NAME¶
BN_add, BN_sub, BN_mul, BN_sqr, BN_div, BN_mod, BN_nnmod, BN_mod_add,
BN_mod_sub, BN_mod_mul, BN_mod_sqr, BN_exp, BN_mod_exp, BN_gcd - arithmetic
operations on BIGNUMs
SYNOPSIS¶
#include <openssl/bn.h>
int BN_add(BIGNUM *r, const BIGNUM *a, const BIGNUM *b);
int BN_sub(BIGNUM *r, const BIGNUM *a, const BIGNUM *b);
int BN_mul(BIGNUM *r, BIGNUM *a, BIGNUM *b, BN_CTX *ctx);
int BN_sqr(BIGNUM *r, BIGNUM *a, BN_CTX *ctx);
int BN_div(BIGNUM *dv, BIGNUM *rem, const BIGNUM *a, const BIGNUM *d,
BN_CTX *ctx);
int BN_mod(BIGNUM *rem, const BIGNUM *a, const BIGNUM *m, BN_CTX *ctx);
int BN_nnmod(BIGNUM *r, const BIGNUM *a, const BIGNUM *m, BN_CTX *ctx);
int BN_mod_add(BIGNUM *r, BIGNUM *a, BIGNUM *b, const BIGNUM *m,
BN_CTX *ctx);
int BN_mod_sub(BIGNUM *r, BIGNUM *a, BIGNUM *b, const BIGNUM *m,
BN_CTX *ctx);
int BN_mod_mul(BIGNUM *r, BIGNUM *a, BIGNUM *b, const BIGNUM *m,
BN_CTX *ctx);
int BN_mod_sqr(BIGNUM *r, BIGNUM *a, const BIGNUM *m, BN_CTX *ctx);
int BN_exp(BIGNUM *r, BIGNUM *a, BIGNUM *p, BN_CTX *ctx);
int BN_mod_exp(BIGNUM *r, BIGNUM *a, const BIGNUM *p,
const BIGNUM *m, BN_CTX *ctx);
int BN_gcd(BIGNUM *r, BIGNUM *a, BIGNUM *b, BN_CTX *ctx);
DESCRIPTION¶
BN_add() adds
a and
b and places the result in
r
("r=a+b").
r may be the same
BIGNUM as
a or
b.
BN_sub() subtracts
b from
a and places the result in
r ("r=a-b").
BN_mul() multiplies
a and
b and places the result in
r ("r=a*b").
r may be the same
BIGNUM as
a or
b. For multiplication by powers of 2, use
BN_lshift(3).
BN_sqr() takes the square of
a and places the result in
r
("r=a^2").
r and
a may be the same
BIGNUM. This
function is faster than BN_mul(r,a,a).
BN_div() divides
a by
d and places the result in
dv
and the remainder in
rem ("dv=a/d, rem=a%d"). Either of
dv and
rem may be
NULL, in which case the respective
value is not returned. The result is rounded towards zero; thus if
a is
negative, the remainder will be zero or negative. For division by powers of 2,
use
BN_rshift(3).
BN_mod() corresponds to
BN_div() with
dv set to
NULL.
BN_nnmod() reduces
a modulo
m and places the non-negative
remainder in
r.
BN_mod_add() adds
a to
b modulo
m and places the
non-negative result in
r.
BN_mod_sub() subtracts
b from
a modulo
m and places
the non-negative result in
r.
BN_mod_mul() multiplies
a by
b and finds the non-negative
remainder respective to modulus
m ("r=(a*b) mod m").
r
may be the same
BIGNUM as
a or
b. For more efficient
algorithms for repeated computations using the same modulus, see
BN_mod_mul_montgomery(3) and
BN_mod_mul_reciprocal(3).
BN_mod_sqr() takes the square of
a modulo
m and places the
result in
r.
BN_exp() raises
a to the
p-th power and places the result
in
r ("r=a^p"). This function is faster than repeated
applications of
BN_mul().
BN_mod_exp() computes
a to the
p-th power modulo
m
("r=a^p % m"). This function uses less time and space than
BN_exp().
BN_gcd() computes the greatest common divisor of
a and
b
and places the result in
r.
r may be the same
BIGNUM as
a or
b.
For all functions,
ctx is a previously allocated
BN_CTX used for
temporary variables; see
BN_CTX_new(3).
Unless noted otherwise, the result
BIGNUM must be different from the
arguments.
RETURN VALUES¶
For all functions, 1 is returned for success, 0 on error. The return value
should always be checked (e.g., "if (!BN_add(r,a,b)) goto err;").
The error codes can be obtained by
ERR_get_error(3).
SEE ALSO¶
bn(3),
ERR_get_error(3),
BN_CTX_new(3),
BN_add_word(3),
BN_set_bit(3)
HISTORY¶
BN_add(),
BN_sub(),
BN_sqr(),
BN_div(),
BN_mod(),
BN_mod_mul(),
BN_mod_exp() and
BN_gcd()
are available in all versions of SSLeay and OpenSSL. The
ctx argument
to
BN_mul() was added in SSLeay 0.9.1b.
BN_exp() appeared in
SSLeay 0.9.0.
BN_nnmod(),
BN_mod_add(),
BN_mod_sub(), and
BN_mod_sqr() were added in OpenSSL 0.9.7.