*/ |
540 |
|
|
if (l != NULL) |
541 |
|
|
{ |
542 |
|
|
lp= &(t[n2]); |
543 |
|
|
c1= (int)(bn_add_words(lp,&(t[n2+n]),&(l[0]),n)); |
544 |
|
|
} |
545 |
|
|
else |
546 |
|
|
{ |
547 |
|
|
lp= &(t[n2+n]); |
548 |
|
|
c1=0; |
549 |
|
|
} |
550 |
|
|
c1+=(int)(bn_add_words(&(t[n2]),lp, &(r[0]),n)); |
551 |
|
|
if (oneg) |
552 |
|
|
c1-=(int)(bn_sub_words(&(t[n2]),&(t[n2]),&(t[0]),n)); |
553 |
|
|
else |
554 |
|
|
c1+=(int)(bn_add_words(&(t[n2]),&(t[n2]),&(t[0]),n)); |
555 |
|
|
|
556 |
|
|
c2 =(int)(bn_add_words(&(r[0]),&(r[0]),&(t[n2+n]),n)); |
557 |
|
|
c2+=(int)(bn_add_words(&(r[0]),&(r[0]),&(r[n]),n)); |
558 |
|
|
if (oneg) |
559 |
|
|
c2-=(int)(bn_sub_words(&(r[0]),&(r[0]),&(t[n]),n)); |
560 |
|
|
else |
561 |
|
|
c2+=(int)(bn_add_words(&(r[0]),&(r[0]),&(t[n]),n)); |
562 |
|
|
|
563 |
|
|
if (c1 != 0) /* Add starting at r[0], could be +ve or -ve */ |
564 |
|
|
{ |
565 |
|
|
i=0; |
566 |
|
|
if (c1 > 0) |
567 |
|
|
{ |
568 |
|
|
lc=c1; |
569 |
|
|
do { |
570 |
|
|
ll=(r[i]+lc)&BN_MASK2; |
571 |
|
|
r[i++]=ll; |
572 |
|
|
lc=(lc > ll); |
573 |
|
|
} while (lc); |
574 |
|
|
} |
575 |
|
|
else |
576 |
|
|
{ |
577 |
|
|
lc= -c1; |
578 |
|
|
do { |
579 |
|
|
ll=r[i]; |
580 |
|
|
r[i++]=(ll-lc)&BN_MASK2; |
581 |
|
|
lc=(lc > ll); |
582 |
|
|
} while (lc); |
583 |
|
|
} |
584 |
|
|
} |
585 |
|
|
if (c2 != 0) /* Add starting at r[1] */ |
586 |
|
|
{ |
587 |
|
|
i=n; |
588 |
|
|
if (c2 > 0) |
589 |
|
|
{ |
590 |
|
|
lc=c2; |
591 |
|
|
do { |
592 |
|
|
ll=(r[i]+lc)&BN_MASK2; |
593 |
|
|
r[i++]=ll; |
594 |
|
|
lc=(lc > ll); |
595 |
|
|
} while (lc); |
596 |
|
|
} |
597 |
|
|
else |
598 |
|
|
{ |
599 |
|
|
lc= -c2; |
600 |
|
|
do { |
601 |
|
|
ll=r[i]; |
602 |
|
|
r[i++]=(ll-lc)&BN_MASK2; |
603 |
|
|
lc=(lc > ll); |
604 |
|
|
} while (lc); |
605 |
|
|
} |
606 |
|
|
} |
607 |
|
|
} |
608 |
|
|
#endif /* BN_RECURSION */ |
609 |
|
|
|
610 |
|
|
int BN_mul(BIGNUM *r, BIGNUM *a, BIGNUM *b, BN_CTX *ctx) |
611 |
|
|
{ |
612 |
|
|
int top,al,bl; |
613 |
|
|
BIGNUM *rr; |
614 |
|
|
int ret = 0; |
615 |
|
|
#if defined(BN_MUL_COMBA) || defined(BN_RECURSION) |
616 |
|
|
int i; |
617 |
|
|
#endif |
618 |
|
|
#ifdef BN_RECURSION |
619 |
|
|
BIGNUM *t; |
620 |
|
|
int j,k; |
621 |
|
|
#endif |
622 |
|
|
|
623 |
|
|
#ifdef BN_COUNT |
624 |
|
|
printf("BN_mul %d * %d\n",a->top,b->top); |
625 |
|
|
#endif |
626 |
|
|
|
627 |
|
|
