On Calculating Square Roots in GF(p)
Number Theory
2016-05-12 v3
Abstract
This article presents a new method for calculating square roots in GF(p) by exponentiating in GF(p^3) 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(p^2). 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(p^3) square root algorithm are mentioned.
Keywords
Cite
@article{arxiv.1309.2831,
title = {On Calculating Square Roots in GF(p)},
author = {David S. Knight},
journal= {arXiv preprint arXiv:1309.2831},
year = {2016}
}
Comments
18 pages; new section 5.2 on cubic reciprocity added