An algorithms for finding the cube roots in finite fields
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 t...
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| Format: | Article |
| Language: | English |
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Elsevier
2021
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| Online Access: | http://umpir.ump.edu.my/id/eprint/32421/ http://umpir.ump.edu.my/id/eprint/32421/1/An%20algorithms%20for%20finding%20the%20cube%20roots%20in%20finite%20fields.pdf |
| _version_ | 1848824014411137024 |
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| author | Faisal, . Rojali, . Mohd Sham, Mohamad |
| author_facet | Faisal, . Rojali, . Mohd Sham, Mohamad |
| author_sort | Faisal, . |
| building | UMP Institutional Repository |
| collection | Online Access |
| description | 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. |
| first_indexed | 2025-11-15T03:06:18Z |
| format | Article |
| id | ump-32421 |
| institution | Universiti Malaysia Pahang |
| institution_category | Local University |
| language | English |
| last_indexed | 2025-11-15T03:06:18Z |
| publishDate | 2021 |
| publisher | Elsevier |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | ump-324212021-11-10T04:49:04Z http://umpir.ump.edu.my/id/eprint/32421/ An algorithms for finding the cube roots in finite fields Faisal, . Rojali, . Mohd Sham, Mohamad QA Mathematics 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. Elsevier 2021-02-19 Article PeerReviewed pdf en cc_by_nc_nd_4 http://umpir.ump.edu.my/id/eprint/32421/1/An%20algorithms%20for%20finding%20the%20cube%20roots%20in%20finite%20fields.pdf 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 1877-0509. (Published) https://doi.org/10.1016/j.procs.2021.01.072 https://doi.org/10.1016/j.procs.2021.01.072 |
| spellingShingle | QA Mathematics Faisal, . Rojali, . Mohd Sham, Mohamad An algorithms for finding the cube roots in finite fields |
| title | An algorithms for finding the cube roots in finite fields |
| title_full | An algorithms for finding the cube roots in finite fields |
| title_fullStr | An algorithms for finding the cube roots in finite fields |
| title_full_unstemmed | An algorithms for finding the cube roots in finite fields |
| title_short | An algorithms for finding the cube roots in finite fields |
| title_sort | algorithms for finding the cube roots in finite fields |
| topic | QA Mathematics |
| url | http://umpir.ump.edu.my/id/eprint/32421/ http://umpir.ump.edu.my/id/eprint/32421/ http://umpir.ump.edu.my/id/eprint/32421/ http://umpir.ump.edu.my/id/eprint/32421/1/An%20algorithms%20for%20finding%20the%20cube%20roots%20in%20finite%20fields.pdf |