the square map is one of the functions used in cryptography. for instance, the square map is used in rabin encryption scheme, block cipher rc6 and stream cipher rabbit, in different forms. in this paper, we study statistical properties of the output of the square map as a vectorial boolean function. we obtain the joint probability distribution of arbitrary number of the upper and the lower bits...

Vectorial Boolean bent functions, which possess the maximal nonlinearity and the minimum differential uniformity, contribute to optimum resistance against linear cryptanalysis and differential cryptanalysis for the cryptographic algorithms that adopt them as nonlinear components. This paper is devoted to the new primary constructions of vectorial Boolean bent functions, including four types: ve...

In this paper, we show that there is no vectorial Boolean function of degree 4e, with e satisfaying certain conditions, which is APN over infinitely many extensions of its field of definition. It is a new step in the proof of the conjecture of Aubry, McGuire and Rodier. Vectorial Boolean function and Almost Perfect Non-linear functions and Algebraic surface and CCZ equivalence

Recently, one of the hot topics on vectorial Boolean bent functions is to construct vectorial Boolean bent functions in the form Tr m(P (x)) from Boolean bent functions in the form Tr 1 (P (x)), where P (x) ∈ F2n [x]. This paper first presents three constructions of vectorial Boolean bent functions in the form Tr m(P (x)), where two of them give answers to two open problems proposed by Pasalic ...

There are two construction methods of designs from $(n,m)$ -bent functions, known as translation and addition designs. In this article we analyze, which equivalence relation for Boolean bent i.e. notation="LaTeX">$(n,1)$ vectorial fun...

Vectorial Boolean bent functions, which possess the maximal nonlinearity and the minimum differential uniformity, contribute to optimum resistance against linear cryptanalysis and differential cryptanalysis. H vectorial functions is an infinite class of vectorial Boolean bent functions presented by S. Mesnager. This paper is devoted to further characterization of the H vectorial functions. It i...

The most important building blocks of symmetric cryptographic primitives such as the DES or the AES, are vectorial Boolean functions, also called S-boxes. In this paper, we extend the definition of normality for Boolean functions into several new affine invariant properties for vectorial Boolean functions. We compute the probability of occurrence of these properties and present practical algori...

APN permutations in even dimension are vectorial Boolean functions that play a special role in the design of block ciphers. We study their properties, providing some general results and some applications to the low-dimension cases. In particular, we prove that none of their components can be quadratic. For an APN vectorial Boolean function (in even dimension) with all cubic components we prove ...

In this paper, we construct a class of vectorial Boolean functions over F2n with high algebraic immunity based on the decomposition of the multiplicative group of F2n . By viewing F2n as G1G2 ∪ {0} (where G1 and G2 are subgroups of F2n , (#G1,#G2) = 1 and #G1 × #G2 = 2 − 1), we give a generalized description for constructing vectorial Boolean functions with high algebraic immunity. Moreover, wh...