1=pod 2 3=head1 NAME 4 5bn_mul_words, bn_mul_add_words, bn_sqr_words, bn_div_words, 6bn_add_words, bn_sub_words, bn_mul_comba4, bn_mul_comba8, 7bn_sqr_comba4, bn_sqr_comba8, bn_cmp_words, bn_mul_normal, 8bn_mul_low_normal, bn_mul_recursive, bn_mul_part_recursive, 9bn_mul_low_recursive, bn_sqr_normal, bn_sqr_recursive, 10bn_expand, bn_wexpand, bn_expand2, bn_fix_top, bn_check_top, 11bn_print, bn_dump, bn_set_max, bn_set_high, bn_set_low - BIGNUM 12library internal functions 13 14=head1 SYNOPSIS 15 16 #include <openssl/bn.h> 17 18 BN_ULONG bn_mul_words(BN_ULONG *rp, BN_ULONG *ap, int num, BN_ULONG w); 19 BN_ULONG bn_mul_add_words(BN_ULONG *rp, BN_ULONG *ap, int num, 20 BN_ULONG w); 21 void bn_sqr_words(BN_ULONG *rp, BN_ULONG *ap, int num); 22 BN_ULONG bn_div_words(BN_ULONG h, BN_ULONG l, BN_ULONG d); 23 BN_ULONG bn_add_words(BN_ULONG *rp, BN_ULONG *ap, BN_ULONG *bp, 24 int num); 25 BN_ULONG bn_sub_words(BN_ULONG *rp, BN_ULONG *ap, BN_ULONG *bp, 26 int num); 27 28 void bn_mul_comba4(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b); 29 void bn_mul_comba8(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b); 30 void bn_sqr_comba4(BN_ULONG *r, BN_ULONG *a); 31 void bn_sqr_comba8(BN_ULONG *r, BN_ULONG *a); 32 33 int bn_cmp_words(BN_ULONG *a, BN_ULONG *b, int n); 34 35 void bn_mul_normal(BN_ULONG *r, BN_ULONG *a, int na, BN_ULONG *b, 36 int nb); 37 void bn_mul_low_normal(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, int n); 38 void bn_mul_recursive(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, int n2, 39 int dna, int dnb, BN_ULONG *tmp); 40 void bn_mul_part_recursive(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, 41 int n, int tna, int tnb, BN_ULONG *tmp); 42 void bn_mul_low_recursive(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, 43 int n2, BN_ULONG *tmp); 44 45 void bn_sqr_normal(BN_ULONG *r, BN_ULONG *a, int n, BN_ULONG *tmp); 46 void bn_sqr_recursive(BN_ULONG *r, BN_ULONG *a, int n2, BN_ULONG *tmp); 47 48 void mul(BN_ULONG r, BN_ULONG a, BN_ULONG w, BN_ULONG c); 49 void mul_add(BN_ULONG r, BN_ULONG a, BN_ULONG w, BN_ULONG c); 50 void sqr(BN_ULONG r0, BN_ULONG r1, BN_ULONG a); 51 52 BIGNUM *bn_expand(BIGNUM *a, int bits); 53 BIGNUM *bn_wexpand(BIGNUM *a, int n); 54 BIGNUM *bn_expand2(BIGNUM *a, int n); 55 void bn_fix_top(BIGNUM *a); 56 57 void bn_check_top(BIGNUM *a); 58 void bn_print(BIGNUM *a); 59 void bn_dump(BN_ULONG *d, int n); 60 void bn_set_max(BIGNUM *a); 61 void bn_set_high(BIGNUM *r, BIGNUM *a, int n); 62 void bn_set_low(BIGNUM *r, BIGNUM *a, int n); 63 64=head1 DESCRIPTION 65 66This page documents the internal functions used by the OpenSSL 67B<BIGNUM> implementation. They are described here to facilitate 68debugging and extending the library. They are I<not> to be used by 69applications. 70 71=head2 The BIGNUM structure 72 73 typedef struct bignum_st BIGNUM; 74 75 struct bignum_st 76 { 77 BN_ULONG *d; /* Pointer to an array of 'BN_BITS2' bit chunks. */ 78 int top; /* Index of last used d +1. */ 79 /* The next are internal book keeping for bn_expand. */ 80 int dmax; /* Size of the d array. */ 81 int neg; /* one if the number is negative */ 82 int flags; 83 }; 84 85 86The integer value is stored in B<d>, a malloc()ed array of words (B<BN_ULONG>), 87least significant word first. A B<BN_ULONG> can be either 16, 32 or 64 bits 88in size, depending on the 'number of bits' (B<BITS2>) specified in 89C<openssl/bn.h>. 