316 lines
10 KiB
Groff
316 lines
10 KiB
Groff
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.\" ========================================================================
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.\"
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.IX Title "bn 3"
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.TH bn 3 "2005-02-24" "0.9.7d" "OpenSSL"
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.SH "NAME"
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bn \- multiprecision integer arithmetics
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.SH "SYNOPSIS"
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.IX Header "SYNOPSIS"
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.Vb 1
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\& #include <openssl/bn.h>
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.Ve
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.PP
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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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.PP
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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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.PP
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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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.PP
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.Vb 1
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\& BIGNUM *BN_swap(BIGNUM *a, BIGNUM *b);
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.Ve
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.PP
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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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.PP
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.Vb 19
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\& int BN_add(BIGNUM *r, const BIGNUM *a, const 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_sqr(BIGNUM *r, BIGNUM *a, 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_mod(BIGNUM *rem, const BIGNUM *a, const BIGNUM *m, BN_CTX *ctx);
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\& int BN_nnmod(BIGNUM *rem, const BIGNUM *a, const BIGNUM *m, BN_CTX *ctx);
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\& int BN_mod_add(BIGNUM *ret, BIGNUM *a, BIGNUM *b, const BIGNUM *m,
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\& BN_CTX *ctx);
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\& int BN_mod_sub(BIGNUM *ret, BIGNUM *a, BIGNUM *b, const BIGNUM *m,
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\& 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_mod_sqr(BIGNUM *ret, BIGNUM *a, const BIGNUM *m, 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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.PP
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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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.PP
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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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.PP
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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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\& const 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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.PP
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.Vb 4
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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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\& int BN_rand_range(BIGNUM *rnd, BIGNUM *range);
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\& int BN_pseudo_rand_range(BIGNUM *rnd, BIGNUM *range);
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.Ve
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.PP
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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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.PP
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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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.PP
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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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.PP
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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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.PP
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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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.PP
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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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.IX Header "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 \s-1RSA\s0
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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 \fB\s-1BIGNUM\s0\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 \fB\s-1BIGNUM\s0\fR objects is described in \fIBN_new\fR\|(3);
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\&\fIBN_add\fR\|(3) describes most of the arithmetic operations.
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Comparison is described in \fIBN_cmp\fR\|(3); \fIBN_zero\fR\|(3)
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describes certain assignments, \fIBN_rand\fR\|(3) the generation of
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random numbers, \fIBN_generate_prime\fR\|(3) deals with prime
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numbers and \fIBN_set_bit\fR\|(3) with bit operations. The conversion
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of \fB\s-1BIGNUM\s0\fRs to external formats is described in \fIBN_bn2bin\fR\|(3).
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.SH "SEE ALSO"
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.IX Header "SEE ALSO"
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\&\fIbn_internal\fR\|(3),
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\&\fIdh\fR\|(3), \fIerr\fR\|(3), \fIrand\fR\|(3), \fIrsa\fR\|(3),
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\&\fIBN_new\fR\|(3), \fIBN_CTX_new\fR\|(3),
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\&\fIBN_copy\fR\|(3), \fIBN_swap\fR\|(3), \fIBN_num_bytes\fR\|(3),
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\&\fIBN_add\fR\|(3), \fIBN_add_word\fR\|(3),
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\&\fIBN_cmp\fR\|(3), \fIBN_zero\fR\|(3), \fIBN_rand\fR\|(3),
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\&\fIBN_generate_prime\fR\|(3), \fIBN_set_bit\fR\|(3),
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\&\fIBN_bn2bin\fR\|(3), \fIBN_mod_inverse\fR\|(3),
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\&\fIBN_mod_mul_reciprocal\fR\|(3),
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\&\fIBN_mod_mul_montgomery\fR\|(3)
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