589 research outputs found
Differentially 4-uniform functions
We give a geometric characterization of vectorial boolean functions with
differential uniformity less or equal to 4
A Highly Nonlinear Differentially 4 Uniform Power Mapping That Permutes Fields of Even Degree
Functions with low differential uniformity can be used as the s-boxes of
symmetric cryptosystems as they have good resistance to differential attacks.
The AES (Advanced Encryption Standard) uses a differentially-4 uniform function
called the inverse function. Any function used in a symmetric cryptosystem
should be a permutation. Also, it is required that the function is highly
nonlinear so that it is resistant to Matsui's linear attack. In this article we
demonstrate that a highly nonlinear permutation discovered by Hans Dobbertin
has differential uniformity of four and hence, with respect to differential and
linear cryptanalysis, is just as suitable for use in a symmetric cryptosystem
as the inverse function.Comment: 10 pages, submitted to Finite Fields and Their Application
On differential uniformity of maps that may hide an algebraic trapdoor
We investigate some differential properties for permutations in the affine
group, of a vector space V over the binary field, with respect to a new group
operation , inducing an alternative vector space structure on .Comment: arXiv admin note: text overlap with arXiv:1411.768
On the Boomerang Uniformity of some Permutation Polynomials
The boomerang attack, introduced by Wagner in 1999, is a cryptanalysis technique against block ciphers based on differential cryptanalysis. In particular it takes into consideration two differentials, one for the upper part of the cipher and one for the lower part, and it exploits the dependency of these two differentials. At Eurocrypt’18, Cid et al. introduced a new tool, called the Boomerang Connectivity Table (BCT), that permits to simplify this analysis. Next, Boura and Canteaut introduced an important parameter for cryptographic S-boxes called boomerang uniformity, that is the maximum value in the BCT. Very recently, the boomerang uniformity of some classes of permutations (in particular quadratic functions) have been studied by Li, Qu, Sun and Li, and by Mesnager, Tang and Xiong. In this paper we further study the boomerang uniformity of some non-quadratic differentially 4-uniform functions. In particular, we consider the case of the Bracken-Leander cubic function and three classes of 4-uniform functions constructed by Li, Wang and Yu, obtained from modifying the inverse functions.publishedVersio
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