90 91B<dmax> is the size of the B<d> array that has been allocated. B<top> 92is the number of words being used, so for a value of 4, bn.d[0]=4 and 93bn.top=1. B<neg> is 1 if the number is negative. When a B<BIGNUM> is 94B<0>, the B<d> field can be B<NULL> and B<top> == B<0>. 95 96B<flags> is a bit field of flags which are defined in C<openssl/bn.h>. The 97flags begin with B<BN_FLG_>. The macros BN_set_flags(b, n) and 98BN_get_flags(b, n) exist to enable or fetch flag(s) B<n> from B<BIGNUM> 99structure B<b>. 100 101Various routines in this library require the use of temporary 102B<BIGNUM> variables during their execution. Since dynamic memory 103allocation to create B<BIGNUM>s is rather expensive when used in 104conjunction with repeated subroutine calls, the B<BN_CTX> structure is 105used. This structure contains B<BN_CTX_NUM> B<BIGNUM>s, see 106L<BN_CTX_start(3)>. 107 108=head2 Low-level arithmetic operations 109 110These functions are implemented in C and for several platforms in 111assembly language: 112 113bn_mul_words(B<rp>, B<ap>, B<num>, B<w>) operates on the B<num> word 114arrays B<rp> and B<ap>. It computes B<ap> * B<w>, places the result 115in B<rp>, and returns the high word (carry). 116 117bn_mul_add_words(B<rp>, B<ap>, B<num>, B<w>) operates on the B<num> 118word arrays B<rp> and B<ap>. It computes B<ap> * B<w> + B<rp>, places 119the result in B<rp>, and returns the high word (carry). 120 121bn_sqr_words(B<rp>, B<ap>, B<n>) operates on the B<num> word array 122B<ap> and the 2*B<num> word array B<ap>. It computes B<ap> * B<ap> 123word-wise, and places the low and high bytes of the result in B<rp>. 124 125bn_div_words(B<h>, B<l>, B<d>) divides the two word number (B<h>, B<l>) 126by B<d> and returns the result. 127 128bn_add_words(B<rp>, B<ap>, B<bp>, B<num>) operates on the B<num> word 129arrays B<ap>, B<bp> and B<rp>. It computes B<ap> + B<bp>, places the 130result in B<rp>, and returns the high word (carry). 131 132bn_sub_words(B<rp>, B<ap>, B<bp>, B<num>) operates on the B<num> word 133arrays B<ap>, B<bp> and B<rp>. It computes B<ap> - B<bp>, places the 134result in B<rp>, and returns the carry (1 if B<bp> E<gt> B<ap>, 0 135otherwise). 136 137bn_mul_comba4(B<r>, B<a>, B<b>) operates on the 4 word arrays B<a> and 138B<b> and the 8 word array B<r>. It computes B<a>*B<b> and places the 139result in B<r>. 140 141bn_mul_comba8(B<r>, B<a>, B<b>) operates on the 8 word arrays B<a> and 142B<b> and the 16 word array B<r>. It computes B<a>*B<b> and places the 143result in B<r>. 144 145bn_sqr_comba4(B<r>, B<a>, B<b>) operates on the 4 word arrays B<a> and 146B<b> and the 8 word array B<r>. 147 148bn_sqr_comba8(B<r>, B<a>, B<b>) operates on the 8 word arrays B<a> and 149B<b> and the 16 word array B<r>. 150 151The following functions are implemented in C: 152 153bn_cmp_words(B<a>, B<b>, B<n>) operates on the B<n> word arrays B<a> 154and B<b>. It returns 1, 0 and -1 if B<a> is greater than, equal and 155less than B<b>. 156 157bn_mul_normal(B<r>, B<a>, B<na>, B<b>, B<nb>) operates on the B<na> 158word array B<a>, the B<nb> word array B<b> and the B<na>+B<nb> word 159array B<r>. It computes B<a>*B<b> and places the result in B<r>. 160 161bn_mul_low_normal(B<r>, B<a>, B<b>, B<n>) operates on the B<n> word 162arrays B<r>, B<a> and B<b>. It computes the B<n> low words of 163B<a>*B<b> and places the result in B<r>. 