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_mod_sqrt, BN_exp, BN_mod_exp,
8       BN_gcd - arithmetic operations on BIGNUMs
9

SYNOPSIS

11        #include <openssl/bn.h>
12
13        int BN_add(BIGNUM *r, const BIGNUM *a, const BIGNUM *b);
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15        int BN_sub(BIGNUM *r, const BIGNUM *a, const BIGNUM *b);
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17        int BN_mul(BIGNUM *r, BIGNUM *a, BIGNUM *b, BN_CTX *ctx);
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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);
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28        int BN_mod_add(BIGNUM *r, BIGNUM *a, BIGNUM *b, const BIGNUM *m,
29                       BN_CTX *ctx);
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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);
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37        int BN_mod_sqr(BIGNUM *r, BIGNUM *a, const BIGNUM *m, BN_CTX *ctx);
38
39        BIGNUM *BN_mod_sqrt(BIGNUM *in, BIGNUM *a, const BIGNUM *p, BN_CTX *ctx);
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41        int BN_exp(BIGNUM *r, BIGNUM *a, BIGNUM *p, BN_CTX *ctx);
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43        int BN_mod_exp(BIGNUM *r, BIGNUM *a, const BIGNUM *p,
44                       const BIGNUM *m, BN_CTX *ctx);
45
46        int BN_gcd(BIGNUM *r, BIGNUM *a, BIGNUM *b, BN_CTX *ctx);
47

DESCRIPTION

49       BN_add() adds a and b and places the result in r ("r=a+b").  r may be
50       the same BIGNUM as a or b.
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52       BN_sub() subtracts b from a and places the result in r ("r=a-b").  r
53       may be the same BIGNUM as a or b.
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55       BN_mul() multiplies a and b and places the result in r ("r=a*b").  r
56       may be the same BIGNUM as a or b.  For multiplication by powers of 2,
57       use BN_lshift(3).
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59       BN_sqr() takes the square of a and places the result in r ("r=a^2"). r
60       and a may be the same BIGNUM.  This function is faster than
61       BN_mul(r,a,a).
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63       BN_div() divides a by d and places the result in dv and the remainder
64       in rem ("dv=a/d, rem=a%d"). Either of dv and rem may be NULL, in which
65       case the respective value is not returned.  The result is rounded
66       towards zero; thus if a is negative, the remainder will be zero or
67       negative.  For division by powers of 2, use BN_rshift(3).
68
69       BN_mod() corresponds to BN_div() with dv set to NULL.
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71       BN_nnmod() reduces a modulo m and places the nonnegative remainder in
72       r.
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74       BN_mod_add() adds a to b modulo m and places the nonnegative result in
75       r.
76
77       BN_mod_sub() subtracts b from a modulo m and places the nonnegative
78       result in r.
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80       BN_mod_mul() multiplies a by b and finds the nonnegative remainder
81       respective to modulus m ("r=(a*b) mod m"). r may be the same BIGNUM as
82       a or b. For more efficient algorithms for repeated computations using
83       the same modulus, see BN_mod_mul_montgomery(3) and
84       BN_mod_mul_reciprocal(3).
85
86       BN_mod_sqr() takes the square of a modulo m and places the result in r.
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88       BN_mod_sqrt() returns the modular square root of a such that "in^2 = a
89       (mod p)". The modulus p must be a prime, otherwise an error or an
90       incorrect "result" will be returned.  The result is stored into in
91       which can be NULL. The result will be newly allocated in that case.
92
93       BN_exp() raises a to the p-th power and places the result in r
94       ("r=a^p"). This function is faster than repeated applications of
95       BN_mul().
96
97       BN_mod_exp() computes a to the p-th power modulo m ("r=a^p % m"). This
98       function uses less time and space than BN_exp(). Do not call this
99       function when m is even and any of the parameters have the
100       BN_FLG_CONSTTIME flag set.
101
102       BN_gcd() computes the greatest common divisor of a and b and places the
103       result in r. r may be the same BIGNUM as a or b.
104
105       For all functions, ctx is a previously allocated BN_CTX used for
106       temporary variables; see BN_CTX_new(3).
107
108       Unless noted otherwise, the result BIGNUM must be different from the
109       arguments.
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RETURN VALUES

112       The BN_mod_sqrt() returns the result (possibly incorrect if p is not a
113       prime), or NULL.
114
115       For all remaining functions, 1 is returned for success, 0 on error. The
116       return value should always be checked (e.g., "if (!BN_add(r,a,b)) goto
117       err;").  The error codes can be obtained by ERR_get_error(3).
118

SEE ALSO

120       ERR_get_error(3), BN_CTX_new(3), BN_add_word(3), BN_set_bit(3)
121

123       Copyright 2000-2022 The OpenSSL Project Authors. All Rights Reserved.
124
125       Licensed under the OpenSSL license (the "License").  You may not use
126       this file except in compliance with the License.  You can obtain a copy
127       in the file LICENSE in the source distribution or at
128       <https://www.openssl.org/source/license.html>.
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1321.1.1q                            2022-07-07                         BN_ADD(3)
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