1BN_ADD(3)                           OpenSSL                          BN_ADD(3)
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NAME

6       BN_add, BN_sub, BN_mul, BN_sqr, BN_div, BN_mod, BN_nnmod, BN_mod_add,
7       BN_mod_sub, BN_mod_mul, BN_mod_sqr, BN_exp, BN_mod_exp, BN_gcd -
8       arithmetic operations on BIGNUMs
9

SYNOPSIS

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
19        int BN_sqr(BIGNUM *r, BIGNUM *a, BN_CTX *ctx);
20
21        int BN_div(BIGNUM *dv, BIGNUM *rem, const BIGNUM *a, const BIGNUM *d,
22                   BN_CTX *ctx);
23
24        int BN_mod(BIGNUM *rem, const BIGNUM *a, const BIGNUM *m, BN_CTX *ctx);
25
26        int BN_nnmod(BIGNUM *r, const BIGNUM *a, const BIGNUM *m, BN_CTX *ctx);
27
28        int BN_mod_add(BIGNUM *r, BIGNUM *a, BIGNUM *b, const BIGNUM *m,
29                       BN_CTX *ctx);
30
31        int BN_mod_sub(BIGNUM *r, BIGNUM *a, BIGNUM *b, const BIGNUM *m,
32                       BN_CTX *ctx);
33
34        int BN_mod_mul(BIGNUM *r, BIGNUM *a, BIGNUM *b, const BIGNUM *m,
35                       BN_CTX *ctx);
36
37        int BN_mod_sqr(BIGNUM *r, BIGNUM *a, const BIGNUM *m, BN_CTX *ctx);
38
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,
42                       const BIGNUM *m, BN_CTX *ctx);
43
44        int BN_gcd(BIGNUM *r, BIGNUM *a, BIGNUM *b, BN_CTX *ctx);
45

DESCRIPTION

47       BN_add() adds a and b and places the result in r ("r=a+b").  r may be
48       the same BIGNUM as a or b.
49
50       BN_sub() subtracts b from a and places the result in r ("r=a-b").  r
51       may be the same BIGNUM as a or b.
52
53       BN_mul() multiplies a and b and places the result in r ("r=a*b").  r
54       may be the same BIGNUM as a or b.  For multiplication by powers of 2,
55       use BN_lshift(3).
56
57       BN_sqr() takes the square of a and places the result in r ("r=a^2"). r
58       and a may be the same BIGNUM.  This function is faster than
59       BN_mul(r,a,a).
60
61       BN_div() divides a by d and places the result in dv and the remainder
62       in rem ("dv=a/d, rem=a%d"). Either of dv and rem may be NULL, in which
63       case the respective value is not returned.  The result is rounded
64       towards zero; thus if a is negative, the remainder will be zero or
65       negative.  For division by powers of 2, use BN_rshift(3).
66
67       BN_mod() corresponds to BN_div() with dv set to NULL.
68
69       BN_nnmod() reduces a modulo m and places the non-negative remainder in
70       r.
71
72       BN_mod_add() adds a to b modulo m and places the non-negative result in
73       r.
74
75       BN_mod_sub() subtracts b from a modulo m and places the non-negative
76       result in r.
77
78       BN_mod_mul() multiplies a by b and finds the non-negative remainder
79       respective to modulus m ("r=(a*b) mod m"). r may be the same BIGNUM as
80       a or b. For more efficient algorithms for repeated computations using
81       the same modulus, see BN_mod_mul_montgomery(3) and
82       BN_mod_mul_reciprocal(3).
83
84       BN_mod_sqr() takes the square of a modulo m and places the result in r.
85
86       BN_exp() raises a to the p-th power and places the result in r
87       ("r=a^p"). This function is faster than repeated applications of
88       BN_mul().
89
90       BN_mod_exp() computes a to the p-th power modulo m ("r=a^p % m"). This
91       function uses less time and space than BN_exp(). Do not call this
92       function when m is even and any of the parameters have the
93       BN_FLG_CONSTTIME flag set.
94
95       BN_gcd() computes the greatest common divisor of a and b and places the
96       result in r. r may be the same BIGNUM as a or b.
97
98       For all functions, ctx is a previously allocated BN_CTX used for
99       temporary variables; see BN_CTX_new(3).
100
101       Unless noted otherwise, the result BIGNUM must be different from the
102       arguments.
103

RETURN VALUES

105       For all functions, 1 is returned for success, 0 on error. The return
106       value should always be checked (e.g., "if (!BN_add(r,a,b)) goto err;").
107       The error codes can be obtained by ERR_get_error(3).
108

SEE ALSO

110       ERR_get_error(3), BN_CTX_new(3), BN_add_word(3), BN_set_bit(3)
111

113       Copyright 2000-2018 The OpenSSL Project Authors. All Rights Reserved.
114
115       Licensed under the OpenSSL license (the "License").  You may not use
116       this file except in compliance with the License.  You can obtain a copy
117       in the file LICENSE in the source distribution or at
118       <https://www.openssl.org/source/license.html>.
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1221.1.1d                            2019-10-03                         BN_ADD(3)
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