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Register a new userA complete characterization of the APN property of a class of quadrinomials
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Added by
Kangquan Li
Publication date
2020
fields
Informatics Engineering
and research's language is
English
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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.
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For the finite field $mathbb{F}_{2^{3m}}$, permutation polynomials of the form $(x^{2^m}+x+delta)^{s}+cx$ are studied. Necessary and sufficient conditions are given for the polynomials to be permutation polynomials. For this, the structures and properties of the field elements are analyzed.
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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.
Cognitive radios have been studied recently as a means to utilize spectrum in a more efficient manner. This paper focuses on the fundamental limits of operation of a MIMO cognitive radio network with a single licensed user and a single cognitive user. The channel setting is equivalent to an interference channel with degraded message sets (with the cognitive user having access to the licensed users message). An achievable region and an outer bound is derived for such a network setting. It is shown that under certain conditions, the achievable region is optimal for a portion of the capacity region that includes sum capacity.
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