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About permutations on the sets of tuples from elements of the finite field
V. S. Kugurakov, A. F. Gainutdinova, V. T. Dubrovin Kazan Federal University, Kazan, 420008
Russia
Abstract:
The following problem was considered: let S=S1×S2×⋯×SmS=S1×S2×⋯×Sm be the Cartesian product of subsets SiSi 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∈Fq[x1,…,xm]. 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.
Keywords:
cryptography, error-correcting codes, finite fields, permutation polynomials.
Received: 11.03.2019
Citation:
V. S. Kugurakov, A. F. Gainutdinova, V. T. Dubrovin, “About permutations on the sets of tuples from elements of the finite field”, Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki, 161, no. 2, Kazan University, Kazan, 2019, 292–300
Linking options:
https://www.mathnet.ru/eng/uzku1518 https://www.mathnet.ru/eng/uzku/v161/i2/p292
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Abstract page: | 252 | Full-text PDF : | 116 | References: | 26 |
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