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, 11mul, mul_add, sqr - 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 BIGNUM *bn_expand(BIGNUM *a, int bits); 49 BIGNUM *bn_wexpand(BIGNUM *a, int n); 50 BIGNUM *bn_expand2(BIGNUM *a, int n); 51 void bn_fix_top(BIGNUM *a); 52 53The following are macros: 54 55 void mul(BN_ULONG r, BN_ULONG a, BN_ULONG w, BN_ULONG c); 56 void mul_add(BN_ULONG r, BN_ULONG a, BN_ULONG w, BN_ULONG c); 57 void sqr(BN_ULONG r0, BN_ULONG r1, BN_ULONG a); 58 59 void bn_check_top(BIGNUM *a); 60 61=head1 DESCRIPTION 62 63This page documents the internal functions used by the OpenSSL 64B<BIGNUM> implementation. They are described here to facilitate 65debugging and extending the library. They are I<not> to be used by 66applications. 67 68=head2 The BIGNUM structure 69 70 typedef struct bignum_st BIGNUM; 71 72 struct bignum_st 73 { 74 BN_ULONG *d; /* Pointer to an array of 'BN_BITS2' bit chunks. */ 75 int top; /* Index of last used d +1. */ 76 /* The next are internal book keeping for bn_expand. */ 77 int dmax; /* Size of the d array. */ 78 int neg; /* one if the number is negative */ 79 int flags; 80 }; 81 82 83The integer value is stored in B<d>, a malloc()ed array of words (B<BN_ULONG>), 84least significant word first. A B<BN_ULONG> can be either 16, 32 or 64 bits 85in size, depending on the 'number of bits' (B<BITS2>) specified in 86C<openssl/bn.h>. 87 88B<dmax> is the size of the B<d> array that has been allocated. B<top> 89is the number of words being used, so for a value of 4, bn.d[0]=4 and 90bn.top=1. B<neg> is 1 if the number is negative. When a B<BIGNUM> is 91B<0>, the B<d> field can be B<NULL> and B<top> == B<0>. 92 93B<flags> is a bit field of flags which are defined in C<openssl/bn.h>. The 94flags begin with B<BN_FLG_>. The macros BN_set_flags(b, n) and 95BN_get_flags(b, n) exist to enable or fetch flag(s) B<n> from B<BIGNUM> 96structure B<b>. 97 98Various routines in this library require the use of temporary 99B<BIGNUM> variables during their execution. Since dynamic memory 100allocation to create B<BIGNUM>s is rather expensive when used in 101conjunction with repeated subroutine calls, the B<BN_CTX> structure is 102used. This structure contains B<BN_CTX_NUM> B<BIGNUM>s, see 103L<BN_CTX_start(3)>. 104 105=head2 Low-level arithmetic operations 106 107These functions are implemented in C and for several platforms in 108assembly language: 109 110bn_mul_words(B<rp>, B<ap>, B<num>, B<w>) operates on the B<num> word 111arrays B<rp> and B<ap>. It computes B<ap> * B<w>, places the result 112in B<rp>, and returns the high word (carry). 113 114bn_mul_add_words(B<rp>, B<ap>, B<num>, B<w>) operates on the B<num> 115word arrays B<rp> and B<ap>. It computes B<ap> * B<w> + B<rp>, places 116the result in B<rp>, and returns the high word (carry). 117 118bn_sqr_words(B<rp>, B<ap>, B<n>) operates on the B<num> word array 119B<ap> and the 2*B<num> word array B<ap>. It computes B<ap> * B<ap> 120word-wise, and places the low and high bytes of the result in B<rp>. 121 122bn_div_words(B<h>, B<l>, B<d>) divides the two word number (B<h>, B<l>) 123by B<d> and returns the result. 124 125bn_add_words(B<rp>, B<ap>, B<bp>, B<num>) operates on the B<num> word 126arrays B<ap>, B<bp> and B<rp>. It computes B<ap> + B<bp>, places the 127result in B<rp>, and returns the high word (carry). 128 129bn_sub_words(B<rp>, B<ap>, B<bp>, B<num>) operates on the B<num> word 130arrays B<ap>, B<bp> and B<rp>. It computes B<ap> - B<bp>, places the 131result in B<rp>, and returns the carry (1 if B<bp> E<gt> B<ap>, 0 132otherwise). 133 134bn_mul_comba4(B<r>, B<a>, B<b>) operates on the 4 word arrays B<a> and 135B<b> and the 8 word array B<r>. It computes B<a>*B<b> and places the 136result in B<r>. 137 138bn_mul_comba8(B<r>, B<a>, B<b>) operates on the 8 word arrays B<a> and 139B<b> and the 16 word array B<r>. It computes B<a>*B<b> and places the 140result in B<r>. 