Motivated by recent works on the butterfly structure, particularly by its generalization
introduced by Canteaut et al.(IEEE Trans Inf Theory 63 (11): 7575–7591, 2017), we first …

Very recently, a class of cryptographically strong permutations with boomerang uniformity 4
and the best known nonlinearity is constructed from the closed butterfly structure in Li et …

In the present article, we provide a complete characterization of permutations on the finite
field F 4 m of shape f ϵ _ (X):= ϵ 1 X‾ q+ 1+ ϵ 2 X‾ q X+ ϵ 3 X‾ X q+ ϵ 4 X q+ 1, definitively …

Motivated by recent results on the constructions of permutation polynomials with few terms
over the finite field 𝔽 2 n \mathbbF_2^n, where n is a positive even integer, we focus on the …

Let F 2 n be a finite field with 2 n elements and fc _ (x)= c 0 x 2 m (2 k+ 1)+ c 1 x 2 m+ k+ 1+ c
2 x 2 m+ 2 k+ c 3 x 2 k+ 1∈ F 2 n [x], where n, m and k are positive integers with n= 2 m and …

Differentially 4 uniform permutations with high nonlinearity on fields of even degree are
crucial to the design of S-boxes in many symmetric cryptographic algorithms. Until now …

Boomerang connectivity table is a new tool to characterize the vulnerability of cryptographic
functions against boomerang attacks. Consequently, a cryptographic function is desired to …

Many block ciphers use permutations defined over the finite field $\mathbb {F} _ {2^{2k}} $
with low differential uniformity, high nonlinearity, and high algebraic degree to provide …

Abstract At Eurocrypt'18, Cid, Huang, Peyrin, Sasaki, and Song introduced a new tool called
Boomerang Connectivity Table (BCT) for measuring the resistance of a block cipher against …

Permutation polynomials over finite fields have been studied extensively recently due to
their wide applications in cryptography, coding theory, communication theory, among others …