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arXiv · 1309.2831

On Calculating Square Roots in GF(p)

David S. Knight
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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.

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David S. Knight. 2013-09-10. On Calculating Square Roots in GF(p). https://arxiv.org/abs/1309.2831

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