357 lines
10 KiB
Groff
357 lines
10 KiB
Groff
.rn '' }`
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'''
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'''
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.de Sh
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.br
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.if t .Sp
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.ne 5
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.PP
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\fB\\$1\fR
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.PP
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..
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.de Sp
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'''
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'''
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''' Set up \*(-- to give an unbreakable dash;
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''' string Tr holds user defined translation string.
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''' Bell System Logo is used as a dummy character.
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'''
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.tr \(*W-|\(bv\*(Tr
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.ie n \{\
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.ds -- \(*W-
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.ds PI pi
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.if (\n(.H=4u)&(1m=24u) .ds -- \(*W\h'-12u'\(*W\h'-12u'-\" diablo 10 pitch
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''' \*(L" and \*(R", except that they are used on ".xx" lines,
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''' such as .IP and .SH, which do another additional levels of
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.\" If the F register is turned on, we'll generate
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.\" index entries out stderr for the following things:
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.\" TH Title
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.\" SH Header
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.\" Sh Subsection
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.\" Ip Item
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.\" X<> Xref (embedded
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.\" Of course, you have to process the output yourself
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.\" in some meaninful fashion.
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.if \nF \{
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.de IX
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.tm Index:\\$1\t\\n%\t"\\$2"
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.nr % 0
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.rr F
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.\}
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.TH bn 3 "0.9.5a" "22/Jul/2000" "OpenSSL"
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.UC
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.if n .hy 0
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.if n .na
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.ds C+ C\v'-.1v'\h'-1p'\s-2+\h'-1p'+\s0\v'.1v'\h'-1p'
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.de CQ \" put $1 in typewriter font
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.ft CW
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'if n "\c
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'if t \\&\\$1\c
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'if n \\&\\$1\c
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\\&\\$2 \\$3 \\$4 \\$5 \\$6 \\$7
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..
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.\" @(#)ms.acc 1.5 88/02/08 SMI; from UCB 4.2
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. \" AM - accent mark definitions
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.bd B 3
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.if n \{\
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. ds #H 0
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. ds #F .3m
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. ds #] \fP
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.\}
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.if t \{\
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. ds #H ((1u-(\\\\n(.fu%2u))*.13m)
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. ds #V .6m
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. ds #] \&
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.\}
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.if n \{\
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.\}
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.if t \{\
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\{\
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.\}
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.rm #[ #] #H #V #F C
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.SH "NAME"
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bn \- multiprecision integer arithmetics
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.SH "LIBRARY"
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libcrypto, -lcrypto
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.SH "SYNOPSIS"
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.PP
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.Vb 1
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\& #include <openssl/bn.h>
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.Ve
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.Vb 5
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\& BIGNUM *BN_new(void);
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\& void BN_free(BIGNUM *a);
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\& void BN_init(BIGNUM *);
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\& void BN_clear(BIGNUM *a);
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\& void BN_clear_free(BIGNUM *a);
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.Ve
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.Vb 3
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\& BN_CTX *BN_CTX_new(void);
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\& void BN_CTX_init(BN_CTX *c);
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\& void BN_CTX_free(BN_CTX *c);
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.Ve
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.Vb 2
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\& BIGNUM *BN_copy(BIGNUM *a, const BIGNUM *b);
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\& BIGNUM *BN_dup(const BIGNUM *a);
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.Ve
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.Vb 3
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\& int BN_num_bytes(const BIGNUM *a);
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\& int BN_num_bits(const BIGNUM *a);
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\& int BN_num_bits_word(BN_ULONG w);
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.Ve
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.Vb 13
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\& int BN_add(BIGNUM *r, BIGNUM *a, BIGNUM *b);
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\& int BN_sub(BIGNUM *r, const BIGNUM *a, const BIGNUM *b);
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\& int BN_mul(BIGNUM *r, BIGNUM *a, BIGNUM *b, BN_CTX *ctx);
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\& int BN_div(BIGNUM *dv, BIGNUM *rem, const BIGNUM *a, const BIGNUM *d,
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\& BN_CTX *ctx);
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\& int BN_sqr(BIGNUM *r, BIGNUM *a, BN_CTX *ctx);
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\& int BN_mod(BIGNUM *rem, const BIGNUM *a, const BIGNUM *m, BN_CTX *ctx);
