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Register a new userOn permutation quadrinomials and $4$-uniform BCT
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Added by
Maosheng Xiong
Publication date
2020
fields
Informatics Engineering
and research's language is
English
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We study a class of general quadrinomials over the field of size $2^{2m}$ with odd $m$ and characterize conditions under which they are permutations with the best boomerang uniformity, a new and important parameter related to boomerang-style attacks. This vastly extends previous results from several recent papers.
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As a generalization of Dillons APN permutation, butterfly structure and generalizations have been of great interest since they generate permutations with the best known differential and nonlinear properties over the field of size $2^{4k+2}$. Complementary to these results, we show in this paper that butterfly structure, more precisely the closed butterfly also yields permutations with the best boomerang uniformity, a new and important parameter related to boomerang-style attacks. This is the sixth known infinite family of permutations in the literature with the best known boomerang uniformity over such fields.
In this paper, by the Hasse-Weil bound, we determine the necessary and sufficient condition on coefficients $a_1,a_2,a_3inmathbb{F}_{2^n}$ with $n=2m$ such that $f(x) = {x}^{3cdot2^m} + a_1x^{2^{m+1}+1} + a_2 x^{2^m+2} + a_3x^3$ is an APN function over $mathbb{F}_{2^n}$. Our result resolves the first half of an open problem by Carlet in International Workshop on the Arithmetic of Finite Fields, 83-107, 2014.
Permutation polynomials over finite fields have important applications in many areas of science and engineering such as coding theory, cryptography, combinatorial design, etc. In this paper, we construct several new classes of permutation polynomials, and the necessities of some permutation polynomials are studied.
Let $mathbb{F}_q$ denote the finite fields with $q$ elements. The permutation behavior of several classes of infinite families of permutation polynomials over finite fields have been studied in recent years. In this paper, we continue with their studies, and get some further results about the permutation properties of the permutation polynomials. Also, some new classes of permutation polynomials are constructed. For these, we alter the coefficients, exponents or the underlying fields, etc.
In this work we establish some new interleavers based on permutation functions. The inverses of these interleavers are known over a finite field $mathbb{F}_q$. For the first time M{o}bius and Redei functions are used to give new deterministic interleavers. Furthermore we employ Skolem sequences in order to find new interleavers with known cycle structure. In the case of Redei functions an exact formula for the inverse function is derived. The cycle structure of Redei functions is also investigated. The self-inverse and non-self-inver
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