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Diffstat (limited to 'openssl/doc/crypto/bn_internal.pod')
-rw-r--r-- | openssl/doc/crypto/bn_internal.pod | 238 |
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diff --git a/openssl/doc/crypto/bn_internal.pod b/openssl/doc/crypto/bn_internal.pod deleted file mode 100644 index 91840b0..0000000 --- a/openssl/doc/crypto/bn_internal.pod +++ /dev/null @@ -1,238 +0,0 @@ -=pod - -=head1 NAME - -bn_mul_words, bn_mul_add_words, bn_sqr_words, bn_div_words, -bn_add_words, bn_sub_words, bn_mul_comba4, bn_mul_comba8, -bn_sqr_comba4, bn_sqr_comba8, bn_cmp_words, bn_mul_normal, -bn_mul_low_normal, bn_mul_recursive, bn_mul_part_recursive, -bn_mul_low_recursive, bn_mul_high, bn_sqr_normal, bn_sqr_recursive, -bn_expand, bn_wexpand, bn_expand2, bn_fix_top, bn_check_top, -bn_print, bn_dump, bn_set_max, bn_set_high, bn_set_low - BIGNUM -library internal functions - -=head1 SYNOPSIS - - #include <openssl/bn.h> - - BN_ULONG bn_mul_words(BN_ULONG *rp, BN_ULONG *ap, int num, BN_ULONG w); - BN_ULONG bn_mul_add_words(BN_ULONG *rp, BN_ULONG *ap, int num, - BN_ULONG w); - void bn_sqr_words(BN_ULONG *rp, BN_ULONG *ap, int num); - BN_ULONG bn_div_words(BN_ULONG h, BN_ULONG l, BN_ULONG d); - BN_ULONG bn_add_words(BN_ULONG *rp, BN_ULONG *ap, BN_ULONG *bp, - int num); - BN_ULONG bn_sub_words(BN_ULONG *rp, BN_ULONG *ap, BN_ULONG *bp, - int num); - - void bn_mul_comba4(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b); - void bn_mul_comba8(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b); - void bn_sqr_comba4(BN_ULONG *r, BN_ULONG *a); - void bn_sqr_comba8(BN_ULONG *r, BN_ULONG *a); - - int bn_cmp_words(BN_ULONG *a, BN_ULONG *b, int n); - - void bn_mul_normal(BN_ULONG *r, BN_ULONG *a, int na, BN_ULONG *b, - int nb); - void bn_mul_low_normal(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, int n); - void bn_mul_recursive(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, int n2, - int dna,int dnb,BN_ULONG *tmp); - void bn_mul_part_recursive(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, - int n, int tna,int tnb, BN_ULONG *tmp); - void bn_mul_low_recursive(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, - int n2, BN_ULONG *tmp); - void bn_mul_high(BN_ULONG *r, BN_ULONG *a, BN_ULONG *b, BN_ULONG *l, - int n2, BN_ULONG *tmp); - - void bn_sqr_normal(BN_ULONG *r, BN_ULONG *a, int n, BN_ULONG *tmp); - void bn_sqr_recursive(BN_ULONG *r, BN_ULONG *a, int n2, BN_ULONG *tmp); - - void mul(BN_ULONG r, BN_ULONG a, BN_ULONG w, BN_ULONG c); - void mul_add(BN_ULONG r, BN_ULONG a, BN_ULONG w, BN_ULONG c); - void sqr(BN_ULONG r0, BN_ULONG r1, BN_ULONG a); - - BIGNUM *bn_expand(BIGNUM *a, int bits); - BIGNUM *bn_wexpand(BIGNUM *a, int n); - BIGNUM *bn_expand2(BIGNUM *a, int n); - void bn_fix_top(BIGNUM *a); - - void bn_check_top(BIGNUM *a); - void bn_print(BIGNUM *a); - void bn_dump(BN_ULONG *d, int n); - void bn_set_max(BIGNUM *a); - void bn_set_high(BIGNUM *r, BIGNUM *a, int n); - void bn_set_low(BIGNUM *r, BIGNUM *a, int n); - -=head1 DESCRIPTION - -This page documents the internal functions used by the OpenSSL -B<BIGNUM> implementation. They are described here to facilitate -debugging and extending the library. They are I<not> to be used by -applications. - -=head2 The BIGNUM structure - - typedef struct bignum_st BIGNUM; - - struct bignum_st - { - BN_ULONG *d; /* Pointer to an