5 bn - multiprecision integer arithmetics
9 #include <openssl/bn.h>
12 void BN_free(BIGNUM *a);
13 void BN_init(BIGNUM *);
14 void BN_clear(BIGNUM *a);
15 void BN_clear_free(BIGNUM *a);
17 BN_CTX *BN_CTX_new(void);
18 void BN_CTX_init(BN_CTX *c);
19 void BN_CTX_free(BN_CTX *c);
21 BIGNUM *BN_copy(BIGNUM *a, const BIGNUM *b);
22 BIGNUM *BN_dup(const BIGNUM *a);
24 BIGNUM *BN_swap(BIGNUM *a, BIGNUM *b);
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);
30 int BN_add(BIGNUM *r, const BIGNUM *a, const BIGNUM *b);
31 int BN_sub(BIGNUM *r, const BIGNUM *a, const BIGNUM *b);
32 int BN_mul(BIGNUM *r, BIGNUM *a, BIGNUM *b, BN_CTX *ctx);
33 int BN_sqr(BIGNUM *r, BIGNUM *a, BN_CTX *ctx);
34 int BN_div(BIGNUM *dv, BIGNUM *rem, const BIGNUM *a, const BIGNUM *d,
36 int BN_mod(BIGNUM *rem, const BIGNUM *a, const BIGNUM *m, BN_CTX *ctx);
37 int BN_nnmod(BIGNUM *rem, const BIGNUM *a, const BIGNUM *m, BN_CTX *ctx);
38 int BN_mod_add(BIGNUM *ret, BIGNUM *a, BIGNUM *b, const BIGNUM *m,
40 int BN_mod_sub(BIGNUM *ret, BIGNUM *a, BIGNUM *b, const BIGNUM *m,
42 int BN_mod_mul(BIGNUM *ret, BIGNUM *a, BIGNUM *b, const BIGNUM *m,
44 int BN_mod_sqr(BIGNUM *ret, BIGNUM *a, const BIGNUM *m, BN_CTX *ctx);
45 int BN_exp(BIGNUM *r, BIGNUM *a, BIGNUM *p, BN_CTX *ctx);
46 int BN_mod_exp(BIGNUM *r, BIGNUM *a, const BIGNUM *p,
47 const BIGNUM *m, BN_CTX *ctx);
48 int BN_gcd(BIGNUM *r, BIGNUM *a, BIGNUM *b, BN_CTX *ctx);
50 int BN_add_word(BIGNUM *a, BN_ULONG w);
51 int BN_sub_word(BIGNUM *a, BN_ULONG w);
52 int BN_mul_word(BIGNUM *a, BN_ULONG w);
53 BN_ULONG BN_div_word(BIGNUM *a, BN_ULONG w);
54 BN_ULONG BN_mod_word(const BIGNUM *a, BN_ULONG w);
56 int BN_cmp(BIGNUM *a, BIGNUM *b);
57 int BN_ucmp(BIGNUM *a, BIGNUM *b);
58 int BN_is_zero(BIGNUM *a);
59 int BN_is_one(BIGNUM *a);
60 int BN_is_word(BIGNUM *a, BN_ULONG w);
61 int BN_is_odd(BIGNUM *a);
63 int BN_zero(BIGNUM *a);
64 int BN_one(BIGNUM *a);
65 BIGNUM *BN_value_one(void);
66 int BN_set_word(BIGNUM *a, unsigned long w);
67 unsigned long BN_get_word(BIGNUM *a);
69 int BN_rand(BIGNUM *rnd, int bits, int top, int bottom);
70 int BN_pseudo_rand(BIGNUM *rnd, int bits, int top, int bottom);
72 BIGNUM *BN_generate_prime(BIGNUM *ret, int bits,int safe, BIGNUM *add,
73 BIGNUM *rem, void (*callback)(int, int, void *), void *cb_arg);
74 int BN_is_prime(const BIGNUM *p, int nchecks,
75 void (*callback)(int, int, void *), BN_CTX *ctx, void *cb_arg);
77 int BN_set_bit(BIGNUM *a, int n);
78 int BN_clear_bit(BIGNUM *a, int n);
79 int BN_is_bit_set(const BIGNUM *a, int n);
80 int BN_mask_bits(BIGNUM *a, int n);
81 int BN_lshift(BIGNUM *r, const BIGNUM *a, int n);
82 int BN_lshift1(BIGNUM *r, BIGNUM *a);
83 int BN_rshift(BIGNUM *r, BIGNUM *a, int n);
84 int BN_rshift1(BIGNUM *r, BIGNUM *a);
86 int BN_bn2bin(const BIGNUM *a, unsigned char *to);
87 BIGNUM *BN_bin2bn(const unsigned char *s, int len, BIGNUM *ret);
88 char *BN_bn2hex(const BIGNUM *a);
89 char *BN_bn2dec(const BIGNUM *a);
90 int BN_hex2bn(BIGNUM **a, const char *str);
