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).
r may be the same BIGNUM as
a or 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). If the flag
BN_FLG_CONSTTIME is set on a
or d, it operates in constant time. 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. It is
implemented as a macro.
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)%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). If the
flag BN_FLG_CONSTTIME is set on
p, it operates in constant time. 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, for example:
if (!BN_add(r,a,b)) goto
err;The error codes can be obtained by ERR_get_error(3).
SEE ALSO
BN_add_word(3), BN_CTX_new(3), BN_new(3), BN_set_bit(3), BN_set_flags(3), BN_set_negative(3)
HISTORY
BN_add(),
BN_sub(), BN_mul(),
BN_sqr(), BN_div(),
BN_mod(), BN_mod_mul(),
BN_mod_exp(), and BN_gcd()
first appeared in SSLeay 0.5.1. BN_exp() first
appeared in SSLeay 0.9.0. All these functions have been available since
OpenBSD 2.4.
The ctx argument to
BN_mul() was added in SSLeay 0.9.1 and
OpenBSD 2.6.
BN_nnmod(),
BN_mod_add(), BN_mod_sub(),
and BN_mod_sqr() first appeared in OpenSSL 0.9.7 and
have been available since OpenBSD 3.2.
BUGS
Even if the BN_FLG_CONSTTIME flag is set
on a or b,
BN_gcd() neither fails nor operates in constant
time, potentially allowing timing side-channel attacks.
Even if the BN_FLG_CONSTTIME flag is set
on p, if the modulus m is even,
BN_mod_exp() does not operate in constant time,
potentially allowing timing side-channel attacks.
If BN_FLG_CONSTTIME is set on
p, BN_exp() fails instead of
operating in constant time.