array of 'BN_BITS2' bit chunks. */ - int top; /* Index of last used d +1. */ - /* The next are internal book keeping for bn_expand. */ - int dmax; /* Size of the d array. */ - int neg; /* one if the number is negative */ - int flags; - }; - - -The integer value is stored in B<d>, a malloc()ed array of words (B<BN_ULONG>), -least significant word first. A B<BN_ULONG> can be either 16, 32 or 64 bits -in size, depending on the 'number of bits' (B<BITS2>) specified in -C<openssl/bn.h>. - -B<dmax> is the size of the B<d> array that has been allocated. B<top> -is the number of words being used, so for a value of 4, bn.d[0]=4 and -bn.top=1. B<neg> is 1 if the number is negative. When a B<BIGNUM> is -B<0>, the B<d> field can be B<NULL> and B<top> == B<0>. - -B<flags> is a bit field of flags which are defined in C<openssl/bn.h>. The -flags begin with B<BN_FLG_>. The macros BN_set_flags(b,n) and -BN_get_flags(b,n) exist to enable or fetch flag(s) B<n> from B<BIGNUM> -structure B<b>. - -Various routines in this library require the use of temporary -B<BIGNUM> variables during their execution. Since dynamic memory -allocation to create B<BIGNUM>s is rather expensive when used in -conjunction with repeated subroutine calls, the B<BN_CTX> structure is -used. This structure contains B<BN_CTX_NUM> B<BIGNUM>s, see -L<BN_CTX_start(3)|BN_CTX_start(3)>. - -=head2 Low-level arithmetic operations - -These functions are implemented in C and for several platforms in -assembly language: - -bn_mul_words(B<rp>, B<ap>, B<num>, B<w>) operates on the B<num> word -arrays B<rp> and B<ap>. It computes B<ap> * B<w>, places the result -in B<rp>, and returns the high word (carry). - -bn_mul_add_words(B<rp>, B<ap>, B<num>, B<w>) operates on the B<num> -word arrays B<rp> and B<ap>. It computes B<ap> * B<w> + B<rp>, places -the result in B<rp>, and returns the high word (carry). - -bn_sqr_words(B<rp>, B<ap>, B<n>) operates on the B<num> word array -B<ap> and the 2*B<num> word array B<ap>. It computes B<ap> * B<ap> -word-wise, and places the low and high bytes of the result in B<rp>. - -bn_div_words(B<h>, B<l>, B<d>) divides the two word number (B<h>,B<l>) -by B<d> and returns the result. - -bn_add_words(B<rp>, B<ap>, B<bp>, B<num>) operates on the B<num> word -arrays B<ap>, B<bp> and B<rp>. It computes B<ap> + B<bp>, places the -result in B<rp>, and returns the high word (carry). - -bn_sub_words(B<rp>, B<ap>, B<bp>, B<num>) operates on the B<num> word -arrays B<ap>, B<bp> and B<rp>. It computes B<ap> - B<bp>, places the -result in B<rp>, and returns the carry (1 if B<bp> E<gt> B<ap>, 0 -otherwise). - -bn_mul_comba4(B<r>, B<a>, B<b>) operates on the 4 word arrays B<a> and -B<b> and the 8 word array B<r>. It computes B<a>*B<b> and places the -result in B<r>. - -bn_mul_comba8(B<r>, B<a>, B<b>) operates on the 8 word arrays B<a> and -B<b> and the 16 word array B<r>. It computes B<a>*B<b> and places the -result in B<r>. - -bn_sqr_comba4(B<r>, B<a>, B<b>) operates on the 4 word arrays B<a> and -B<b> and the 8 word array B<r>. - -bn_sqr_comba8(B<r>, B<a>, B<b>) operates on the 8 word arrays B<a> and -B<b> and the 16 word array B<r>. - -The following functions are implemented in C: - -bn_cmp_words(B<a>, B<b>, B<n>) operates on the B<n> word arrays B<a> -and B<b>. It returns 1, 0 and -1 if B<a> is greater than, equal and -less than B<b>. - -bn_mul_normal(B<r>, B<a>, B<na>, B<b>, B<nb>) operates