bn_check_top(a); |
628 |
|
|
bn_check_top(b); |
629 |
|
|
bn_check_top(r); |
630 |
|
|
|
631 |
|
|
al=a->top; |
632 |
|
|
bl=b->top; |
633 |
|
|
|
634 |
|
|
if ((al == 0) || (bl == 0)) |
635 |
|
|
{ |
636 |
|
|
BN_zero(r); |
637 |
|
|
return(1); |
638 |
|
|
} |
639 |
|
|
top=al+bl; |
640 |
|
|
|
641 |
|
|
BN_CTX_start(ctx); |
642 |
|
|
if ((r == a) || (r == b)) |
643 |
|
|
{ |
644 |
|
|
if ((rr = BN_CTX_get(ctx)) == NULL) goto err; |
645 |
|
|
} |
646 |
|
|
else |
647 |
|
|
rr = r; |
648 |
|
|
rr->neg=a->neg^b->neg; |
649 |
|
|
|
650 |
|
|
#if defined(BN_MUL_COMBA) || defined(BN_RECURSION) |
651 |
|
|
i = al-bl; |
652 |
|
|
#endif |
653 |
|
|
#ifdef BN_MUL_COMBA |
654 |
|
|
if (i == 0) |
655 |
|
|
{ |
656 |
|
|
# if 0 |
657 |
|
|
if (al == 4) |
658 |
|
|
{ |
659 |
|
|
if (bn_wexpand(rr,8) == NULL) goto err; |
660 |
|
|
rr->top=8; |
661 |
|
|
bn_mul_comba4(rr->d,a->d,b->d); |
662 |
|
|
goto end; |
663 |
|
|
} |
664 |
|
|
# endif |
665 |
|
|
if (al == 8) |
666 |
|
|
{ |
667 |
|
|
if (bn_wexpand(rr,16) == NULL) goto err; |
668 |
|
|
rr->top=16; |
669 |
|
|
bn_mul_comba8(rr->d,a->d,b->d); |
670 |
|
|
goto end; |
671 |
|
|
} |
672 |
|
|
} |
673 |
|
|
#endif /* BN_MUL_COMBA */ |
674 |
|
|
#ifdef BN_RECURSION |
675 |
|
|
if ((al >= BN_MULL_SIZE_NORMAL) && (bl >= BN_MULL_SIZE_NORMAL)) |
676 |
|
|
{ |
677 |
|
|
if (i == 1 && !BN_get_flags(b,BN_FLG_STATIC_DATA)) |
678 |
|
|
{ |
679 |
|
|
bn_wexpand(b,al); |
680 |
|
|
b->d[bl]=0; |
681 |
|
|
bl++; |
682 |
|
|
i--; |
683 |
|
|
} |
684 |
|
|
else if (i == -1 && !BN_get_flags(a,BN_FLG_STATIC_DATA)) |
685 |
|
|
{ |
686 |
|
|
bn_wexpand(a,bl); |
687 |
|
|
a->d[al]=0; |
688 |
|
|
al++; |
689 |
|
|
i++; |
690 |
|
|
} |
691 |
|
|
if (i == 0) |
692 |
|
|
{ |
693 |
|
|
/* symmetric and > 4 */ |
694 |
|
|
/* 16 or larger */ |
695 |
|
|
j=BN_num_bits_word((BN_ULONG)al); |
696 |
|
|
j=1<<(j-1); |
697 |
|
|
k=j+j; |
698 |
|
|
t = BN_CTX_get(ctx); |
699 |
|
|
if (al == j) /* exact multiple */ |
700 |
|
|
{ |
701 |
|
|
bn_wexpand(t,k*2); |
702 |
|
|
bn_wexpand(rr,k*2); |
703 |
|
|
bn_mul_recursive(rr->d,a->d,b->d,al,t->d); |
704 |
|
|
} |
705 |
|
|
else |
706 |
|
|
{ |
707 |
|
|
bn_wexpand(a,k); |
708 |
|
|
bn_wexpand(b,k); |
709 |
|
|
bn_wexpand(t,k*4); |
710 |
|
|
bn_wexpand(rr,k*4); |
711 |
|
|
for (i=a->top; i<k; i++) |
712 |
|
|
a->d[i]=0; |
713 |
|
|
for (i=b->top; i<k; i++) |
