English

Square Root Computation In Finite Fields

Number Theory 2024-01-31 v3

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.

Keywords

Cite

@article{arxiv.2206.07145,
  title  = {Square Root Computation In Finite Fields},
  author = {Ebru Adiguzel-Goktas and Enver Ozdemir},
  journal= {arXiv preprint arXiv:2206.07145},
  year   = {2024}
}

Comments

13 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)

R2 v1 2026-06-24T11:51:29.262Z