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 int BN_num_bytes(const BIGNUM *a);
25 int BN_num_bits(const BIGNUM *a);
26 int BN_num_bits_word(BN_ULONG w);
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,
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,
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);
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(BIGNUM *a, BN_ULONG w);
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);
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);
61 int BN_rand(BIGNUM *rnd, int bits, int top,int bottom);
63 BIGNUM *BN_generate_prime(BIGNUM *ret,int bits,int safe,BIGNUM *add,
64 BIGNUM *rem,void (*callback)(int,int,void *),void *cb_arg);
65 int BN_is_prime(BIGNUM *p,int nchecks,void (*callback)(int,int,void *),
66 BN_CTX *ctx,void *cb_arg);
68 int BN_set_bit(BIGNUM *a, int n);
69 int BN_clear_bit(BIGNUM *a, int n);
70 int BN_is_bit_set(const BIGNUM *a, int n);
71 int BN_mask_bits(BIGNUM *a, int n);
72 int BN_lshift(BIGNUM *r, const BIGNUM *a, int n);
73 int BN_lshift1(BIGNUM *r, BIGNUM *a);
74 int BN_rshift(BIGNUM *r, BIGNUM *a, int n);
75 int BN_rshift1(BIGNUM *r, BIGNUM *a);
77 int BN_bn2bin(const BIGNUM *a, unsigned char *to);
78 BIGNUM *BN_bin2bn(const unsigned char *s, int len, BIGNUM *ret);
79 char *BN_bn2hex(const BIGNUM *a);
80 char *BN_bn2dec(const BIGNUM *a);
81 int BN_hex2bn(BIGNUM **a, const char *str);
82 int BN_dec2bn(BIGNUM **a, const char *str);
83 int BN_print(BIO *fp, const BIGNUM *a);
84 int BN_print_fp(FILE *fp, BIGNUM *a);
85 int BN_bn2mpi(const BIGNUM *a, unsigned char *to);
86 BIGNUM *BN_mpi2bn(unsigned char *s, int len, BIGNUM *ret);
88 BIGNUM *BN_mod_inverse(BIGNUM *r, BIGNUM *a, const BIGNUM *n,
91 BN_RECP_CTX *BN_RECP_CTX_new(void);
92 void BN_RECP_CTX_init(BN_RECP_CTX *recp);
93 void BN_RECP_CTX_free(BN_RECP_CTX *recp);
94 int BN_RECP_CTX_set(BN_RECP_CTX *recp, const BIGNUM *m, BN_CTX *ctx);
95 int BN_mod_mul_reciprocal(BIGNUM *r, BIGNUM *a, BIGNUM *b,
96 BN_RECP_CTX *recp, BN_CTX *ctx);
98 BN_MONT_CTX *BN_MONT_CTX_new(void);
99 void BN_MONT_CTX_init(BN_MONT_CTX *ctx);
100 void BN_MONT_CTX_free(BN_MONT_CTX *mont);
101 int BN_MONT_CTX_set(BN_MONT_CTX *mont, const BIGNUM *m, BN_CTX *ctx);
102 BN_MONT_CTX *BN_MONT_CTX_copy(BN_MONT_CTX *to, BN_MONT_CTX *from);
103 int BN_mod_mul_montgomery(BIGNUM *r, BIGNUM *a, BIGNUM *b,
104 BN_MONT_CTX *mont, BN_CTX *ctx);
105 int BN_from_montgomery(BIGNUM *r, BIGNUM *a, BN_MONT_CTX *mont,
107 int BN_to_montgomery(BIGNUM *r, BIGNUM *a, BN_MONT_CTX *mont,
113 This library performs arithmetic operations on integers of arbitrary
114 size. It was written for use in public key cryptography, such as RSA
117 It uses dynamic memory allocation for storing its data structures.
118 That means that there is no limit on the size of the numbers
119 manipulated by these functions, but return values must always be
120 checked in case a memory allocation error has occurred.
122 The basic object in this library is a B<BIGNUM>. It is used to hold a
123 single large integer. This type should be considered opaque and fields
124 should not be modified or accessed directly.
126 The creation of B<BIGNUM> objects is described in L<BN_new(3)|BN_new(3)>;
127 L<BN_add(3)|BN_add(3)> describes most of the arithmetic operations.
128 Comparision is described in L<BN_cmp(3)|BN_cmp(3)>; L<BN_zero(3)|BN_zero(3)>
129 describes certain assignments, L<BN_rand(3)|BN_rand(3)> the generation of
130 random numbers, L<BN_generate_prime(3)|BN_generate_prime(3)> deals with prime
131 numbers and L<BN_set_bit(3)|BN_set_bit(3)> with bit operations. The conversion
132 of B<BIGNUM>s to external formats is described in L<BN_bn2bin(3)|BN_bn2bin(3)>.
136 The following description is based on the SSLeay documentation:
138 typedef struct bignum_st
140 int top; /* Index of last used d. */
141 BN_ULONG *d; /* Pointer to an array of 'BITS2' bit chunks. */
142 int max; /* Size of the d array. */
146 The big number is stored in B<d>, a malloc()ed array of B<BN_ULONG>s.
147 A B<BN_ULONG> can be either 16, 32 or 64 bits in size, depending on
148 the 'number of bits' specified in bn.h.
150 B<max> is the size of the B<d> array that has been allocated. B<top>
151 is the 'last' entry being used, so for a value of 4, bn.d[0]=4 and
152 bn.top=1. B<neg> is 1 if the number is negative. When a BIGNUM is
153 '0', the B<d> field can be NULL and B<top> == 0. Various routines in
154 this library require the use of temporary B<BIGNUM> variables during
155 their execution. Since dynamic memory allocation to create B<BIGNUM>s
156 is rather expensive when used in conjunction with repeated subroutine
157 calls, the B<BN_CTX> structure is used. This structure contains
158 B<BN_CTX_NUM> B<BIGNUM>s. B<BN_CTX_NUM> is the maximum number of
159 temporary B<BIGNUM>s any publicly exported function will use.
161 #define BN_CTX_NUM 12
162 typedef struct bignum_ctx
164 int tos; /* top of stack */
165 BIGNUM *bn[BN_CTX_NUM]; /* The variables */
170 L<dh(3)|dh(3)>, L<err(3)|err(3)>, L<rand(3)|rand(3)>, L<rsa(3)|rsa(3)>,
171 L<BN_new(3)|BN_new(3)>, L<BN_CTX_new(3)|BN_CTX_new(3)>,
172 L<BN_copy(3)|BN_copy(3)>, L<BN_num_bytes(3)|BN_num_bytes(3)>,
173 L<BN_add(3)|BN_add(3)>, L<BN_add_word(3)|BN_add_word(3)>,
174 L<BN_cmp(3)|BN_cmp(3)>, L<BN_zero(3)|BN_zero(3)>, L<BN_rand(3)|BN_rand(3)>,
175 L<BN_generate_prime(3)|BN_generate_prime(3)>, L<BN_set_bit(3)|BN_set_bit(3)>,
176 L<BN_bn2bin(3)|BN_bn2bin(3)>, L<BN_mod_inverse(3)|BN_mod_inverse(3)>,
177 L<BN_mod_mul_reciprocal(3)|BN_mod_mul_reciprocal(3)>,
178 L<BN_mod_mul_montgomery(3)|BN_mod_mul_montgomery(3)>