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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 int BN_num_bytes(const BIGNUM *a);
25 int BN_num_bits(const BIGNUM *a);
26 int BN_num_bits_word(BN_ULONG w);
27
28 int BN_add(BIGNUM *r, BIGNUM *a, BIGNUM *b);
29 int BN_sub(BIGNUM *r, const BIGNUM *a, const BIGNUM *b);
30 int BN_mul(BIGNUM *r, BIGNUM *a, BIGNUM *b, BN_CTX *ctx);
31 int BN_div(BIGNUM *dv, BIGNUM *rem, const BIGNUM *a, const BIGNUM *d,
32 BN_CTX *ctx);
33 int BN_sqr(BIGNUM *r, BIGNUM *a, BN_CTX *ctx);
34 int BN_mod(BIGNUM *rem, const BIGNUM *a, const BIGNUM *m, BN_CTX *ctx);
35 int BN_mod_mul(BIGNUM *ret, BIGNUM *a, BIGNUM *b, const BIGNUM *m,
36 BN_CTX *ctx);
37 int BN_exp(BIGNUM *r, BIGNUM *a, BIGNUM *p, BN_CTX *ctx);
38 int BN_mod_exp(BIGNUM *r, BIGNUM *a, const BIGNUM *p,
39 const BIGNUM *m, BN_CTX *ctx);
40 int BN_gcd(BIGNUM *r, BIGNUM *a, BIGNUM *b, BN_CTX *ctx);
41
42 int BN_add_word(BIGNUM *a, BN_ULONG w);
43 int BN_sub_word(BIGNUM *a, BN_ULONG w);
44 int BN_mul_word(BIGNUM *a, BN_ULONG w);
45 BN_ULONG BN_div_word(BIGNUM *a, BN_ULONG w);
46 BN_ULONG BN_mod_word(const BIGNUM *a, BN_ULONG w);
47
48 int BN_cmp(BIGNUM *a, BIGNUM *b);
49 int BN_ucmp(BIGNUM *a, BIGNUM *b);
50 int BN_is_zero(BIGNUM *a);
51 int BN_is_one(BIGNUM *a);
52 int BN_is_word(BIGNUM *a, BN_ULONG w);
53 int BN_is_odd(BIGNUM *a);
54
55 int BN_zero(BIGNUM *a);
56 int BN_one(BIGNUM *a);
57 BIGNUM *BN_value_one(void);
58 int BN_set_word(BIGNUM *a, unsigned long w);
59 unsigned long BN_get_word(BIGNUM *a);
60
61 int BN_rand(BIGNUM *rnd, int bits, int top, int bottom);
62 int BN_pseudo_rand(BIGNUM *rnd, int bits, int top, int bottom);
63
64 BIGNUM *BN_generate_prime(BIGNUM *ret, int bits,int safe, BIGNUM *add,
65 BIGNUM *rem, void (*callback)(int, int, void *), void *cb_arg);
66 int BN_is_prime(const BIGNUM *p, int nchecks,
67 void (*callback)(int, int, void *), BN_CTX *ctx, void *cb_arg);
68
69 int BN_set_bit(BIGNUM *a, int n);
70 int BN_clear_bit(BIGNUM *a, int n);
71 int BN_is_bit_set(const BIGNUM *a, int n);
72 int BN_mask_bits(BIGNUM *a, int n);
73 int BN_lshift(BIGNUM *r, const BIGNUM *a, int n);
74 int BN_lshift1(BIGNUM *r, BIGNUM *a);
75 int BN_rshift(BIGNUM *r, BIGNUM *a, int n);
76 int BN_rshift1(BIGNUM *r, BIGNUM *a);
77
78 int BN_bn2bin(const BIGNUM *a, unsigned char *to);
79 BIGNUM *BN_bin2bn(const unsigned char *s, int len, BIGNUM *ret);
80 char *BN_bn2hex(const BIGNUM *a);
81 char *BN_bn2dec(const BIGNUM *a);
82 int BN_hex2bn(BIGNUM **a, const char *str);
83 int BN_dec2bn(BIGNUM **a, const char *str);
84 int BN_print(BIO *fp, const BIGNUM *a);
85 int BN_print_fp(FILE *fp, const BIGNUM *a);
86 int BN_bn2mpi(const BIGNUM *a, unsigned char *to);
87 BIGNUM *BN_mpi2bn(unsigned char *s, int len, BIGNUM *ret);
88
89 BIGNUM *BN_mod_inverse(BIGNUM *r, BIGNUM *a, const BIGNUM *n,
