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dd8dec69 UM |
1 | =pod |
2 | ||
3 | =head1 NAME | |
4 | ||
78a0c1f1 BM |
5 | BN_add, BN_sub, BN_mul, BN_sqr, BN_div, BN_mod, BN_nnmod, BN_mod_add, |
6 | BN_mod_sub, BN_mod_mul, BN_mod_sqr, BN_exp, BN_mod_exp, BN_gcd - | |
7 | arithmetic operations on BIGNUMs | |
dd8dec69 UM |
8 | |
9 | =head1 SYNOPSIS | |
10 | ||
11 | #include <openssl/bn.h> | |
12 | ||
13 | int BN_add(BIGNUM *r, const BIGNUM *a, const BIGNUM *b); | |
14 | ||
15 | int BN_sub(BIGNUM *r, const BIGNUM *a, const BIGNUM *b); | |
16 | ||
17 | int BN_mul(BIGNUM *r, BIGNUM *a, BIGNUM *b, BN_CTX *ctx); | |
18 | ||
78a0c1f1 BM |
19 | int BN_sqr(BIGNUM *r, BIGNUM *a, BN_CTX *ctx); |
20 | ||
dd8dec69 | 21 | int BN_div(BIGNUM *dv, BIGNUM *rem, const BIGNUM *a, const BIGNUM *d, |
e9b77246 | 22 | BN_CTX *ctx); |
dd8dec69 | 23 | |
dd8dec69 UM |
24 | int BN_mod(BIGNUM *rem, const BIGNUM *a, const BIGNUM *m, BN_CTX *ctx); |
25 | ||
5acaa495 | 26 | int BN_nnmod(BIGNUM *r, const BIGNUM *a, const BIGNUM *m, BN_CTX *ctx); |
78a0c1f1 BM |
27 | |
28 | int BN_mod_add(BIGNUM *r, BIGNUM *a, BIGNUM *b, const BIGNUM *m, | |
e9b77246 | 29 | BN_CTX *ctx); |
78a0c1f1 BM |
30 | |
31 | int BN_mod_sub(BIGNUM *r, BIGNUM *a, BIGNUM *b, const BIGNUM *m, | |
e9b77246 | 32 | BN_CTX *ctx); |
78a0c1f1 BM |
33 | |
34 | int BN_mod_mul(BIGNUM *r, BIGNUM *a, BIGNUM *b, const BIGNUM *m, | |
e9b77246 | 35 | BN_CTX *ctx); |
dd8dec69 | 36 | |
78a0c1f1 BM |
37 | int BN_mod_sqr(BIGNUM *r, BIGNUM *a, const BIGNUM *m, BN_CTX *ctx); |
38 | ||
dd8dec69 UM |
39 | int BN_exp(BIGNUM *r, BIGNUM *a, BIGNUM *p, BN_CTX *ctx); |
40 | ||
41 | int BN_mod_exp(BIGNUM *r, BIGNUM *a, const BIGNUM *p, | |
e9b77246 | 42 | const BIGNUM *m, BN_CTX *ctx); |
dd8dec69 UM |
43 | |
44 | int BN_gcd(BIGNUM *r, BIGNUM *a, BIGNUM *b, BN_CTX *ctx); | |
45 | ||
46 | =head1 DESCRIPTION | |
47 | ||
78a0c1f1 BM |
48 | BN_add() adds I<a> and I<b> and places the result in I<r> (C<r=a+b>). |
49 | I<r> may be the same B<BIGNUM> as I<a> or I<b>. | |
dd8dec69 | 50 | |
78a0c1f1 | 51 | BN_sub() subtracts I<b> from I<a> and places the result in I<r> (C<r=a-b>). |
32c74814 | 52 | I<r> may be the same B<BIGNUM> as I<a> or I<b>. |
dd8dec69 | 53 | |
78a0c1f1 BM |
54 | BN_mul() multiplies I<a> and I<b> and places the result in I<r> (C<r=a*b>). |
55 | I<r> may be the same B<BIGNUM> as I<a> or I<b>. | |
9b86974e | 56 | For multiplication by powers of 2, use L<BN_lshift(3)>. |
dd8dec69 | 57 | |
78a0c1f1 BM |
58 | BN_sqr() takes the square of I<a> and places the result in I<r> |
59 | (C<r=a^2>). I<r> and I<a> may be the same B<BIGNUM>. | |
60 | This function is faster than BN_mul(r,a,a). | |
61 | ||
62 | BN_div() divides I<a> by I<d> and places the result in I<dv> and the | |
63 | remainder in I<rem> (C<dv=a/d, rem=a%d>). Either of I<dv> and I<rem> may | |
64 | be B<NULL>, in which case the respective value is not returned. | |
65 | The result is rounded towards zero; thus if I<a> is negative, the | |
66 | remainder will be zero or negative. | |