91 int BN_dec2bn(BIGNUM **a, const char *str);
92 int BN_print(BIO *fp, const BIGNUM *a);
93 int BN_print_fp(FILE *fp, const BIGNUM *a);
94 int BN_bn2mpi(const BIGNUM *a, unsigned char *to);
95 BIGNUM *BN_mpi2bn(unsigned char *s, int len, BIGNUM *ret);
97 BIGNUM *BN_mod_inverse(BIGNUM *r, BIGNUM *a, const BIGNUM *n,
100 BN_RECP_CTX *BN_RECP_CTX_new(void);
101 void BN_RECP_CTX_init(BN_RECP_CTX *recp);
102 void BN_RECP_CTX_free(BN_RECP_CTX *recp);
103 int BN_RECP_CTX_set(BN_RECP_CTX *recp, const BIGNUM *m, BN_CTX *ctx);
104 int BN_mod_mul_reciprocal(BIGNUM *r, BIGNUM *a, BIGNUM *b,
105 BN_RECP_CTX *recp, BN_CTX *ctx);
107 BN_MONT_CTX *BN_MONT_CTX_new(void);
108 void BN_MONT_CTX_init(BN_MONT_CTX *ctx);
109 void BN_MONT_CTX_free(BN_MONT_CTX *mont);
110 int BN_MONT_CTX_set(BN_MONT_CTX *mont, const BIGNUM *m, BN_CTX *ctx);
111 BN_MONT_CTX *BN_MONT_CTX_copy(BN_MONT_CTX *to, BN_MONT_CTX *from);
112 int BN_mod_mul_montgomery(BIGNUM *r, BIGNUM *a, BIGNUM *b,
113 BN_MONT_CTX *mont, BN_CTX *ctx);
114 int BN_from_montgomery(BIGNUM *r, BIGNUM *a, BN_MONT_CTX *mont,
116 int BN_to_montgomery(BIGNUM *r, BIGNUM *a, BN_MONT_CTX *mont,
122 This library performs arithmetic operations on integers of arbitrary
123 size. It was written for use in public key cryptography, such as RSA
126 It uses dynamic memory allocation for storing its data structures.
127 That means that there is no limit on the size of the numbers
128 manipulated by these functions, but return values must always be
129 checked in case a memory allocation error has occurred.
131 The basic object in this library is a B<BIGNUM>. It is used to hold a
132 single large integer. This type should be considered opaque and fields
133 should not be modified or accessed directly.
135 The creation of B<BIGNUM> objects is described in L<BN_new(3)|BN_new(3)>;
136 L<BN_add(3)|BN_add(3)> describes most of the arithmetic operations.
137 Comparison is described in L<BN_cmp(3)|BN_cmp(3)>; L<BN_zero(3)|BN_zero(3)>
138 describes certain assignments, L<BN_rand(3)|BN_rand(3)> the generation of
139 random numbers, L<BN_generate_prime(3)|BN_generate_prime(3)> deals with prime
140 numbers and L<BN_set_bit(3)|BN_set_bit(3)> with bit operations. The conversion
141 of B<BIGNUM>s to external formats is described in L<BN_bn2bin(3)|BN_bn2bin(3)>.
145 L<bn_internal(3)|bn_internal(3)>,
146 L<dh(3)|dh(3)>, L<err(3)|err(3)>, L<rand(3)|rand(3)>, L<rsa(3)|rsa(3)>,
147 L<BN_new(3)|BN_new(3)>, L<BN_CTX_new(3)|BN_CTX_new(3)>,
148 L<BN_copy(3)|BN_copy(3)>, L<BN_swap(3)|BN_swap(3)>, L<BN_num_bytes(3)|BN_num_bytes(3)>,
149 L<BN_add(3)|BN_add(3)>, L<BN_add_word(3)|BN_add_word(3)>,
150 L<BN_cmp(3)|BN_cmp(3)>, L<BN_zero(3)|BN_zero(3)>, L<BN_rand(3)|BN_rand(3)>,
151 L<BN_generate_prime(3)|BN_generate_prime(3)>, L<BN_set_bit(3)|BN_set_bit(3)>,
152 L<BN_bn2bin(3)|BN_bn2bin(3)>, L<BN_mod_inverse(3)|BN_mod_inverse(3)>,
153 L<BN_mod_mul_reciprocal(3)|BN_mod_mul_reciprocal(3)>,
154 L<BN_mod_mul_montgomery(3)|BN_mod_mul_montgomery(3)>