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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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Kazan Federal University
2019-06-01
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| Series: | Учёные записки Казанского университета: Серия Физико-математические науки |
| Subjects: | |
| Online Access: | https://kpfu.ru/uz-eng-phm-2019-2-9.html |
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| Summary: | 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. |
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| ISSN: | 2541-7746 2500-2198 |