bn(3ssl)

1bn(3)                               OpenSSL                              bn(3)
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NAME

6       bn - multiprecision integer arithmetics
7

SYNOPSIS

9        #include <openssl/bn.h>
10
11        BIGNUM *BN_new(void);
12        void BN_free(BIGNUM *a);
13        void BN_init(BIGNUM *);
14        void BN_clear(BIGNUM *a);
15        void BN_clear_free(BIGNUM *a);
16
17        BN_CTX *BN_CTX_new(void);
18        void BN_CTX_init(BN_CTX *c);
19        void BN_CTX_free(BN_CTX *c);
20
21        BIGNUM *BN_copy(BIGNUM *a, const BIGNUM *b);
22        BIGNUM *BN_dup(const BIGNUM *a);
23
24        BIGNUM *BN_swap(BIGNUM *a, BIGNUM *b);
25
26        int BN_num_bytes(const BIGNUM *a);
27        int BN_num_bits(const BIGNUM *a);
28        int BN_num_bits_word(BN_ULONG w);
29
30        void BN_set_negative(BIGNUM *a, int n);
31        int  BN_is_negative(const BIGNUM *a);
32
33        int BN_add(BIGNUM *r, const BIGNUM *a, const BIGNUM *b);
34        int BN_sub(BIGNUM *r, const BIGNUM *a, const BIGNUM *b);
35        int BN_mul(BIGNUM *r, BIGNUM *a, BIGNUM *b, BN_CTX *ctx);
36        int BN_sqr(BIGNUM *r, BIGNUM *a, BN_CTX *ctx);
37        int BN_div(BIGNUM *dv, BIGNUM *rem, const BIGNUM *a, const BIGNUM *d,
38                BN_CTX *ctx);
39        int BN_mod(BIGNUM *rem, const BIGNUM *a, const BIGNUM *m, BN_CTX *ctx);
40        int BN_nnmod(BIGNUM *rem, const BIGNUM *a, const BIGNUM *m, BN_CTX *ctx);
41        int BN_mod_add(BIGNUM *ret, BIGNUM *a, BIGNUM *b, const BIGNUM *m,
42                BN_CTX *ctx);
43        int BN_mod_sub(BIGNUM *ret, BIGNUM *a, BIGNUM *b, const BIGNUM *m,
44                BN_CTX *ctx);
45        int BN_mod_mul(BIGNUM *ret, BIGNUM *a, BIGNUM *b, const BIGNUM *m,
46                BN_CTX *ctx);
47        int BN_mod_sqr(BIGNUM *ret, BIGNUM *a, const BIGNUM *m, BN_CTX *ctx);
48        int BN_exp(BIGNUM *r, BIGNUM *a, BIGNUM *p, BN_CTX *ctx);
49        int BN_mod_exp(BIGNUM *r, BIGNUM *a, const BIGNUM *p,
50                const BIGNUM *m, BN_CTX *ctx);
51        int BN_gcd(BIGNUM *r, BIGNUM *a, BIGNUM *b, BN_CTX *ctx);
52
53        int BN_add_word(BIGNUM *a, BN_ULONG w);
54        int BN_sub_word(BIGNUM *a, BN_ULONG w);
55        int BN_mul_word(BIGNUM *a, BN_ULONG w);
56        BN_ULONG BN_div_word(BIGNUM *a, BN_ULONG w);
57        BN_ULONG BN_mod_word(const BIGNUM *a, BN_ULONG w);
58
59        int BN_cmp(BIGNUM *a, BIGNUM *b);
60        int BN_ucmp(BIGNUM *a, BIGNUM *b);
61        int BN_is_zero(BIGNUM *a);
62        int BN_is_one(BIGNUM *a);
63        int BN_is_word(BIGNUM *a, BN_ULONG w);
64        int BN_is_odd(BIGNUM *a);
65
66        int BN_zero(BIGNUM *a);
67        int BN_one(BIGNUM *a);
68        const BIGNUM *BN_value_one(void);
69        int BN_set_word(BIGNUM *a, unsigned long w);
70        unsigned long BN_get_word(BIGNUM *a);
71
72        int BN_rand(BIGNUM *rnd, int bits, int top, int bottom);
73        int BN_pseudo_rand(BIGNUM *rnd, int bits, int top, int bottom);
74        int BN_rand_range(BIGNUM *rnd, BIGNUM *range);
75        int BN_pseudo_rand_range(BIGNUM *rnd, BIGNUM *range);
76
77        BIGNUM *BN_generate_prime(BIGNUM *ret, int bits,int safe, BIGNUM *add,
78                BIGNUM *rem, void (*callback)(int, int, void *), void *cb_arg);
79        int BN_is_prime(const BIGNUM *p, int nchecks,
80                void (*callback)(int, int, void *), BN_CTX *ctx, void *cb_arg);
81
82        int BN_set_bit(BIGNUM *a, int n);
83        int BN_clear_bit(BIGNUM *a, int n);
84        int BN_is_bit_set(const BIGNUM *a, int n);
85        int BN_mask_bits(BIGNUM *a, int n);
86        int BN_lshift(BIGNUM *r, const BIGNUM *a, int n);
87        int BN_lshift1(BIGNUM *r, BIGNUM *a);
88        int BN_rshift(BIGNUM *r, BIGNUM *a, int n);
89        int BN_rshift1(BIGNUM *r, BIGNUM *a);
90
91        int BN_bn2bin(const BIGNUM *a, unsigned char *to);
92        BIGNUM *BN_bin2bn(const unsigned char *s, int len, BIGNUM *ret);
93        char *BN_bn2hex(const BIGNUM *a);
