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bn(3)                               OpenSSL                              bn(3)

       bn - multiprecision integer arithmetics

        #include <openssl/bn.h>

        BIGNUM *BN_new(void);
        void BN_free(BIGNUM *a);
        void BN_init(BIGNUM *);
        void BN_clear(BIGNUM *a);
        void BN_clear_free(BIGNUM *a);

        BN_CTX *BN_CTX_new(void);
        void BN_CTX_init(BN_CTX *c);
        void BN_CTX_free(BN_CTX *c);

        BIGNUM *BN_copy(BIGNUM *a, const BIGNUM *b);
        BIGNUM *BN_dup(const BIGNUM *a);

        BIGNUM *BN_swap(BIGNUM *a, BIGNUM *b);

        int BN_num_bytes(const BIGNUM *a);
        int BN_num_bits(const BIGNUM *a);
        int BN_num_bits_word(BN_ULONG w);

        int BN_add(BIGNUM *r, const BIGNUM *a, const BIGNUM *b);
        int BN_sub(BIGNUM *r, const BIGNUM *a, const BIGNUM *b);
        int BN_mul(BIGNUM *r, BIGNUM *a, BIGNUM *b, BN_CTX *ctx);
        int BN_sqr(BIGNUM *r, BIGNUM *a, BN_CTX *ctx);
        int BN_div(BIGNUM *dv, BIGNUM *rem, const BIGNUM *a, const BIGNUM *d,
                BN_CTX *ctx);
        int BN_mod(BIGNUM *rem, const BIGNUM *a, const BIGNUM *m, BN_CTX *ctx);
        int BN_nnmod(BIGNUM *rem, const BIGNUM *a, const BIGNUM *m, BN_CTX *ctx);
        int BN_mod_add(BIGNUM *ret, BIGNUM *a, BIGNUM *b, const BIGNUM *m,
                BN_CTX *ctx);
        int BN_mod_sub(BIGNUM *ret, BIGNUM *a, BIGNUM *b, const BIGNUM *m,
                BN_CTX *ctx);
        int BN_mod_mul(BIGNUM *ret, BIGNUM *a, BIGNUM *b, const BIGNUM *m,
                BN_CTX *ctx);
        int BN_mod_sqr(BIGNUM *ret, BIGNUM *a, const BIGNUM *m, BN_CTX *ctx);
        int BN_exp(BIGNUM *r, BIGNUM *a, BIGNUM *p, BN_CTX *ctx);
        int BN_mod_exp(BIGNUM *r, BIGNUM *a, const BIGNUM *p,
                const BIGNUM *m, BN_CTX *ctx);
        int BN_gcd(BIGNUM *r, BIGNUM *a, BIGNUM *b, BN_CTX *ctx);

        int BN_add_word(BIGNUM *a, BN_ULONG w);
        int BN_sub_word(BIGNUM *a, BN_ULONG w);
        int BN_mul_word(BIGNUM *a, BN_ULONG w);
        BN_ULONG BN_div_word(BIGNUM *a, BN_ULONG w);
        BN_ULONG BN_mod_word(const BIGNUM *a, BN_ULONG w);

        int BN_cmp(BIGNUM *a, BIGNUM *b);
        int BN_ucmp(BIGNUM *a, BIGNUM *b);
        int BN_is_zero(BIGNUM *a);
        int BN_is_one(BIGNUM *a);
        int BN_is_word(BIGNUM *a, BN_ULONG w);
        int BN_is_odd(BIGNUM *a);

        int BN_zero(BIGNUM *a);
        int BN_one(BIGNUM *a);
        const BIGNUM *BN_value_one(void);
        int BN_set_word(BIGNUM *a, unsigned long w);
        unsigned long BN_get_word(BIGNUM *a);

        int BN_rand(BIGNUM *rnd, int bits, int top, int bottom);
        int BN_pseudo_rand(BIGNUM *rnd, int bits, int top, int bottom);
        int BN_rand_range(BIGNUM *rnd, BIGNUM *range);
        int BN_pseudo_rand_range(BIGNUM *rnd, BIGNUM *range);

