=pod

=head1 NAME

bn - Multiprecision integer arithmetics

=head1 SYNOPSIS

 #include <openssl/bn.h>

 #define BN_prime_checks(b)
 #define BN_num_bytes(a)
 #define BN_is_word(a,w)
 #define BN_is_zero(a)
 #define BN_is_one(a)
 #define BN_is_odd(a)
 #define BN_one(a)
 #define BN_zero(a)
 
 #define bn_expand(n,b)
 #define bn_wexpand(n,b)
 
 #define bn_fix_top(a)
 
 BIGNUM *BN_value_one(void);
 char *	BN_options(void);
 BN_CTX *BN_CTX_new(void);
 void	BN_CTX_init(BN_CTX *c);
 void	BN_CTX_free(BN_CTX *c);
 int     BN_rand(BIGNUM *rnd, int bits, int top,int bottom);
 int	BN_num_bits(const BIGNUM *a);
 int	BN_num_bits_word(BN_ULONG);
 BIGNUM *BN_new(void);
 void	BN_init(BIGNUM *);
 void	BN_clear_free(BIGNUM *a);
 BIGNUM *BN_copy(BIGNUM *a, const BIGNUM *b);
 BIGNUM *BN_bin2bn(const unsigned char *s,int len,BIGNUM *ret);
 int	BN_bn2bin(const BIGNUM *a, unsigned char *to);
 BIGNUM *BN_mpi2bn(unsigned char *s,int len,BIGNUM *ret);
 int	BN_bn2mpi(const BIGNUM *a, unsigned char *to);
 int	BN_sub(BIGNUM *r, const BIGNUM *a, const BIGNUM *b);
 int	BN_usub(BIGNUM *r, const BIGNUM *a, const BIGNUM *b);
 int	BN_uadd(BIGNUM *r, const BIGNUM *a, const BIGNUM *b);
 int	BN_add(BIGNUM *r, BIGNUM *a, BIGNUM *b);
 int	BN_mod(BIGNUM *rem, const BIGNUM *m, const BIGNUM *d, BN_CTX *ctx);
 int	BN_div(BIGNUM *dv, BIGNUM *rem, const BIGNUM *m, const BIGNUM *d,
 	       BN_CTX *ctx);
 int	BN_mul(BIGNUM *r, BIGNUM *a, BIGNUM *b,BN_CTX *ctx);
 int	BN_sqr(BIGNUM *r, BIGNUM *a,BN_CTX *ctx);
 BN_ULONG BN_mod_word(BIGNUM *a, BN_ULONG w);
 BN_ULONG BN_div_word(BIGNUM *a, BN_ULONG w);
 int	BN_mul_word(BIGNUM *a, BN_ULONG w);
 int	BN_add_word(BIGNUM *a, BN_ULONG w);
 int	BN_sub_word(BIGNUM *a, BN_ULONG w);
 int	BN_set_word(BIGNUM *a, BN_ULONG w);
 BN_ULONG BN_get_word(BIGNUM *a);
 int	BN_cmp(const BIGNUM *a, const BIGNUM *b);
 void	BN_free(BIGNUM *a);
 int	BN_is_bit_set(const BIGNUM *a, int n);
 int	BN_lshift(BIGNUM *r, const BIGNUM *a, int n);
 int	BN_lshift1(BIGNUM *r, BIGNUM *a);
 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_mod_exp_mont(BIGNUM *r, BIGNUM *a, const BIGNUM *p,
 			const BIGNUM *m, BN_CTX *ctx, BN_MONT_CTX *m_ctx);
 int	BN_mod_exp2_mont(BIGNUM *r, BIGNUM *a1, BIGNUM *p1,BIGNUM *a2,
 		BIGNUM *p2,BIGNUM *m,BN_CTX *ctx,BN_MONT_CTX *m_ctx);
 int	BN_mod_exp_simple(BIGNUM *r, BIGNUM *a, BIGNUM *p,
 	BIGNUM *m,BN_CTX *ctx);
 int	BN_mask_bits(BIGNUM *a,int n);
 int	BN_mod_mul(BIGNUM *ret, BIGNUM *a, BIGNUM *b, const BIGNUM *m, BN_CTX *ctx);
 int	BN_print_fp(FILE *fp, BIGNUM *a);
 int	BN_print(BIO *fp, const BIGNUM *a);
 int	BN_reciprocal(BIGNUM *r, BIGNUM *m, int len, BN_CTX *ctx);
 int	BN_rshift(BIGNUM *r, BIGNUM *a, int n);
 int	BN_rshift1(BIGNUM *r, BIGNUM *a);
 void	BN_clear(BIGNUM *a);
 BIGNUM *bn_expand2(BIGNUM *b, int bits);
 BIGNUM *BN_dup(const BIGNUM *a);
 int	BN_ucmp(const BIGNUM *a, const BIGNUM *b);
 int	BN_set_bit(BIGNUM *a, int n);
 int	BN_clear_bit(BIGNUM *a, int n);
 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_gcd(BIGNUM *r,BIGNUM *in_a,BIGNUM *in_b,BN_CTX *ctx);
 BIGNUM *BN_mod_inverse(BIGNUM *ret,BIGNUM *a, const BIGNUM *n,BN_CTX *ctx);
 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(BIGNUM *p,int nchecks,void (*callback)(int,int,void *),
 		BN_CTX *ctx,void *cb_arg);
 void	ERR_load_BN_strings(void );
 
