A simple and fast probabilistic algorithm for computing square roots modulo a prime number (Corresp.)

A probabilistic polynomial-time algorithm for computing the square root of a number
x \in {\bf Z}/P{\bf Z}
, where
P = 2^{S}Q + 1(Q
odd,
s > 0)
is a prime number, is described. In contrast to the Adleman, Manders, and Miller algorithm, this algorithm gets faster as s grows. As with the Berlekamp-Rabin algorithm, the expected running time of the algorithm is independent of
x
. However, the algorithm presented here is considerably faster for values of
s
greater than
2
.