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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; |
| 269 |
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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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} |
| 275 |
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/* The zero case isn't yet implemented here. The speedup |
| 276 |
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would probably be negligible. */ |
| 277 |
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# if 0 |
| 278 |
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if (n == 4) |
| 279 |
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{ |
| 280 |
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bn_mul_comba4(&(t[n2]),t,&(t[n])); |
| 281 |
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bn_mul_comba4(r,a,b); |
| 282 |
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bn_mul_normal(&(r[n2]),&(a[n]),tn,&(b[n]),tn); |
| 283 |
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memset(&(r[n2+tn*2]),0,sizeof(BN_ULONG)*(n2-tn*2)); |
| 284 |
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} |
| 285 |
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else |
| 286 |
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# endif |
| 287 |
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if (n == 8) |
| 288 |
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{ |
| 289 |
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bn_mul_comba8(&(t[n2]),t,&(t[n])); |
| 290 |
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bn_mul_comba8(r,a,b); |
| 291 |
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bn_mul_normal(&(r[n2]),&(a[n]),tn,&(b[n]),tn); |
| 292 |
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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); |
| 298 |
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bn_mul_recursive(r,a,b,n,p); |
| 299 |
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i=n/2; |
| 300 |
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/* If there is only a bottom half to the number, |
| 301 |
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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); |
| 306 |
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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]), |
| 311 |
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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 |
|
|
c1=(int)(bn_add_words(t,r,&(r[n2]),n2)); |
| 352 |
|
|
|
| 353 |
|
|
if (neg) /* if t[32] is negative */ |
| 354 |
|
|
{ |
| 355 |
|
|
c1-=(int)(bn_sub_words(&(t[n2]),t,&(t[n2]),n2)); |
| 356 |
|
|
} |
| 357 |
|
|
else |
| 358 |
|
|
{ |
| 359 |
|
|
/* Might have a carry */ |
| 360 |
|
|
c1+=(int)(bn_add_words(&(t[n2]),&(t[n2]),t,n2)); |
| 361 |
|
|
} |
| 362 |
|
|
|
| 363 |
|
|
/* t[32] holds (a[0]-a[1])*(b[1]-b[0])+(a[0]*b[0])+(a[1]*b[1]) |
| 364 |
|
|
* 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 |
|
|
} |
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