Zobrazeno 1 - 10
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pro vyhledávání: '"Stănică, Pantelimon"'
In this note we show (for a large enough dimension of the underlying field) a conjecture of [C. Beierle, C. Carlet, G. Leander, L. Perrin, {\em A further study of quadratic APN permutations in dimension nine}, Finite Fields Appl. 81 (2022), 102049] o
Externí odkaz:
http://arxiv.org/abs/2410.23097
In this paper we use algebraic curves and other algebraic number theory methods to show the validity of a permutation polynomial conjecture regarding $f(X)=X^{q(p-1)+1} +\alpha X^{pq}+X^{q+p-1}$, on finite fields $\mathbb{F}_{q^2}, q=p^k$, from [A. R
Externí odkaz:
http://arxiv.org/abs/2410.22692
Secure multiparty computation (MPC) schemes allow two or more parties to conjointly compute a function on their private input sets while revealing nothing but the output. Existing state-of-the-art number-theoretic-based designs face the threat of att
Externí odkaz:
http://arxiv.org/abs/2312.16318
Autor:
Pal, Mohit, Stanica, Pantelimon
This paper makes the first bridge between the classical differential/boomerang uniformity and the newly introduced $c$-differential uniformity. We show that the boomerang uniformity of an odd APN function is given by the maximum of the entries (excep
Externí odkaz:
http://arxiv.org/abs/2312.01434
Finding functions, particularly permutations, with good differential properties has received a lot of attention due to their possible applications. For instance, in combinatorial design theory, a correspondence of perfect $c$-nonlinear functions and
Externí odkaz:
http://arxiv.org/abs/2310.20205
The Feistel Boomerang Connectivity Table and the related notion of $F$-Boomerang uniformity (also known as the second-order zero differential uniformity) has been recently introduced by Boukerrou et al.~\cite{Bouk}. These tools shall provide a major
Externí odkaz:
http://arxiv.org/abs/2310.13775
In 1953, Carlitz~\cite{Car53} showed that all permutation polynomials over $\F_q$, where $q>2$ is a power of a prime, are generated by the special permutation polynomials $x^{q-2}$ (the inversion) and $ ax+b$ (affine functions, where $0\neq a, b\in \
Externí odkaz:
http://arxiv.org/abs/2309.17424
It was shown by Boukerrou et al.~\cite{Bouk} [IACR Trans. Symmetric Cryptol. 1 2020, 331--362] that the $F$-boomerang uniformity (which is the same as the second-order zero differential uniformity in even characteristic) of perfect nonlinear function
Externí odkaz:
http://arxiv.org/abs/2309.04219