BN_MOD_SQRT(3) Library Functions Manual BN_MOD_SQRT(3)
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
r sup 2 == a ( roman mod p )
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”. GNU December 6, 2022 BN_MOD_SQRT(3)