Square Root Computation In Finite Fields

TL;DR

This paper reviews three practical algorithms for square root computation in finite fields, introduces a unifying framework that encompasses these methods, and suggests potential improvements and new algorithms within this framework.

Contribution

It provides a unifying framework for existing algorithms, enabling comparison and potential enhancement of square root computations in finite fields.

Findings

The framework unifies three well-known algorithms.

Singular curves offer new avenues for algorithm development.

Potential for improved efficiency in finite field square root computations.

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.