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238 lines
9.3 KiB
238 lines
9.3 KiB
=pod |
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=head1 NAME |
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bn_mul_words, bn_mul_add_words, bn_sqr_words, bn_div_words, |
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bn_add_words, bn_sub_words, bn_mul_comba4, bn_mul_comba8, |
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bn_sqr_comba4, bn_sqr_comba8, bn_cmp_words, bn_mul_normal, |
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bn_mul_low_normal, bn_mul_recursive, bn_mul_part_recursive, |
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bn_mul_low_recursive, bn_mul_high, bn_sqr_normal, bn_sqr_recursive, |
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bn_expand, bn_wexpand, bn_expand2, bn_fix_top, bn_check_top, |
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bn_print, bn_dump, bn_set_max, bn_set_high, bn_set_low - BIGNUM |
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library internal functions |
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=head1 SYNOPSIS |
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#include <openssl/bn.h> |
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BN_ULONG bn_mul_words(BN_ULONG *rp, BN_ULONG *ap, int num, BN_ULONG w); |
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BN_ULONG bn_mul_add_words(BN_ULONG *rp, BN_ULONG *ap, int num, |
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BN_ULONG w); |
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void bn_sqr_words(BN_ULONG *rp, BN_ULONG *ap, int num); |
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BN_ULONG bn_div_words(BN_ULONG h, BN_ULONG l, BN_ULONG d); |
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BN_ULONG bn_add_words(BN_ULONG *rp, BN_ULONG *ap, BN_ULONG *bp, |
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int num); |
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BN_ULONG bn_sub_words(BN_ULONG *rp, BN_ULONG *ap, BN_ULONG *bp, |
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int num); |
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void bn_mul_comba4(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b); |
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void bn_mul_comba8(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b); |
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void bn_sqr_comba4(BN_ULONG *r, BN_ULONG *a); |
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void bn_sqr_comba8(BN_ULONG *r, BN_ULONG *a); |
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int bn_cmp_words(BN_ULONG *a, BN_ULONG *b, int n); |
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void bn_mul_normal(BN_ULONG *r, BN_ULONG *a, int na, BN_ULONG *b, |
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int nb); |
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void bn_mul_low_normal(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, int n); |
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void bn_mul_recursive(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, int n2, |
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int dna,int dnb,BN_ULONG *tmp); |
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void bn_mul_part_recursive(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, |
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int n, int tna,int tnb, BN_ULONG *tmp); |
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void bn_mul_low_recursive(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, |
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int n2, BN_ULONG *tmp); |
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void bn_mul_high(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, BN_ULONG *l, |
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int n2, BN_ULONG *tmp); |
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void bn_sqr_normal(BN_ULONG *r, BN_ULONG *a, int n, BN_ULONG *tmp); |
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void bn_sqr_recursive(BN_ULONG *r, BN_ULONG *a, int n2, BN_ULONG *tmp); |
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void mul(BN_ULONG r, BN_ULONG a, BN_ULONG w, BN_ULONG c); |
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void mul_add(BN_ULONG r, BN_ULONG a, BN_ULONG w, BN_ULONG c); |
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void sqr(BN_ULONG r0, BN_ULONG r1, BN_ULONG a); |
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BIGNUM *bn_expand(BIGNUM *a, int bits); |
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BIGNUM *bn_wexpand(BIGNUM *a, int n); |
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BIGNUM *bn_expand2(BIGNUM *a, int n); |
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void bn_fix_top(BIGNUM *a); |
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void bn_check_top(BIGNUM *a); |
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void bn_print(BIGNUM *a); |
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void bn_dump(BN_ULONG *d, int n); |
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void bn_set_max(BIGNUM *a); |
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void bn_set_high(BIGNUM *r, BIGNUM *a, int n); |
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void bn_set_low(BIGNUM *r, BIGNUM *a, int n); |
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=head1 DESCRIPTION |
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This page documents the internal functions used by the OpenSSL |
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B<BIGNUM> implementation. They are described here to facilitate |
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debugging and extending the library. They are I<not> to be used by |
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applications. |
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=head2 The BIGNUM structure |
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typedef struct bignum_st BIGNUM; |
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struct bignum_st |
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{ |
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BN_ULONG *d; /* Pointer to an array of 'BN_BITS2' bit chunks. */ |
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int top; /* Index of last used d +1. */ |
