A new method to investigate the CCZ-equivalence between functions with low differential uniformity
نویسندگان
چکیده
منابع مشابه
A new method to investigate the CCZ-equivalence between functions with low differential uniformity
Recently, many new classes of differentially 4-uniform permutations have been constructed. However, it is difficult to decide whether they are CCZ-inequivalent or not. In this paper, we propose a new notion called ”Projected Differential Spectrum”. By considering the properties of the projected differential spectrum, we find several relations that should be satisfied by CCZ-equivalent functions...
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We study further CCZ-equivalence of (n,m)-functions. We prove that for Boolean functions (that is, for m = 1), CCZ-equivalence coincides with EA-equivalence. On the contrary, we show that for (n,m)functions, CCZ-equivalence is strictly more general than EAequivalence when n ≥ 5 and m is greater or equal to the smallest positive divisor of n different from 1. Our result on Boolean functions allo...
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In this paper, for an odd prime p, the differential spectrum of the power function x pk+1 2 in Fpn is calculated. For an odd prime p such that p ≡ 3 mod 4 and odd n with k|n, the differential spectrum of the power function x pn+1 pk+1 + p n −1 2 in Fpn is also derived. From their differential spectrums, the differential uniformities of these two power functions are determined. We also find some...
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EA-equivalence classes and the more general CCZ-equivalence classes of functions over GF (2) each preserve APN and AB properties desirable for S-box functions. We show that they can be related to subsets c[T ] and g[T ] of equivalence classes [T ] of transversals, respectively, thus clarifying their relationship and providing a new approach to their study. We derive a formula which characterise...
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A function F from Fpn to itself is planar if for any a ∈F ∗ pn the function F (x+ a)−F (x) is a permutation. CCZ-equivalence is the most general known equivalence relation of functions preserving planar property. This paper considers two possible extensions of CCZ-equivalence for functions over fields of odd characteristics, one proposed by Coulter and Henderson and the other by Budaghyan and C...
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ژورنال
عنوان ژورنال: Finite Fields and Their Applications
سال: 2016
ISSN: 1071-5797
DOI: 10.1016/j.ffa.2016.07.007