164 165bn_mul_recursive(B<r>, B<a>, B<b>, B<n2>, B<dna>, B<dnb>, B<t>) operates 166on the word arrays B<a> and B<b> of length B<n2>+B<dna> and B<n2>+B<dnb> 167(B<dna> and B<dnb> are currently allowed to be 0 or negative) and the 2*B<n2> 168word arrays B<r> and B<t>. B<n2> must be a power of 2. It computes 169B<a>*B<b> and places the result in B<r>. 170 171bn_mul_part_recursive(B<r>, B<a>, B<b>, B<n>, B<tna>, B<tnb>, B<tmp>) 172operates on the word arrays B<a> and B<b> of length B<n>+B<tna> and 173B<n>+B<tnb> and the 4*B<n> word arrays B<r> and B<tmp>. 174 175bn_mul_low_recursive(B<r>, B<a>, B<b>, B<n2>, B<tmp>) operates on the 176B<n2> word arrays B<r> and B<tmp> and the B<n2>/2 word arrays B<a> 177and B<b>. 178 179BN_mul() calls bn_mul_normal(), or an optimized implementation if the 180factors have the same size: bn_mul_comba8() is used if they are 8 181words long, bn_mul_recursive() if they are larger than 182B<BN_MULL_SIZE_NORMAL> and the size is an exact multiple of the word 183size, and bn_mul_part_recursive() for others that are larger than 184B<BN_MULL_SIZE_NORMAL>. 185 186bn_sqr_normal(B<r>, B<a>, B<n>, B<tmp>) operates on the B<n> word array 187B<a> and the 2*B<n> word arrays B<tmp> and B<r>. 188 189The implementations use the following macros which, depending on the 190architecture, may use "long long" C operations or inline assembler. 191They are defined in C<bn_local.h>. 192 193mul(B<r>, B<a>, B<w>, B<c>) computes B<w>*B<a>+B<c> and places the 194low word of the result in B<r> and the high word in B<c>. 195 196mul_add(B<r>, B<a>, B<w>, B<c>) computes B<w>*B<a>+B<r>+B<c> and 197places the low word of the result in B<r> and the high word in B<c>. 198 199sqr(B<r0>, B<r1>, B<a>) computes B<a>*B<a> and places the low word 200of the result in B<r0> and the high word in B<r1>. 201 202=head2 Size changes 203 204bn_expand() ensures that B<b> has enough space for a B<bits> bit 205number. bn_wexpand() ensures that B<b> has enough space for an 206B<n> word number. If the number has to be expanded, both macros 207call bn_expand2(), which allocates a new B<d> array and copies the 208data. They return B<NULL> on error, B<b> otherwise. 209 210The bn_fix_top() macro reduces B<a-E<gt>top> to point to the most 211significant non-zero word plus one when B<a> has shrunk. 212 213=head2 Debugging 214 215bn_check_top() verifies that C<((a)-E<gt>top E<gt>= 0 && (a)-E<gt>top 216E<lt>= (a)-E<gt>dmax)>. A violation will cause the program to abort. 217 218bn_print() prints B<a> to stderr. bn_dump() prints B<n> words at B<d> 219(in reverse order, i.e. most significant word first) to stderr. 220 221bn_set_max() makes B<a> a static number with a B<dmax> of its current size. 222This is used by bn_set_low() and bn_set_high() to make B<r> a read-only 223B<BIGNUM> that contains the B<n> low or high words of B<a>. 224 225If B<BN_DEBUG> is not defined, bn_check_top(), bn_print(), bn_dump() 226and bn_set_max() are defined as empty macros. 227 228=head1 SEE ALSO 229 230L<bn(3)> 231 232=head1 COPYRIGHT 233 234Copyright 2000-2016 The OpenSSL Project Authors. All Rights Reserved. 235 236Licensed under the Apache License 2.0 (the "License"). You may not use 237this file except in compliance with the License. You can obtain a copy 238in the file LICENSE in the source distribution or at 239L<https://www.openssl.org/source/license.html>. 240 241=cut 242
