相关论文: On the representation of bent functions by bent re…

Semi-bent Boolean functions are interesting from a cryptographic standpoint, since they possess several desirable properties such as having a low and flat Walsh spectrum, which is useful to resist linear cryptanalysis. In this paper, we…

We investigate subclasses of generalized Bernstein functions related to complete Bernstein and Thorin-Bernstein functions. Representations in terms of incomplete beta and gamma as well as hypergeometric functions are presented. Several…

Bent functions, or equivalently, Hadamard difference sets in the elementary Abelian group $(\gf(2^{2m}), +)$, have been employed to construct symmetric and quasi-symmetric designs having the symmetric difference property. The main objective…

Logical models have been successfully used to describe regulatory and signaling networks without requiring quantitative data. However, existing data is insufficient to adequately define a unique model, rendering the parametrization of a…

Dillon-like Boolean functions are known, in the literature, to be those trace polynomial functions from $\mathbb{F}_{2^{2n}}$ to $\mathbb{F}_{2}$, with all the exponents being multiples of $2^n-1$ often called Dillon-like exponents. This…

We present a construction of partial spread bent functions using subspaces generated by linear recurring sequences (LRS). We first show that the kernels of the linear mappings defined by two LRS have a trivial intersection if and only if…

In several domains, data objects can be decomposed into sets of simpler objects. It is then natural to represent each object as the set of its components or parts. Many conventional machine learning algorithms are unable to process this…

We study a new method of constructing Boolean bent functions from cyclotomic mappings. Three generic constructions are obtained by considering different branch functions such as Dillon functions, Niho functions and Kasami functions over…

In this paper, we first present a new secondary construction of bent functions (building new bent functions from two already defined ones). Furthermore, we apply the construction using as initial functions some specific bent functions and…

We propose a new approach to combine Restricted Boltzmann Machines (RBMs) that can be used to solve combinatorial optimization problems. This allows synthesis of larger models from smaller RBMs that have been pretrained, thus effectively…

Idempotent Boolean functions form a highly structured subclass of Boolean functions that is closely related to rotation symmetry under a normal-basis representation and to invariance under a fixed linear map in a polynomial basis. These…

Given a function from $\mathbb{Z}_n$ to itself one can determine its polynomial representability by using Kempner function. In this paper we present an alternative characterization of polynomial functions over $\mathbb{Z}_n$ by constructing…

Classification of Non-linear Boolean functions is a long-standing problem in the area of theoretical computer science. In this paper, effort has been made to achieve a systematic classification of all n-variable Boolean functions, where…

Starting from special near-bent functions in dimension 2t-1 we construct bent functions in dimension 2t having a specific derivative. We deduce new famillies of bent functions

Horn functions form a subclass of Boolean functions and appear in many different areas of computer science and mathematics as a general tool to describe implications and dependencies. Finding minimum sized representations for such functions…

Boolean functions with strong cryptographic properties, such as high nonlinearity and algebraic degree, are important for the security of stream and block ciphers. These functions can be designed using algebraic constructions or…

We show that the graph of a bent function is a Salem set in an appropriate sense. We also establish a simple result that quantifies redundancies in the difference operators of a function, which applies to bent functions over fields of odd…

In this paper we study the complexity of quantum query algorithms computing the value of Boolean function and its relation to the degree of algebraic polynomial representing this function. We pay special attention to Boolean functions with…

We study the space of functions computed by random-layered machines, including deep neural networks and Boolean circuits. Investigating the distribution of Boolean functions computed on the recurrent and layer-dependent architectures, we…

Let L be a bounded distributive lattice. We give several characterizations of those L^n --> L mappings that are polynomial functions, i.e., functions which can be obtained from projections and constant functions using binary joins and…