714 |
|
|
b->d[i]=0; |
715 |
|
|
bn_mul_part_recursive(rr->d,a->d,b->d,al-j,j,t->d); |
716 |
|
|
} |
717 |
|
|
rr->top=top; |
718 |
|
|
goto end; |
719 |
|
|
} |
720 |
|
|
} |
721 |
|
|
#endif /* BN_RECURSION */ |
722 |
|
|
if (bn_wexpand(rr,top) == NULL) goto err; |
723 |
|
|
rr->top=top; |
724 |
|
|
bn_mul_normal(rr->d,a->d,al,b->d,bl); |
725 |
|
|
|
726 |
|
|
#if defined(BN_MUL_COMBA) || defined(BN_RECURSION) |
727 |
|
|
end: |
728 |
|
|
#endif |
729 |
|
|
bn_fix_top(rr); |
730 |
|
|
if (r != rr) BN_copy(r,rr); |
731 |
|
|
ret=1; |
732 |
|
|
err: |
733 |
|
|
BN_CTX_end(ctx); |
734 |
|
|
return(ret); |
735 |
|
|
} |
736 |
|
|
|
737 |
|
|
void bn_mul_normal(BN_ULONG *r, BN_ULONG *a, int na, BN_ULONG *b, int nb) |
738 |
|
|
{ |
739 |
|
|
BN_ULONG *rr; |
740 |
|
|
|
741 |
|
|
#ifdef BN_COUNT |
742 |
|
|
printf(" bn_mul_normal %d * %d\n",na,nb); |
743 |
|
|
#endif |
744 |
|
|
|
745 |
|
|
if (na < nb) |
746 |
|
|
{ |
747 |
|
|
int itmp; |
748 |
|
|
BN_ULONG *ltmp; |
749 |
|
|
|
750 |
|
|
itmp=na; na=nb; nb=itmp; |
751 |
|
|
ltmp=a; a=b; b=ltmp; |
752 |
|
|
|
753 |
|
|
} |
754 |
|
|
rr= &(r[na]); |
755 |
|
|
rr[0]=bn_mul_words(r,a,na,b[0]); |
756 |
|
|
|
757 |
|
|
for (;;) |
758 |
|
|
{ |
759 |
|
|
if (--nb <= 0) return; |
760 |
|
|
rr[1]=bn_mul_add_words(&(r[1]),a,na,b[1]); |
761 |
|
|
if (--nb <= 0) return; |
762 |
|
|
rr[2]=bn_mul_add_words(&(r[2]),a,na,b[2]); |
763 |
|
|
if (--nb <= 0) return; |
764 |
|
|
rr[3]=bn_mul_add_words(&(r[3]),a,na,b[3]); |
765 |
|
|
if (--nb <= 0) return; |
766 |
|
|
rr[4]=bn_mul_add_words(&(r[4]),a,na,b[4]); |
767 |
|
|
rr+=4; |
768 |
|
|
r+=4; |
769 |
|
|
b+=4; |
770 |
|
|
} |
771 |
|
|
} |
772 |
|
|
|
773 |
|
|
void bn_mul_low_normal(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, int n) |
774 |
|
|
{ |
775 |
|
|
#ifdef BN_COUNT |
776 |
|
|
printf(" bn_mul_low_normal %d * %d\n",n,n); |
777 |
|
|
#endif |
778 |
|
|
bn_mul_words(r,a,n,b[0]); |
779 |
|
|
|
780 |
|
|
for (;;) |
781 |
|
|
{ |
782 |
|
|
if (--n <= 0) return; |
783 |
|
|
bn_mul_add_words(&(r[1]),a,n,b[1]); |
784 |
|
|
if (--n <= 0) return; |
785 |
|
|
bn_mul_add_words(&(r[2]),a,n,b[2]); |
786 |
|
|
if (--n <= 0) return; |
787 |
|
|
bn_mul_add_words(&(r[3]),a,n,b[3]); |
788 |
|
|
if (--n <= 0) return; |
789 |
|
|
bn_mul_add_words(&(r[4]),a,n,b[4]); |
790 |
|
|
r+=4; |
791 |
|
|
b+=4; |
792 |
|
|
} |
793 |
|
|
} |