 BN_ULONG bn_mul_add_words(BN_ULONG *rp, BN_ULONG *ap, int num, BN_ULONG w);
 BN_ULONG bn_mul_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);
 
 BN_MONT_CTX *BN_MONT_CTX_new(void );
 void BN_MONT_CTX_init(BN_MONT_CTX *ctx);
 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);
 void BN_MONT_CTX_free(BN_MONT_CTX *mont);
 int BN_MONT_CTX_set(BN_MONT_CTX *mont,const BIGNUM *modulus,BN_CTX *ctx);
 BN_MONT_CTX *BN_MONT_CTX_copy(BN_MONT_CTX *to,BN_MONT_CTX *from);
 
 BN_BLINDING *BN_BLINDING_new(BIGNUM *A,BIGNUM *Ai,BIGNUM *mod);
 void BN_BLINDING_free(BN_BLINDING *b);
 int BN_BLINDING_update(BN_BLINDING *b,BN_CTX *ctx);
 int BN_BLINDING_convert(BIGNUM *n, BN_BLINDING *r, BN_CTX *ctx);
 int BN_BLINDING_invert(BIGNUM *n, BN_BLINDING *b, BN_CTX *ctx);
 
 void BN_set_params(int mul,int high,int low,int mont);
 int BN_get_params(int which);
 
 void	BN_RECP_CTX_init(BN_RECP_CTX *recp);
 BN_RECP_CTX *BN_RECP_CTX_new(void);
 void	BN_RECP_CTX_free(BN_RECP_CTX *recp);
 int	BN_RECP_CTX_set(BN_RECP_CTX *recp,const BIGNUM *rdiv,BN_CTX *ctx);
 int	BN_mod_mul_reciprocal(BIGNUM *r, BIGNUM *x, BIGNUM *y,
 		BN_RECP_CTX *recp,BN_CTX *ctx);
 int	BN_mod_exp_recp(BIGNUM *r, const BIGNUM *a, const BIGNUM *p,
 			const BIGNUM *m, BN_CTX *ctx);
 int	BN_div_recp(BIGNUM *dv, BIGNUM *rem, BIGNUM *m,
 		BN_RECP_CTX *recp, BN_CTX *ctx);

=head1 DESCRIPTION

=head1 SEE ALSO

err(3), rand(3)

=cut