About permutations on the sets of tuples from elements of the finite field
The following problem was considered: let S = S1× S2×…× Sm be the Cartesian product of subsets Si that are subgroups of the multiplicative group of a finite field Fq of q elements or their extensions by adding a zero element; a map f: S→ S of S into itself can be specified by a system of polynomials...
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| Format: | Article |
| Language: | English |
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Kazan Federal University
2019-06-01
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| Series: | Учёные записки Казанского университета: Серия Физико-математические науки |
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| Online Access: | https://kpfu.ru/uz-eng-phm-2019-2-9.html |
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| author | V.S. Kugurakov A.F. Gainutdinova V.T. Dubrovin |
| author_facet | V.S. Kugurakov A.F. Gainutdinova V.T. Dubrovin |
| author_sort | V.S. Kugurakov |
| collection | DOAJ |
| description | The following problem was considered: let S = S1× S2×…× Sm be the Cartesian product of subsets Si that are subgroups of the multiplicative group of a finite field Fq of q elements or their extensions by adding a zero element; a map f: S→ S of S into itself can be specified by a system of polynomials f1,…,fm є Fq[x1,…,x m]. Necessary and sufficient conditions, for which the map f =< f1,…,fm > is bijective, were obtained. Then this problem was generalized to the case when the subsets Si are any subsets of Fq. The obtained results can be used to construct S-boxes and P-boxes in block ciphers and to calculate automorphism groups of error-correcting codes. |
| format | Article |
| id | doaj-art-ef695839b74d4b7a9a591ab8458e4934 |
| institution | Kabale University |
| issn | 2541-7746 2500-2198 |
| language | English |
| publishDate | 2019-06-01 |
| publisher | Kazan Federal University |
| record_format | Article |
| series | Учёные записки Казанского университета: Серия Физико-математические науки |
| spelling | doaj-art-ef695839b74d4b7a9a591ab8458e49342025-01-03T00:04:28ZengKazan Federal UniversityУчёные записки Казанского университета: Серия Физико-математические науки2541-77462500-21982019-06-01161229230010.26907/2541-7746.2019.2.292-300About permutations on the sets of tuples from elements of the finite fieldV.S. Kugurakov0A.F. Gainutdinova1V.T. Dubrovin2Kazan Federal University, Kazan, 420008 RussiaKazan Federal University, Kazan, 420008 RussiaKazan Federal University, Kazan, 420008 RussiaThe following problem was considered: let S = S1× S2×…× Sm be the Cartesian product of subsets Si that are subgroups of the multiplicative group of a finite field Fq of q elements or their extensions by adding a zero element; a map f: S→ S of S into itself can be specified by a system of polynomials f1,…,fm є Fq[x1,…,x m]. Necessary and sufficient conditions, for which the map f =< f1,…,fm > is bijective, were obtained. Then this problem was generalized to the case when the subsets Si are any subsets of Fq. The obtained results can be used to construct S-boxes and P-boxes in block ciphers and to calculate automorphism groups of error-correcting codes.https://kpfu.ru/uz-eng-phm-2019-2-9.htmlcryptographyerror-correcting codesfinite fieldspermutation polynomials |
| spellingShingle | V.S. Kugurakov A.F. Gainutdinova V.T. Dubrovin About permutations on the sets of tuples from elements of the finite field Учёные записки Казанского университета: Серия Физико-математические науки cryptography error-correcting codes finite fields permutation polynomials |
| title | About permutations on the sets of tuples from elements of the finite field |
| title_full | About permutations on the sets of tuples from elements of the finite field |
| title_fullStr | About permutations on the sets of tuples from elements of the finite field |
| title_full_unstemmed | About permutations on the sets of tuples from elements of the finite field |
| title_short | About permutations on the sets of tuples from elements of the finite field |
| title_sort | about permutations on the sets of tuples from elements of the finite field |
| topic | cryptography error-correcting codes finite fields permutation polynomials |
| url | https://kpfu.ru/uz-eng-phm-2019-2-9.html |
| work_keys_str_mv | AT vskugurakov aboutpermutationsonthesetsoftuplesfromelementsofthefinitefield AT afgainutdinova aboutpermutationsonthesetsoftuplesfromelementsofthefinitefield AT vtdubrovin aboutpermutationsonthesetsoftuplesfromelementsofthefinitefield |