On Calculating Square Roots in GF(p)
Abstract
This article presents a new method for calculating square roots in GF(p) by exponentiating in GF(p3) or equivalently modulo irreducible cubic polynomials. This algorithm is in some ways similar to the Cipolla-Lehmer algorithm which is based on exponentiating in GF(p2). Another less well known square root algorithm based on quadratic sums is also given. In addition to this, several conjectures about the output of this GF(p3) square root algorithm are mentioned.
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