Square Root Computation In Finite Fields

Abstract

In this paper, we present a review of three widely-used practical square root algorithms. We then describe a unifying framework where each of these well-known algorithms can be seen as a special case of it. The framework with singular curves offers a broad perspective to compare and further improve the existing methods in addition to offering a new avenue for square root computation algorithms in finite fields.

arXiv comment13 Pages. For the case when p is 5 (mod 8), a fault in the second case removed. We have included a simple example to explain each of algorithm via a singular cubic. We have implemented the three algorithms and the algorithm with a singular cubic in the same environment. The curve has been changed and then the new singular point will be (-a,0)