e93f9a32 | 67 | For division by powers of 2, use BN_rshift(3). |
dd8dec69 | 68 | |
78a0c1f1 BM |
69 | BN_mod() corresponds to BN_div() with I<dv> set to B<NULL>. |
70 | ||
5acaa495 BM |
71 | BN_nnmod() reduces I<a> modulo I<m> and places the non-negative |
72 | remainder in I<r>. | |
78a0c1f1 BM |
73 | |
74 | BN_mod_add() adds I<a> to I<b> modulo I<m> and places the non-negative | |
75 | result in I<r>. | |
76 | ||
3b80e3aa | 77 | BN_mod_sub() subtracts I<b> from I<a> modulo I<m> and places the |
78a0c1f1 | 78 | non-negative result in I<r>. |
dd8dec69 | 79 | |
78a0c1f1 BM |
80 | BN_mod_mul() multiplies I<a> by I<b> and finds the non-negative |
81 | remainder respective to modulus I<m> (C<r=(a*b) mod m>). I<r> may be | |
82 | the same B<BIGNUM> as I<a> or I<b>. For more efficient algorithms for | |
83 | repeated computations using the same modulus, see | |
9b86974e RS |
84 | L<BN_mod_mul_montgomery(3)> and |
85 | L<BN_mod_mul_reciprocal(3)>. | |
dd8dec69 | 86 | |
78a0c1f1 BM |
87 | BN_mod_sqr() takes the square of I<a> modulo B<m> and places the |
88 | result in I<r>. | |
dd8dec69 | 89 | |
78a0c1f1 | 90 | BN_exp() raises I<a> to the I<p>-th power and places the result in I<r> |
dd8dec69 UM |
91 | (C<r=a^p>). This function is faster than repeated applications of |
92 | BN_mul(). | |
93 | ||
78a0c1f1 | 94 | BN_mod_exp() computes I<a> to the I<p>-th power modulo I<m> (C<r=a^p % |
3a070e25 MC |
95 | m>). This function uses less time and space than BN_exp(). Do not call this |
96 | function when B<m> is even and any of the parameters have the | |
97 | B<BN_FLG_CONSTTIME> flag set. | |
dd8dec69 | 98 | |
78a0c1f1 BM |
99 | BN_gcd() computes the greatest common divisor of I<a> and I<b> and |
100 | places the result in I<r>. I<r> may be the same B<BIGNUM> as I<a> or | |
101 | I<b>. | |
dd8dec69 | 102 | |
78a0c1f1 | 103 | For all functions, I<ctx> is a previously allocated B<BN_CTX> used for |
9b86974e | 104 | temporary variables; see L<BN_CTX_new(3)>. |
dd8dec69 UM |
105 | |
106 | Unless noted otherwise, the result B<BIGNUM> must be different from | |
107 | the arguments. | |
108 | ||
109 | =head1 RETURN VALUES | |
110 | ||
111 | For all functions, 1 is returned for success, 0 on error. The return | |
112 | value should always be checked (e.g., C<if (!BN_add(r,a,b)) goto err;>). | |
9b86974e | 113 | The error codes can be obtained by L<ERR_get_error(3)>. |
dd8dec69 UM |
114 | |
115 | =head1 SEE ALSO | |
116 | ||
9e183d22 | 117 | L<ERR_get_error(3)>, L<BN_CTX_new(3)>, |
9b86974e | 118 | L<BN_add_word(3)>, L<BN_set_bit(3)> |
dd8dec69 | 119 | |
e2f92610 RS |
120 | =head1 COPYRIGHT |
121 | ||
83cf7abf | 122 | Copyright 2000-2018 The OpenSSL Project Authors. All Rights Reserved. |
e2f92610 | 123 | |
4746f25a | 124 | Licensed under the Apache License 2.0 (the "License"). You may not use |
e2f92610 RS |
125 | this file except in compliance with the License. You can obtain a copy |
126 | in the file LICENSE in the source distribution or at | |
127 | L<https://www.openssl.org/source/license.html>. | |
128 | ||
129 | =cut |