Faisal, . and Rojali, . and Mohd Sham, Mohamad (2021) An algorithms for finding the cube roots in finite fields. Procedia Computer Science, 179. 838 844. ISSN 18770509. (Published)

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Abstract
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.
Item Type:  Article 

Additional Information:  Indexed by Scopus 
Uncontrolled Keywords:  Cube root; Cubic residue; Finite field; Primitive element 
Subjects:  Q Science > QA Mathematics 
Faculty/Division:  Faculty of Industrial Sciences And Technology Center for Mathematical Science 
Depositing User:  Mrs Norsaini Abdul Samat 
Date Deposited:  10 Nov 2021 04:49 
Last Modified:  10 Nov 2021 04:49 
URI:  http://umpir.ump.edu.my/id/eprint/32421 
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