        BIGNUM *BN_generate_prime(BIGNUM *ret, int bits,int safe, BIGNUM *add,
                BIGNUM *rem, void (*callback)(int, int, void *), void *cb_arg);
        int BN_is_prime(const BIGNUM *p, int nchecks,
                void (*callback)(int, int, void *), BN_CTX *ctx, void *cb_arg);

        int BN_set_bit(BIGNUM *a, int n);
        int BN_clear_bit(BIGNUM *a, int n);
        int BN_is_bit_set(const BIGNUM *a, int n);
        int BN_mask_bits(BIGNUM *a, int n);
        int BN_lshift(BIGNUM *r, const BIGNUM *a, int n);
        int BN_lshift1(BIGNUM *r, BIGNUM *a);
        int BN_rshift(BIGNUM *r, BIGNUM *a, int n);
        int BN_rshift1(BIGNUM *r, BIGNUM *a);

        int BN_bn2bin(const BIGNUM *a, unsigned char *to);
        BIGNUM *BN_bin2bn(const unsigned char *s, int len, BIGNUM *ret);
        char *BN_bn2hex(const BIGNUM *a);
        char *BN_bn2dec(const BIGNUM *a);
        int BN_hex2bn(BIGNUM **a, const char *str);
        int BN_dec2bn(BIGNUM **a, const char *str);
        int BN_print(BIO *fp, const BIGNUM *a);
        int BN_print_fp(FILE *fp, const BIGNUM *a);
        int BN_bn2mpi(const BIGNUM *a, unsigned char *to);
        BIGNUM *BN_mpi2bn(unsigned char *s, int len, BIGNUM *ret);

        BIGNUM *BN_mod_inverse(BIGNUM *r, BIGNUM *a, const BIGNUM *n,
            BN_CTX *ctx);

        BN_RECP_CTX *BN_RECP_CTX_new(void);
        void BN_RECP_CTX_init(BN_RECP_CTX *recp);
        void BN_RECP_CTX_free(BN_RECP_CTX *recp);
        int BN_RECP_CTX_set(BN_RECP_CTX *recp, const BIGNUM *m, BN_CTX *ctx);
        int BN_mod_mul_reciprocal(BIGNUM *r, BIGNUM *a, BIGNUM *b,
               BN_RECP_CTX *recp, BN_CTX *ctx);

        BN_MONT_CTX *BN_MONT_CTX_new(void);
        void BN_MONT_CTX_init(BN_MONT_CTX *ctx);
        void BN_MONT_CTX_free(BN_MONT_CTX *mont);
        int BN_MONT_CTX_set(BN_MONT_CTX *mont, const BIGNUM *m, BN_CTX *ctx);
        BN_MONT_CTX *BN_MONT_CTX_copy(BN_MONT_CTX *to, BN_MONT_CTX *from);
        int BN_mod_mul_montgomery(BIGNUM *r, BIGNUM *a, BIGNUM *b,
                BN_MONT_CTX *mont, BN_CTX *ctx);
        int BN_from_montgomery(BIGNUM *r, BIGNUM *a, BN_MONT_CTX *mont,
                BN_CTX *ctx);
        int BN_to_montgomery(BIGNUM *r, BIGNUM *a, BN_MONT_CTX *mont,
                BN_CTX *ctx);

       This library performs arithmetic operations on integers of arbitrary
       size. It was written for use in public key cryptography, such as RSA
       and Diffie-Hellman.

       It uses dynamic memory allocation for storing its data structures.
       That means that there is no limit on the size of the numbers manipu-
       lated by these functions, but return values must always be checked in
       case a memory allocation error has occurred.

       The basic object in this library is a BIGNUM. It is used to hold a sin-
       gle large integer. This type should be considered opaque and fields
       should not be modified or accessed directly.

       The creation of BIGNUM objects is described in BN_new(3); BN_add(3)
       describes most of the arithmetic operations.  Comparison is described
       in BN_cmp(3); BN_zero(3) describes certain assignments, BN_rand(3) the
       generation of random numbers, BN_generate_prime(3) deals with prime
       numbers and BN_set_bit(3) with bit operations. The conversion of
       BIGNUMs to external formats is described in BN_bn2bin(3).

       bn_internal(3), dh(3), err(3), rand(3), rsa(3), BN_new(3),
       BN_CTX_new(3), BN_copy(3), BN_swap(3), BN_num_bytes(3), BN_add(3),
       BN_add_word(3), BN_cmp(3), BN_zero(3), BN_rand(3), BN_gener-
       ate_prime(3), BN_set_bit(3), BN_bn2bin(3), BN_mod_inverse(3),
       BN_mod_mul_reciprocal(3), BN_mod_mul_montgomery(3)

0.9.7d                            2005-02-24                             bn(3)


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