NAME
BN_mod_sqrt —
square root in a prime field
SYNOPSIS
#include
<openssl/bn.h>
BIGNUM *
BN_mod_sqrt(BIGNUM *r,
const BIGNUM *a, const BIGNUM
*p, BN_CTX *ctx);
DESCRIPTION
BN_mod_sqrt()
solves
for r in the prime field of characteristic p using the Tonelli-Shanks algorithm if needed and places one of the two solutions into r. The other solution is p - r.
The argument p is expected to be a prime number.
RETURN VALUES
In case of success, BN_mod_sqrt() returns
r, or a newly allocated BIGNUM
object if the r argument is
NULL.
In case of failure, NULL is returned. This
for example happens if a is not a quadratic residue or
if memory allocation fails.
SEE ALSO
BN_CTX_new(3), BN_kronecker(3), BN_mod_sqr(3), BN_new(3)
Henri Cohen, A Course in Computational Algebraic Number Theory, Springer, Berlin, 1993, Algorithm 1.5.1.
HISTORY
BN_mod_sqrt() first appeared in OpenSSL
0.9.7 and has been available since OpenBSD 3.2.
CAVEATS
If p is not prime,
BN_mod_sqrt() may succeed or fail. If it succeeds,
the square of the returned value is congruent to a
modulo p. If it fails, the reason reported by
ERR_get_error(3) is often misleading. In particular, even if
a is a perfect square,
BN_mod_sqrt() often reports “not a
square” instead of “p is not prime”.