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/* The next are internal book keeping for bn_expand. */ |
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int dmax; /* Size of the d array. */ |
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int neg; /* one if the number is negative */ |
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int flags; |
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}; |
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The integer value is stored in B<d>, a malloc()ed array of words (B<BN_ULONG>), |
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least significant word first. A B<BN_ULONG> can be either 16, 32 or 64 bits |
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in size, depending on the 'number of bits' (B<BITS2>) specified in |
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C<openssl/bn.h>. |
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B<dmax> is the size of the B<d> array that has been allocated. B<top> |
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is the number of words being used, so for a value of 4, bn.d[0]=4 and |
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bn.top=1. B<neg> is 1 if the number is negative. When a B<BIGNUM> is |
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B<0>, the B<d> field can be B<NULL> and B<top> == B<0>. |
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B<flags> is a bit field of flags which are defined in C<openssl/bn.h>. The |
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flags begin with B<BN_FLG_>. The macros BN_set_flags(b,n) and |
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BN_get_flags(b,n) exist to enable or fetch flag(s) B<n> from B<BIGNUM> |
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structure B<b>. |
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Various routines in this library require the use of temporary |
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B<BIGNUM> variables during their execution. Since dynamic memory |
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allocation to create B<BIGNUM>s is rather expensive when used in |
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conjunction with repeated subroutine calls, the B<BN_CTX> structure is |
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used. This structure contains B<BN_CTX_NUM> B<BIGNUM>s, see |
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L<BN_CTX_start(3)|BN_CTX_start(3)>. |
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=head2 Low-level arithmetic operations |
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These functions are implemented in C and for several platforms in |
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assembly language: |
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bn_mul_words(B<rp>, B<ap>, B<num>, B<w>) operates on the B<num> word |
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arrays B<rp> and B<ap>. It computes B<ap> * B<w>, places the result |
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in B<rp>, and returns the high word (carry). |
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bn_mul_add_words(B<rp>, B<ap>, B<num>, B<w>) operates on the B<num> |
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word arrays B<rp> and B<ap>. It computes B<ap> * B<w> + B<rp>, places |
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the result in B<rp>, and returns the high word (carry). |
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bn_sqr_words(B<rp>, B<ap>, B<n>) operates on the B<num> word array |
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B<ap> and the 2*B<num> word array B<ap>. It computes B<ap> * B<ap> |
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word-wise, and places the low and high bytes of the result in B<rp>. |
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bn_div_words(B<h>, B<l>, B<d>) divides the two word number (B<h>,B<l>) |
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by B<d> and returns the result. |
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bn_add_words(B<rp>, B<ap>, B<bp>, B<num>) operates on the B<num> word |
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arrays B<ap>, B<bp> and B<rp>. It computes B<ap> + B<bp>, places the |
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result in B<rp>, and returns the high word (carry). |
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bn_sub_words(B<rp>, B<ap>, B<bp>, B<num>) operates on the B<num> word |
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arrays B<ap>, B<bp> and B<rp>. It computes B<ap> - B<bp>, places the |
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result in B<rp>, and returns the carry (1 if B<bp> E<gt> B<ap>, 0 |
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otherwise). |
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bn_mul_comba4(B<r>, B<a>, B<b>) operates on the 4 word arrays B<a> and |
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B<b> and the 8 word array B<r>. It computes B<a>*B<b> and places the |
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result in B<r>. |
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bn_mul_comba8(B<r>, B<a>, B<b>) operates on the 8 word arrays B<a> and |
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B<b> and the 16 word array B<r>. It computes B<a>*B<b> and places the |
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result in B<r>. |
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bn_sqr_comba4(B<r>, B<a>, B<b>) operates on the 4 word arrays B<a> and |
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B<b> and the 8 word array B<r>. |
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bn_sqr_comba8(B<r>, B<a>, B<b>) operates on the 8 word arrays B<a> and |
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B<b> and the 16 word array B<r>. |
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The following functions are implemented in C: |
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bn_cmp_words(B<a>, B<b>, B<n>) operates on the B<n> word arrays B<a> |
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and B<b>. It returns 1, 0 and -1 if B<a> is greater than, equal and |
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less than B<b>. |
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bn_mul_normal(B<r>, B<a>, B<na>, B<b>, B<nb>) operates on the B<na> |
