An algorithms for finding the cube roots in finite fields

• Main Authors: Faisal, ., Rojali, ., Mohd Sham, Mohamad
• Format: Article
• Language: English
• Published: Elsevier 2021
• Subjects: QA Mathematics
• Online Access: http://umpir.ump.edu.my/id/eprint/32421/1/An%20algorithms%20for%20finding%20the%20cube%20roots%20in%20finite%20fields.pdf; http://umpir.ump.edu.my/id/eprint/32421/; https://doi.org/10.1016/j.procs.2021.01.072; https://doi.org/10.1016/j.procs.2021.01.072
• Institution: Universiti Malaysia Pahang

Let Fq be a finite field with q elements. Quadratic residues in number theory and finite fields is an important theory that has many applications in various aspects. The main problem of quadratic residues is to find the solution of the equation x2 = a, given an element a. It is interesting to find the solutions of x3 = a in Fq. If the solutions exist for a we say that a is a cubic residue of Fq and x is a cube root of a in Fq. In this paper we examine the solubility of x3 = a in general finite fields. Here, we give some results about the cube roots of cubic residue, and we propose an algorithm to find the cube roots using primitive elements.