Related papers: Two Boolean functions with five-valued Walsh spect…

This paper presents noise analysis for the two-stage and the three-stage quantum cryptographic protocols based on random polarization rotations. The noise model used is that of uniform distribution of error over a certain small range that…

Linear codes with few weights have applications in authentication codes, secrete sharing schemes, association schemes, consumer electronics and data storage system. In this paper, several classes of linear codes with two or three weights…

The r-th order nonlinearity of a Boolean function is the minimum number of elements that have to be changed in its truth table to arrive at a Boolean function of degree at most r. It is shown that the (suitably normalised) r-th order…

First, we construct a class of functions with good local avalanche characteristics, but bad global avalanche characteristics. We also derive some bounds for the nonlinearity of such functions. It improves upon the results of Son et al., and…

Boolean functions and binary sequences are main tools used in cryptography. In this work, we introduce a new bijection between the set of Boolean functions and the set of binary sequences with period a power of two. We establish a…

Boolean functions are mathematical objects used in diverse domains and have been actively researched for several decades already. One domain where Boolean functions play an important role is cryptography. There, the plethora of settings one…

Bernstein-Vazirani algorithm (the one-query algorithm) can identify a completely specified linear Boolean function using a single query to the oracle with certainty. The first aim of the paper is to show that if the provided Boolean…

In this paper, we study the value distributions of perfect nonlinear functions, i.e., we investigate the sizes of image and preimage sets. Using purely combinatorial tools, we develop a framework that deals with perfect nonlinear functions…

Boolean functions with good cryptographic properties like high nonlinearity and algebraic degree play an important in the security of stream and block ciphers. Such functions may be designed, for instance, by algebraic constructions or…

Although the strengths of optical non-linearities available experimentally have been rapidly increasing in recent years, significant challenges remain to using such non-linearities to produce useful quantum devices such as efficient optical…

The success of non-linear optics relies largely on pulse-to-pulse consistency. In contrast, covariance based techniques used in photoionization electron spectroscopy and mass spectrometry have shown that wealth of information can be…

A new method is used to resolve a long-standing conjecture of Niho concerning the crosscorrelation spectrum of a pair of maximum length linear recursive sequences of length $2^{2 m}-1$ with relative decimation $d=2^{m+2}-3$, where $m$ is…

Boolean functions are mathematical objects used in diverse applications. Different applications also have different requirements, making the research on Boolean functions very active. In the last 30 years, evolutionary algorithms have been…

Functions with low differential uniformity have relevant applications in cryptography. Recently, functions with low $c$-differential uniformity attracted lots of attention. In particular, so-called APcN and PcN functions (generalization of…

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…

The work offers a new approach to the formation of functions which are used in cryptography and cryptanalysis. It will use alternative forms of representation of Boolean functions, that is, those which are different from the classical form,…

The exact formulae for spectra of equilibrium diffusion in a fixed bistable piecewise linear potential and in a randomly flipping monostable potential are derived. Our results are valid for arbitrary intensity of driving white Gaussian…

The goal in function property testing is to determine whether a black-box Boolean function has a certain property or is epsilon-far from having that property. The performance of the algorithm is judged by how many calls need to be made to…

In this paper, we study different cryptographically significant spectra of Boolean functions, including the Walsh-Hadamard, cross-correlation, and autocorrelation. The $2^k$-variation by Stanica [IEEE-IT 2016] is considered here with the…

Monotone Boolean functions are a structurally important class of Boolean functions, but their restricted form imposes strong limitations on achievable nonlinearity. In this paper, we investigate whether evolutionary computation can evolve…