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word array B<a>, the B<nb> word array B<b> and the B<na>+B<nb> word |
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array B<r>. It computes B<a>*B<b> and places the result in B<r>. |
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bn_mul_low_normal(B<r>, B<a>, B<b>, B<n>) operates on the B<n> word |
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arrays B<r>, B<a> and B<b>. It computes the B<n> low words of |
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B<a>*B<b> and places the result in B<r>. |
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bn_mul_recursive(B<r>, B<a>, B<b>, B<n2>, B<dna>, B<dnb>, B<t>) operates |
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on the word arrays B<a> and B<b> of length B<n2>+B<dna> and B<n2>+B<dnb> |
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(B<dna> and B<dnb> are currently allowed to be 0 or negative) and the 2*B<n2> |
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word arrays B<r> and B<t>. B<n2> must be a power of 2. It computes |
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B<a>*B<b> and places the result in B<r>. |
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bn_mul_part_recursive(B<r>, B<a>, B<b>, B<n>, B<tna>, B<tnb>, B<tmp>) |
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operates on the word arrays B<a> and B<b> of length B<n>+B<tna> and |
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B<n>+B<tnb> and the 4*B<n> word arrays B<r> and B<tmp>. |
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bn_mul_low_recursive(B<r>, B<a>, B<b>, B<n2>, B<tmp>) operates on the |
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B<n2> word arrays B<r> and B<tmp> and the B<n2>/2 word arrays B<a> |
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and B<b>. |
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bn_mul_high(B<r>, B<a>, B<b>, B<l>, B<n2>, B<tmp>) operates on the |
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B<n2> word arrays B<r>, B<a>, B<b> and B<l> (?) and the 3*B<n2> word |
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array B<tmp>. |
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BN_mul() calls bn_mul_normal(), or an optimized implementation if the |
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factors have the same size: bn_mul_comba8() is used if they are 8 |
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words long, bn_mul_recursive() if they are larger than |
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B<BN_MULL_SIZE_NORMAL> and the size is an exact multiple of the word |
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size, and bn_mul_part_recursive() for others that are larger than |
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B<BN_MULL_SIZE_NORMAL>. |
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bn_sqr_normal(B<r>, B<a>, B<n>, B<tmp>) operates on the B<n> word array |
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B<a> and the 2*B<n> word arrays B<tmp> and B<r>. |
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The implementations use the following macros which, depending on the |
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architecture, may use "long long" C operations or inline assembler. |
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They are defined in C<bn_lcl.h>. |
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mul(B<r>, B<a>, B<w>, B<c>) computes B<w>*B<a>+B<c> and places the |
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low word of the result in B<r> and the high word in B<c>. |
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mul_add(B<r>, B<a>, B<w>, B<c>) computes B<w>*B<a>+B<r>+B<c> and |
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places the low word of the result in B<r> and the high word in B<c>. |
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sqr(B<r0>, B<r1>, B<a>) computes B<a>*B<a> and places the low word |
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of the result in B<r0> and the high word in B<r1>. |
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=head2 Size changes |
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bn_expand() ensures that B<b> has enough space for a B<bits> bit |
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number. bn_wexpand() ensures that B<b> has enough space for an |
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B<n> word number. If the number has to be expanded, both macros |
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call bn_expand2(), which allocates a new B<d> array and copies the |
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data. They return B<NULL> on error, B<b> otherwise. |
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The bn_fix_top() macro reduces B<a-E<gt>top> to point to the most |
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significant non-zero word plus one when B<a> has shrunk. |
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=head2 Debugging |
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bn_check_top() verifies that C<((a)-E<gt>top E<gt>= 0 && (a)-E<gt>top |
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E<lt>= (a)-E<gt>dmax)>. A violation will cause the program to abort. |
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bn_print() prints B<a> to stderr. bn_dump() prints B<n> words at B<d> |
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(in reverse order, i.e. most significant word first) to stderr. |
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bn_set_max() makes B<a> a static number with a B<dmax> of its current size. |
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This is used by bn_set_low() and bn_set_high() to make B<r> a read-only |
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B<BIGNUM> that contains the B<n> low or high words of B<a>. |
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If B<BN_DEBUG> is not defined, bn_check_top(), bn_print(), bn_dump() |
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and bn_set_max() are defined as empty macros. |
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=head1 SEE ALSO |
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L<bn(3)|bn(3)> |
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=cut
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