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1=pod
2
3=head1 NAME
4
5bn - multiprecision integer arithmetics
6
7=head1 SYNOPSIS
8
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 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,
35 BN_CTX *ctx);
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,
39 BN_CTX *ctx);
40 int BN_mod_sub(BIGNUM *ret, BIGNUM *a, BIGNUM *b, const BIGNUM *m,
41 BN_CTX *ctx);
42 int BN_mod_mul(BIGNUM *ret, BIGNUM *a, BIGNUM *b, const BIGNUM *m,
43 BN_CTX *ctx);
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);
49
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);
55
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);
62
63 int BN_zero(BIGNUM *a);
64 int BN_one(BIGNUM *a);
65 const BIGNUM *BN_value_one(void);
66 int BN_set_word(BIGNUM *a, unsigned long w);
67 unsigned long BN_get_word(BIGNUM *a);
68
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);
71 int BN_rand_range(BIGNUM *rnd, BIGNUM *range);
72 int BN_pseudo_rand_range(BIGNUM *rnd, BIGNUM *range);
73
74 BIGNUM *BN_generate_prime(BIGNUM *ret, int bits,int safe, BIGNUM *add,
75 BIGNUM *rem, void (*callback)(int, int, void *), void *cb_arg);
76 int BN_is_prime(const BIGNUM *p, int nchecks,
77 void (*callback)(int, int, void *), BN_CTX *ctx, void *cb_arg);
78
79 int BN_set_bit(BIGNUM *a, int n);
80 int BN_clear_bit(BIGNUM *a, int n);
81 int BN_is_bit_set(const BIGNUM *a, int n);
82 int BN_mask_bits(BIGNUM *a, int n);
83 int BN_lshift(BIGNUM *r, const BIGNUM *a, int n);
84 int BN_lshift1(BIGNUM *r, BIGNUM *a);
85 int BN_rshift(BIGNUM *r, BIGNUM *a, int n);
86 int BN_rshift1(BIGNUM *r, BIGNUM *a);
87
88 int BN_bn2bin(const BIGNUM *a, unsigned char *to);
89 BIGNUM *BN_bin2bn(const unsigned char *s, int len, BIGNUM *ret);
90 char *BN_bn2hex(const BIGNUM *a);
91 char *BN_bn2dec(const BIGNUM *a);
92 int BN_hex2bn(BIGNUM **a, const char *str);
93 int BN_dec2bn(BIGNUM **a, const char *str);
94 int BN_print(BIO *fp, const BIGNUM *a);
95 int BN_print_fp(FILE *fp, const BIGNUM *a);
96 int BN_bn2mpi(const BIGNUM *a, unsigned char *to);
97 BIGNUM *BN_mpi2bn(unsigned char *s, int len, BIGNUM *ret);
98
99 BIGNUM *BN_mod_inverse(BIGNUM *r, BIGNUM *a, const BIGNUM *n,
100 BN_CTX *ctx);
101
102 BN_RECP_CTX *BN_RECP_CTX_new(void);
103 void BN_RECP_CTX_init(BN_RECP_CTX *recp);
104 void BN_RECP_CTX_free(BN_RECP_CTX *recp);
105 int BN_RECP_CTX_set(BN_RECP_CTX *recp, const BIGNUM *m, BN_CTX *ctx);
106 int BN_mod_mul_reciprocal(BIGNUM *r, BIGNUM *a, BIGNUM *b,
107 BN_RECP_CTX *recp, BN_CTX *ctx);
108
109 BN_MONT_CTX *BN_MONT_CTX_new(void);
110 void BN_MONT_CTX_init(BN_MONT_CTX *ctx);
111 void BN_MONT_CTX_free(BN_MONT_CTX *mont);
112 int BN_MONT_CTX_set(BN_MONT_CTX *mont, const BIGNUM *m, BN_CTX *ctx);
113 BN_MONT_CTX *BN_MONT_CTX_copy(BN_MONT_CTX *to, BN_MONT_CTX *from);
114 int BN_mod_mul_montgomery(BIGNUM *r, BIGNUM *a, BIGNUM *b,
115 BN_MONT_CTX *mont, BN_CTX *ctx);
116 int BN_from_montgomery(BIGNUM *r, BIGNUM *a, BN_MONT_CTX *mont,
117 BN_CTX *ctx);
118 int BN_to_montgomery(BIGNUM *r, BIGNUM *a, BN_MONT_CTX *mont,
119 BN_CTX *ctx);
120
121
122=head1 DESCRIPTION
123
124This library performs arithmetic operations on integers of arbitrary
125size. It was written for use in public key cryptography, such as RSA
126and Diffie-Hellman.
127
128It uses dynamic memory allocation for storing its data structures.
129That means that there is no limit on the size of the numbers
130manipulated by these functions, but return values must always be
131checked in case a memory allocation error has occurred.
132
133The basic object in this library is a B<BIGNUM>. It is used to hold a
134single large integer. This type should be considered opaque and fields
135should not be modified or accessed directly.
136
137The creation of B<BIGNUM> objects is described in L<BN_new(3)|BN_new(3)>;
138L<BN_add(3)|BN_add(3)> describes most of the arithmetic operations.
139Comparison is described in L<BN_cmp(3)|BN_cmp(3)>; L<BN_zero(3)|BN_zero(3)>
140describes certain assignments, L<BN_rand(3)|BN_rand(3)> the generation of
141random numbers, L<BN_generate_prime(3)|BN_generate_prime(3)> deals with prime
142numbers and L<BN_set_bit(3)|BN_set_bit(3)> with bit operations. The conversion
143of B<BIGNUM>s to external formats is described in L<BN_bn2bin(3)|BN_bn2bin(3)>.
144
145=head1 SEE ALSO
146
147L<bn_internal(3)|bn_internal(3)>,
148L<dh(3)|dh(3)>, L<err(3)|err(3)>, L<rand(3)|rand(3)>, L<rsa(3)|rsa(3)>,
149L<BN_new(3)|BN_new(3)>, L<BN_CTX_new(3)|BN_CTX_new(3)>,
150L<BN_copy(3)|BN_copy(3)>, L<BN_swap(3)|BN_swap(3)>, L<BN_num_bytes(3)|BN_num_bytes(3)>,
151L<BN_add(3)|BN_add(3)>, L<BN_add_word(3)|BN_add_word(3)>,
152L<BN_cmp(3)|BN_cmp(3)>, L<BN_zero(3)|BN_zero(3)>, L<BN_rand(3)|BN_rand(3)>,
153L<BN_generate_prime(3)|BN_generate_prime(3)>, L<BN_set_bit(3)|BN_set_bit(3)>,
154L<BN_bn2bin(3)|BN_bn2bin(3)>, L<BN_mod_inverse(3)|BN_mod_inverse(3)>,
155L<BN_mod_mul_reciprocal(3)|BN_mod_mul_reciprocal(3)>,
156L<BN_mod_mul_montgomery(3)|BN_mod_mul_montgomery(3)>
157
158=cut
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