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\& int BN_mod_mul(BIGNUM *ret, BIGNUM *a, BIGNUM *b, const BIGNUM *m,
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\& BN_CTX *ctx);
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\& int BN_exp(BIGNUM *r, BIGNUM *a, BIGNUM *p, BN_CTX *ctx);
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\& int BN_mod_exp(BIGNUM *r, BIGNUM *a, const BIGNUM *p,
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\& const BIGNUM *m, BN_CTX *ctx);
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\& int BN_gcd(BIGNUM *r, BIGNUM *a, BIGNUM *b, BN_CTX *ctx);
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.Ve
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.Vb 5
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\& int BN_add_word(BIGNUM *a, BN_ULONG w);
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\& int BN_sub_word(BIGNUM *a, BN_ULONG w);
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\& int BN_mul_word(BIGNUM *a, BN_ULONG w);
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\& BN_ULONG BN_div_word(BIGNUM *a, BN_ULONG w);
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\& BN_ULONG BN_mod_word(const BIGNUM *a, BN_ULONG w);
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.Ve
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.Vb 6
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\& int BN_cmp(BIGNUM *a, BIGNUM *b);
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\& int BN_ucmp(BIGNUM *a, BIGNUM *b);
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\& int BN_is_zero(BIGNUM *a);
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\& int BN_is_one(BIGNUM *a);
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\& int BN_is_word(BIGNUM *a, BN_ULONG w);
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\& int BN_is_odd(BIGNUM *a);
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.Ve
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.Vb 5
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\& int BN_zero(BIGNUM *a);
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\& int BN_one(BIGNUM *a);
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\& BIGNUM *BN_value_one(void);
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\& int BN_set_word(BIGNUM *a, unsigned long w);
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\& unsigned long BN_get_word(BIGNUM *a);
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.Ve
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.Vb 2
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\& int BN_rand(BIGNUM *rnd, int bits, int top, int bottom);
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\& int BN_pseudo_rand(BIGNUM *rnd, int bits, int top, int bottom);
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.Ve
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.Vb 4
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\& BIGNUM *BN_generate_prime(BIGNUM *ret, int bits,int safe, BIGNUM *add,
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\& BIGNUM *rem, void (*callback)(int, int, void *), void *cb_arg);
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\& int BN_is_prime(const BIGNUM *p, int nchecks,
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\& void (*callback)(int, int, void *), BN_CTX *ctx, void *cb_arg);
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.Ve
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.Vb 8
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\& int BN_set_bit(BIGNUM *a, int n);
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\& int BN_clear_bit(BIGNUM *a, int n);
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\& int BN_is_bit_set(const BIGNUM *a, int n);
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\& int BN_mask_bits(BIGNUM *a, int n);
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\& int BN_lshift(BIGNUM *r, const BIGNUM *a, int n);
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\& int BN_lshift1(BIGNUM *r, BIGNUM *a);
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\& int BN_rshift(BIGNUM *r, BIGNUM *a, int n);
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\& int BN_rshift1(BIGNUM *r, BIGNUM *a);
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.Ve
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.Vb 10
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\& int BN_bn2bin(const BIGNUM *a, unsigned char *to);
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\& BIGNUM *BN_bin2bn(const unsigned char *s, int len, BIGNUM *ret);
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\& char *BN_bn2hex(const BIGNUM *a);
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\& char *BN_bn2dec(const BIGNUM *a);
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\& int BN_hex2bn(BIGNUM **a, const char *str);
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\& int BN_dec2bn(BIGNUM **a, const char *str);
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\& int BN_print(BIO *fp, const BIGNUM *a);
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\& int BN_print_fp(FILE *fp, const BIGNUM *a);
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\& int BN_bn2mpi(const BIGNUM *a, unsigned char *to);
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\& BIGNUM *BN_mpi2bn(unsigned char *s, int len, BIGNUM *ret);
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.Ve
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.Vb 2
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\& BIGNUM *BN_mod_inverse(BIGNUM *r, BIGNUM *a, const BIGNUM *n,
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\& BN_CTX *ctx);
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.Ve
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.Vb 6
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\& BN_RECP_CTX *BN_RECP_CTX_new(void);
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\& void BN_RECP_CTX_init(BN_RECP_CTX *recp);
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\& void BN_RECP_CTX_free(BN_RECP_CTX *recp);
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\& int BN_RECP_CTX_set(BN_RECP_CTX *recp, const BIGNUM *m, BN_CTX *ctx);
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\& int BN_mod_mul_reciprocal(BIGNUM *r, BIGNUM *a, BIGNUM *b,
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\& BN_RECP_CTX *recp, BN_CTX *ctx);
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.Ve
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.Vb 11
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\& BN_MONT_CTX *BN_MONT_CTX_new(void);
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\& void BN_MONT_CTX_init(BN_MONT_CTX *ctx);
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\& void BN_MONT_CTX_free(BN_MONT_CTX *mont);
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\& int BN_MONT_CTX_set(BN_MONT_CTX *mont, const BIGNUM *m, BN_CTX *ctx);
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\& BN_MONT_CTX *BN_MONT_CTX_copy(BN_MONT_CTX *to, BN_MONT_CTX *from);
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\& int BN_mod_mul_montgomery(BIGNUM *r, BIGNUM *a, BIGNUM *b,
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\& BN_MONT_CTX *mont, BN_CTX *ctx);
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\& int BN_from_montgomery(BIGNUM *r, BIGNUM *a, BN_MONT_CTX *mont,
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\& BN_CTX *ctx);
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\& int BN_to_montgomery(BIGNUM *r, BIGNUM *a, BN_MONT_CTX *mont,
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\& BN_CTX *ctx);
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.Ve
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.SH "DESCRIPTION"
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This library performs arithmetic operations on integers of arbitrary
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size. It was written for use in public key cryptography, such as RSA
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and Diffie-Hellman.
