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

RETURN VALUES

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

SEE ALSO

107       bn(3), ERR_get_error(3), BN_CTX_new(3), BN_add_word(3), BN_set_bit(3)
108

HISTORY

110       BN_add(), BN_sub(), BN_sqr(), BN_div(), BN_mod(), BN_mod_mul(),
111       BN_mod_exp() and BN_gcd() are available in all versions of SSLeay and
112       OpenSSL. The ctx argument to BN_mul() was added in SSLeay 0.9.1b.
113       BN_exp() appeared in SSLeay 0.9.0.  BN_nnmod(), BN_mod_add(),
114       BN_mod_sub(), and BN_mod_sqr() were added in OpenSSL 0.9.7.
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1181.0.2o                            2020-01-28                         BN_add(3)