Abstract Most of the approaches published in literature to construct S-boxes via Cellular Automata (CA) work by either iterating a finite CA for several time steps, or one-shot application global rule. The main characteristic that brings together these works is they employ single rule define vectorial Boolean function S-box. In this work, we explore different direction design leverages on Ortho...

‎The notion of (Boolean) uni-soft filters‎ ‎in MTL-algebras is introduced‎, ‎and several properties of them are‎ ‎investigated‎. ‎Characterizations of (Boolean) uni-soft filters are discussed‎, ‎and some (necessary and sufficient) conditions‎ ‎for a uni-soft filter to be Boolean are provided‎. ‎The condensational property for a Boolean uni-soft filter is established.

The paper is dealing with two important subclasses of plateaued functions: bent and semi-bent functions. In the first part of the paper, we construct mainly bent and semi-bent functions in the Maiorana-McFarland class using Boolean functions having linear structures (linear translators) systematically. Although most of these results are rather direct applications of some recent results, using l...

This paper is concerned with the problem of Boolean approximation in the following sense: given a Boolean function class and an arbitrary Boolean function, what is the function’s best proxy in the class? Specifically, what is its strongest logical consequence (or envelope) in the class of affine Boolean functions. We prove various properties of affine Boolean functions and their representation ...

A vectorial diffraction theory that considers light polarization is essential to predict the performance of optical systems that have a high numerical aperture or use engineered polarization or phase. Vectorial diffraction integrals to describe light diffraction typically require boundary fields on aperture surfaces. Estimating such boundary fields can be challenging in complex systems that ind...

Specific vectorial boolean functions, such as S-Boxes or APN functions have many applications, for instance in symmetric ciphers. In cryptography they must satisfy some criteria (balancedness, high nonlinearity, high algebraic degree, avalanche, or transparency [2, 7]) to provide best possible resistance against attacks. Functions satisfying most criteria are however difficult to find. Indeed, ...

In Boolean algebra, true statements are denoted 1 and false statements are denoted 0. A Boolean function acts on a set of these Boolean values and outputs a set of Boolean values (usually just one). The most common Boolean operators used are NOT, AND, OR, and XOR. 2.1 NOT NOT is a Boolean function that takes in one Boolean value and outputs its negation. Let x be a Boolean variable. NOT(x) is d...

A method to evaluate the physical realizability of an arbitrary three-dimensional vectorial field distribution in the focal area is proposed. A parameter that measures the similarity between the designed (target) field and the physically achievable beam is provided. This analysis is carried out within the framework of the closest electromagnetic field to a given vectorial function, and the proc...