90 BN_CTX *ctx);
91
92 BN_RECP_CTX *BN_RECP_CTX_new(void);
93 void BN_RECP_CTX_init(BN_RECP_CTX *recp);
94 void BN_RECP_CTX_free(BN_RECP_CTX *recp);
95 int BN_RECP_CTX_set(BN_RECP_CTX *recp, const BIGNUM *m, BN_CTX *ctx);
96 int BN_mod_mul_reciprocal(BIGNUM *r, BIGNUM *a, BIGNUM *b,
97 BN_RECP_CTX *recp, BN_CTX *ctx);
98
99 BN_MONT_CTX *BN_MONT_CTX_new(void);
100 void BN_MONT_CTX_init(BN_MONT_CTX *ctx);
101 void BN_MONT_CTX_free(BN_MONT_CTX *mont);
102 int BN_MONT_CTX_set(BN_MONT_CTX *mont, const BIGNUM *m, BN_CTX *ctx);
103 BN_MONT_CTX *BN_MONT_CTX_copy(BN_MONT_CTX *to, BN_MONT_CTX *from);
104 int BN_mod_mul_montgomery(BIGNUM *r, BIGNUM *a, BIGNUM *b,
105 BN_MONT_CTX *mont, BN_CTX *ctx);
106 int BN_from_montgomery(BIGNUM *r, BIGNUM *a, BN_MONT_CTX *mont,
107 BN_CTX *ctx);
108 int BN_to_montgomery(BIGNUM *r, BIGNUM *a, BN_MONT_CTX *mont,
109 BN_CTX *ctx);
110
111
112=head1 DESCRIPTION
113
114This library performs arithmetic operations on integers of arbitrary
115size. It was written for use in public key cryptography, such as RSA
116and Diffie-Hellman.
117
118It uses dynamic memory allocation for storing its data structures.
119That means that there is no limit on the size of the numbers
120manipulated by these functions, but return values must always be
121checked in case a memory allocation error has occurred.
122
123The basic object in this library is a B<BIGNUM>. It is used to hold a
124single large integer. This type should be considered opaque and fields
125should not be modified or accessed directly.
126
127The creation of B<BIGNUM> objects is described in L<BN_new(3)|BN_new(3)>;
128L<BN_add(3)|BN_add(3)> describes most of the arithmetic operations.
129Comparison is described in L<BN_cmp(3)|BN_cmp(3)>; L<BN_zero(3)|BN_zero(3)>
130describes certain assignments, L<BN_rand(3)|BN_rand(3)> the generation of
131random numbers, L<BN_generate_prime(3)|BN_generate_prime(3)> deals with prime
132numbers and L<BN_set_bit(3)|BN_set_bit(3)> with bit operations. The conversion
133of B<BIGNUM>s to external formats is described in L<BN_bn2bin(3)|BN_bn2bin(3)>.
134
135=head1 SEE ALSO
136
137L<bn_internal(3)|bn_internal(3)>,
138L<dh(3)|dh(3)>, L<err(3)|err(3)>, L<rand(3)|rand(3)>, L<rsa(3)|rsa(3)>,
139L<BN_new(3)|BN_new(3)>, L<BN_CTX_new(3)|BN_CTX_new(3)>,
140L<BN_copy(3)|BN_copy(3)>, L<BN_num_bytes(3)|BN_num_bytes(3)>,
141L<BN_add(3)|BN_add(3)>, L<BN_add_word(3)|BN_add_word(3)>,
142L<BN_cmp(3)|BN_cmp(3)>, L<BN_zero(3)|BN_zero(3)>, L<BN_rand(3)|BN_rand(3)>,
143L<BN_generate_prime(3)|BN_generate_prime(3)>, L<BN_set_bit(3)|BN_set_bit(3)>,
144L<BN_bn2bin(3)|BN_bn2bin(3)>, L<BN_mod_inverse(3)|BN_mod_inverse(3)>,
145L<BN_mod_mul_reciprocal(3)|BN_mod_mul_reciprocal(3)>,
146L<BN_mod_mul_montgomery(3)|BN_mod_mul_montgomery(3)>
147
148=cut