141 142bn_sqr_comba4(B<r>, B<a>, B<b>) operates on the 4 word arrays B<a> and 143B<b> and the 8 word array B<r>. 144 145bn_sqr_comba8(B<r>, B<a>, B<b>) operates on the 8 word arrays B<a> and 146B<b> and the 16 word array B<r>. 147 148The following functions are implemented in C: 149 150bn_cmp_words(B<a>, B<b>, B<n>) operates on the B<n> word arrays B<a> 151and B<b>. It returns 1, 0 and -1 if B<a> is greater than, equal and 152less than B<b>. 153 154bn_mul_normal(B<r>, B<a>, B<na>, B<b>, B<nb>) operates on the B<na> 155word array B<a>, the B<nb> word array B<b> and the B<na>+B<nb> word 156array B<r>. It computes B<a>*B<b> and places the result in B<r>. 157 158bn_mul_low_normal(B<r>, B<a>, B<b>, B<n>) operates on the B<n> word 159arrays B<r>, B<a> and B<b>. It computes the B<n> low words of 160B<a>*B<b> and places the result in B<r>. 161 162bn_mul_recursive(B<r>, B<a>, B<b>, B<n2>, B<dna>, B<dnb>, B<t>) operates 163on the word arrays B<a> and B<b> of length B<n2>+B<dna> and B<n2>+B<dnb> 164(B<dna> and B<dnb> are currently allowed to be 0 or negative) and the 2*B<n2> 165word arrays B<r> and B<t>. B<n2> must be a power of 2. It computes 166B<a>*B<b> and places the result in B<r>. 167 168bn_mul_part_recursive(B<r>, B<a>, B<b>, B<n>, B<tna>, B<tnb>, B<tmp>) 169operates on the word arrays B<a> and B<b> of length B<n>+B<tna> and 170B<n>+B<tnb> and the 4*B<n> word arrays B<r> and B<tmp>. 171 172bn_mul_low_recursive(B<r>, B<a>, B<b>, B<n2>, B<tmp>) operates on the 173B<n2> word arrays B<r> and B<tmp> and the B<n2>/2 word arrays B<a> 174and B<b>. 175 176BN_mul() calls bn_mul_normal(), or an optimized implementation if the 177factors have the same size: bn_mul_comba8() is used if they are 8 178words long, bn_mul_recursive() if they are larger than 179B<BN_MULL_SIZE_NORMAL> and the size is an exact multiple of the word 180size, and bn_mul_part_recursive() for others that are larger than 181B<BN_MULL_SIZE_NORMAL>. 182 183bn_sqr_normal(B<r>, B<a>, B<n>, B<tmp>) operates on the B<n> word array 184B<a> and the 2*B<n> word arrays B<tmp> and B<r>. 185 186The implementations use the following macros which, depending on the 187architecture, may use "long long" C operations or inline assembler. 188They are defined in C<bn_local.h>. 189 190mul(B<r>, B<a>, B<w>, B<c>) computes B<w>*B<a>+B<c> and places the 191low word of the result in B<r> and the high word in B<c>. 192 193mul_add(B<r>, B<a>, B<w>, B<c>) computes B<w>*B<a>+B<r>+B<c> and 194places the low word of the result in B<r> and the high word in B<c>. 195 196sqr(B<r0>, B<r1>, B<a>) computes B<a>*B<a> and places the low word 197of the result in B<r0> and the high word in B<r1>. 198 199=head2 Size changes 200 201bn_expand() ensures that B<b> has enough space for a B<bits> bit 202number. bn_wexpand() ensures that B<b> has enough space for an 203B<n> word number. If the number has to be expanded, both macros 204call bn_expand2(), which allocates a new B<d> array and copies the 205data. They return B<NULL> on error, B<b> otherwise. 206 207The bn_fix_top() macro reduces B<a-E<gt>top> to point to the most 208significant nonzero word plus one when B<a> has shrunk. 209 210=head2 Debugging 211 212bn_check_top() verifies that C<((a)-E<gt>top E<gt>= 0 && (a)-E<gt>top 213E<lt>= (a)-E<gt>dmax)>. A violation will cause the program to abort. 214 215If B<BN_DEBUG> is not defined, bn_check_top() is 216defined as an empty macro. 217 218=head1 RETURN VALUES 219 220Described above. 221 222=head1 COPYRIGHT 223 224Copyright 2000-2025 The OpenSSL Project Authors. All Rights Reserved. 225 226Licensed under the Apache License 2.0 (the "License"). You may not use 227this file except in compliance with the License. You can obtain a copy 228in the file LICENSE in the source distribution or at 229L<https://www.openssl.org/source/license.html>. 230 231=cut 232