on the B<na> -word array B<a>, the B<nb> word array B<b> and the B<na>+B<nb> word -array B<r>. It computes B<a>*B<b> and places the result in B<r>. - -bn_mul_low_normal(B<r>, B<a>, B<b>, B<n>) operates on the B<n> word -arrays B<r>, B<a> and B<b>. It computes the B<n> low words of -B<a>*B<b> and places the result in B<r>. - -bn_mul_recursive(B<r>, B<a>, B<b>, B<n2>, B<dna>, B<dnb>, B<t>) operates -on the word arrays B<a> and B<b> of length B<n2>+B<dna> and B<n2>+B<dnb> -(B<dna> and B<dnb> are currently allowed to be 0 or negative) and the 2*B<n2> -word arrays B<r> and B<t>. B<n2> must be a power of 2. It computes -B<a>*B<b> and places the result in B<r>. - -bn_mul_part_recursive(B<r>, B<a>, B<b>, B<n>, B<tna>, B<tnb>, B<tmp>) -operates on the word arrays B<a> and B<b> of length B<n>+B<tna> and -B<n>+B<tnb> and the 4*B<n> word arrays B<r> and B<tmp>. - -bn_mul_low_recursive(B<r>, B<a>, B<b>, B<n2>, B<tmp>) operates on the -B<n2> word arrays B<r> and B<tmp> and the B<n2>/2 word arrays B<a> -and B<b>. - -bn_mul_high(B<r>, B<a>, B<b>, B<l>, B<n2>, B<tmp>) operates on the -B<n2> word arrays B<r>, B<a>, B<b> and B<l> (?) and the 3*B<n2> word -array B<tmp>. - -BN_mul() calls bn_mul_normal(), or an optimized implementation if the -factors have the same size: bn_mul_comba8() is used if they are 8 -words long, bn_mul_recursive() if they are larger than -B<BN_MULL_SIZE_NORMAL> and the size is an exact multiple of the word -size, and bn_mul_part_recursive() for others that are larger than -B<BN_MULL_SIZE_NORMAL>. - -bn_sqr_normal(B<r>, B<a>, B<n>, B<tmp>) operates on the B<n> word array -B<a> and the 2*B<n> word arrays B<tmp> and B<r>. - -The implementations use the following macros which, depending on the -architecture, may use "long long" C operations or inline assembler. -They are defined in C<bn_lcl.h>. - -mul(B<r>, B<a>, B<w>, B<c>) computes B<w>*B<a>+B<c> and places the -low word of the result in B<r> and the high word in B<c>. - -mul_add(B<r>, B<a>, B<w>, B<c>) computes B<w>*B<a>+B<r>+B<c> and -places the low word of the result in B<r> and the high word in B<c>. - -sqr(B<r0>, B<r1>, B<a>) computes B<a>*B<a> and places the low word -of the result in B<r0> and the high word in B<r1>. - -=head2 Size changes - -bn_expand() ensures that B<b> has enough space for a B<bits> bit -number. bn_wexpand() ensures that B<b> has enough space for an -B<n> word number. If the number has to be expanded, both macros -call bn_expand2(), which allocates a new B<d> array and copies the -data. They return B<NULL> on error, B<b> otherwise. - -The bn_fix_top() macro reduces B<a-E<gt>top> to point to the most -significant non-zero word plus one when B<a> has shrunk. - -=head2 Debugging - -bn_check_top() verifies that C<((a)-E<gt>top E<gt>= 0 && (a)-E<gt>top -E<lt>= (a)-E<gt>dmax)>. A violation will cause the program to abort. - -bn_print() prints B<a> to stderr. bn_dump() prints B<n> words at B<d> -(in reverse order, i.e. most significant word first) to stderr. - -bn_set_max() makes B<a> a static number with a B<dmax> of its current size. -This is used by bn_set_low() and bn_set_high() to make B<r> a read-only -B<BIGNUM> that contains the B<n> low or high words of B<a>. - -If B<BN_DEBUG> is not defined, bn_check_top(), bn_print(), bn_dump() -and bn_set_max() are defined as empty macros. - -=head1 SEE ALSO - -L<bn(3)|bn(3)> - -=cut |