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.PP
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It uses dynamic memory allocation for storing its data structures.
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That means that there is no limit on the size of the numbers
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manipulated by these functions, but return values must always be
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checked in case a memory allocation error has occurred.
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.PP
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The basic object in this library is a \fBBIGNUM\fR. It is used to hold a
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single large integer. This type should be considered opaque and fields
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should not be modified or accessed directly.
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.PP
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The creation of \fBBIGNUM\fR objects is described in the \fIBN_new(3)|BN_new(3)\fR manpage;
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the \fIBN_add(3)|BN_add(3)\fR manpage describes most of the arithmetic operations.
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Comparison is described in the \fIBN_cmp(3)|BN_cmp(3)\fR manpage; the \fIBN_zero(3)|BN_zero(3)\fR manpage
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describes certain assignments, the \fIBN_rand(3)|BN_rand(3)\fR manpage the generation of
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random numbers, the \fIBN_generate_prime(3)|BN_generate_prime(3)\fR manpage deals with prime
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numbers and the \fIBN_set_bit(3)|BN_set_bit(3)\fR manpage with bit operations. The conversion
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of \fBBIGNUM\fRs to external formats is described in the \fIBN_bn2bin(3)|BN_bn2bin(3)\fR manpage.
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.SH "SEE ALSO"
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the \fIbn_internal(3)|bn_internal(3)\fR manpage,
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the \fIdh(3)|dh(3)\fR manpage, the \fIerr(3)|err(3)\fR manpage, the \fIrand(3)|rand(3)\fR manpage, the \fIrsa(3)|rsa(3)\fR manpage,
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the \fIBN_new(3)|BN_new(3)\fR manpage, the \fIBN_CTX_new(3)|BN_CTX_new(3)\fR manpage,
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the \fIBN_copy(3)|BN_copy(3)\fR manpage, the \fIBN_num_bytes(3)|BN_num_bytes(3)\fR manpage,
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the \fIBN_add(3)|BN_add(3)\fR manpage, the \fIBN_add_word(3)|BN_add_word(3)\fR manpage,
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the \fIBN_cmp(3)|BN_cmp(3)\fR manpage, the \fIBN_zero(3)|BN_zero(3)\fR manpage, the \fIBN_rand(3)|BN_rand(3)\fR manpage,
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the \fIBN_generate_prime(3)|BN_generate_prime(3)\fR manpage, the \fIBN_set_bit(3)|BN_set_bit(3)\fR manpage,
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the \fIBN_bn2bin(3)|BN_bn2bin(3)\fR manpage, the \fIBN_mod_inverse(3)|BN_mod_inverse(3)\fR manpage,
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the \fIBN_mod_mul_reciprocal(3)|BN_mod_mul_reciprocal(3)\fR manpage,
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the \fIBN_mod_mul_montgomery(3)|BN_mod_mul_montgomery(3)\fR manpage
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.rn }` ''
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.IX Title "bn 3"
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.IX Name "bn - multiprecision integer arithmetics"
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.IX Header "NAME"
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.IX Header "SYNOPSIS"
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.IX Header "DESCRIPTION"
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.IX Header "SEE ALSO"
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