BN_add.pod revision 337982 
1=pod
2
3=head1 NAME
4
5BN_add, BN_sub, BN_mul, BN_sqr, BN_div, BN_mod, BN_nnmod, BN_mod_add,
6BN_mod_sub, BN_mod_mul, BN_mod_sqr, BN_exp, BN_mod_exp, BN_gcd -
7arithmetic operations on BIGNUMs
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
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
46=head1 DESCRIPTION
47
48BN_add() adds I<a> and I<b> and places the result in I<r> (C<r=a+b>).
49I<r> may be the same B<BIGNUM> as I<a> or I<b>.
50
51BN_sub() subtracts I<b> from I<a> and places the result in I<r> (C<r=a-b>).
52
53BN_mul() multiplies I<a> and I<b> and places the result in I<r> (C<r=a*b>).
54I<r> may be the same B<BIGNUM> as I<a> or I<b>.
55For multiplication by powers of 2, use L<BN_lshift(3)|BN_lshift(3)>.
56
57BN_sqr() takes the square of I<a> and places the result in I<r>
58(C<r=a^2>). I<r> and I<a> may be the same B<BIGNUM>.
59This function is faster than BN_mul(r,a,a).
60
61BN_div() divides I<a> by I<d> and places the result in I<dv> and the
62remainder in I<rem> (C<dv=a/d, rem=a%d>). Either of I<dv> and I<rem> may
63be B<NULL>, in which case the respective value is not returned.
64The result is rounded towards zero; thus if I<a> is negative, the
65remainder will be zero or negative.
66For division by powers of 2, use BN_rshift(3).
67
68BN_mod() corresponds to BN_div() with I<dv> set to B<NULL>.
69
70BN_nnmod() reduces I<a> modulo I<m> and places the non-negative
71remainder in I<r>.
72
73BN_mod_add() adds I<a> to I<b> modulo I<m> and places the non-negative
74result in I<r>.
75
76BN_mod_sub() subtracts I<b> from I<a> modulo I<m> and places the
77non-negative result in I<r>.
78
79BN_mod_mul() multiplies I<a> by I<b> and finds the non-negative
80remainder respective to modulus I<m> (C<r=(a*b) mod m>). I<r> may be
81the same B<BIGNUM> as I<a> or I<b>. For more efficient algorithms for
82repeated computations using the same modulus, see
83L<BN_mod_mul_montgomery(3)|BN_mod_mul_montgomery(3)> and
84L<BN_mod_mul_reciprocal(3)|BN_mod_mul_reciprocal(3)>.
85
86BN_mod_sqr() takes the square of I<a> modulo B<m> and places the
87result in I<r>.
88
89BN_exp() raises I<a> to the I<p>-th power and places the result in I<r>
90(C<r=a^p>). This function is faster than repeated applications of
91BN_mul().
92
93BN_mod_exp() computes I<a> to the I<p>-th power modulo I<m> (C<r=a^p %
94m>). This function uses less time and space than BN_exp(). Do not call this
95function when B<m> is even and any of the parameters have the
96B<BN_FLG_CONSTTIME> flag set.
97
98BN_gcd() computes the greatest common divisor of I<a> and I<b> and
99places the result in I<r>. I<r> may be the same B<BIGNUM> as I<a> or
100I<b>.
101
102For all functions, I<ctx> is a previously allocated B<BN_CTX> used for
103temporary variables; see L<BN_CTX_new(3)|BN_CTX_new(3)>.
104
105Unless noted otherwise, the result B<BIGNUM> must be different from
106the arguments.
107
108=head1 RETURN VALUES
109
110For all functions, 1 is returned for success, 0 on error. The return
111value should always be checked (e.g., C<if (!BN_add(r,a,b)) goto err;>).
112The error codes can be obtained by L<ERR_get_error(3)|ERR_get_error(3)>.
113
114=head1 SEE ALSO
115
116L<bn(3)|bn(3)>, L<ERR_get_error(3)|ERR_get_error(3)>, L<BN_CTX_new(3)|BN_CTX_new(3)>,
117L<BN_add_word(3)|BN_add_word(3)>, L<BN_set_bit(3)|BN_set_bit(3)>
118
119=head1 HISTORY
120
121BN_add(), BN_sub(), BN_sqr(), BN_div(), BN_mod(), BN_mod_mul(),
122BN_mod_exp() and BN_gcd() are available in all versions of SSLeay and
123OpenSSL. The I<ctx> argument to BN_mul() was added in SSLeay
1240.9.1b. BN_exp() appeared in SSLeay 0.9.0.
125BN_nnmod(), BN_mod_add(), BN_mod_sub(), and BN_mod_sqr() were added in
126OpenSSL 0.9.7.
127
128=cut
129