94        char *BN_bn2dec(const BIGNUM *a);
95        int BN_hex2bn(BIGNUM **a, const char *str);
96        int BN_dec2bn(BIGNUM **a, const char *str);
97        int BN_print(BIO *fp, const BIGNUM *a);
98        int BN_print_fp(FILE *fp, const BIGNUM *a);
99        int BN_bn2mpi(const BIGNUM *a, unsigned char *to);
100        BIGNUM *BN_mpi2bn(unsigned char *s, int len, BIGNUM *ret);
101
102        BIGNUM *BN_mod_inverse(BIGNUM *r, BIGNUM *a, const BIGNUM *n,
103            BN_CTX *ctx);
104
105        BN_RECP_CTX *BN_RECP_CTX_new(void);
106        void BN_RECP_CTX_init(BN_RECP_CTX *recp);
107        void BN_RECP_CTX_free(BN_RECP_CTX *recp);
108        int BN_RECP_CTX_set(BN_RECP_CTX *recp, const BIGNUM *m, BN_CTX *ctx);
109        int BN_mod_mul_reciprocal(BIGNUM *r, BIGNUM *a, BIGNUM *b,
110               BN_RECP_CTX *recp, BN_CTX *ctx);
111
112        BN_MONT_CTX *BN_MONT_CTX_new(void);
113        void BN_MONT_CTX_init(BN_MONT_CTX *ctx);
114        void BN_MONT_CTX_free(BN_MONT_CTX *mont);
115        int BN_MONT_CTX_set(BN_MONT_CTX *mont, const BIGNUM *m, BN_CTX *ctx);
116        BN_MONT_CTX *BN_MONT_CTX_copy(BN_MONT_CTX *to, BN_MONT_CTX *from);
117        int BN_mod_mul_montgomery(BIGNUM *r, BIGNUM *a, BIGNUM *b,
118                BN_MONT_CTX *mont, BN_CTX *ctx);
119        int BN_from_montgomery(BIGNUM *r, BIGNUM *a, BN_MONT_CTX *mont,
120                BN_CTX *ctx);
121        int BN_to_montgomery(BIGNUM *r, BIGNUM *a, BN_MONT_CTX *mont,
122                BN_CTX *ctx);
123
124        BN_BLINDING *BN_BLINDING_new(const BIGNUM *A, const BIGNUM *Ai,
125               BIGNUM *mod);
126        void BN_BLINDING_free(BN_BLINDING *b);
127        int BN_BLINDING_update(BN_BLINDING *b,BN_CTX *ctx);
128        int BN_BLINDING_convert(BIGNUM *n, BN_BLINDING *b, BN_CTX *ctx);
129        int BN_BLINDING_invert(BIGNUM *n, BN_BLINDING *b, BN_CTX *ctx);
130        int BN_BLINDING_convert_ex(BIGNUM *n, BIGNUM *r, BN_BLINDING *b,
131               BN_CTX *ctx);
132        int BN_BLINDING_invert_ex(BIGNUM *n,const BIGNUM *r,BN_BLINDING *b,
133               BN_CTX *ctx);
134        unsigned long BN_BLINDING_get_thread_id(const BN_BLINDING *);
135        void BN_BLINDING_set_thread_id(BN_BLINDING *, unsigned long);
136        unsigned long BN_BLINDING_get_flags(const BN_BLINDING *);
137        void BN_BLINDING_set_flags(BN_BLINDING *, unsigned long);
138        BN_BLINDING *BN_BLINDING_create_param(BN_BLINDING *b,
139               const BIGNUM *e, BIGNUM *m, BN_CTX *ctx,
140               int (*bn_mod_exp)(BIGNUM *r, const BIGNUM *a, const BIGNUM *p,
141                                 const BIGNUM *m, BN_CTX *ctx, BN_MONT_CTX *m_ctx),
142               BN_MONT_CTX *m_ctx);
143

DESCRIPTION

145       This library performs arithmetic operations on integers of arbitrary
146       size. It was written for use in public key cryptography, such as RSA
147       and Diffie-Hellman.
148
149       It uses dynamic memory allocation for storing its data structures.
150       That means that there is no limit on the size of the numbers manipu‐
151       lated by these functions, but return values must always be checked in
152       case a memory allocation error has occurred.
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154       The basic object in this library is a BIGNUM. It is used to hold a sin‐
155       gle large integer. This type should be considered opaque and fields
156       should not be modified or accessed directly.
157
158       The creation of BIGNUM objects is described in BN_new(3); BN_add(3)
159       describes most of the arithmetic operations.  Comparison is described
160       in BN_cmp(3); BN_zero(3) describes certain assignments, BN_rand(3) the
161       generation of random numbers, BN_generate_prime(3) deals with prime
162       numbers and BN_set_bit(3) with bit operations. The conversion of
163       BIGNUMs to external formats is described in BN_bn2bin(3).
164

NAME

SYNOPSIS

DESCRIPTION

SEE ALSO