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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…
Boolean functions have very nice applications in cryptography and coding theory, which have led to a lot of research focusing on their applications. The objective of this paper is to construct binary linear codes with few weights from the…
Boolean functions can be used to construct binary linear codes in many ways, and vice versa. The objective of this short article is to point out a connection between the weight distributions of all projective binary linear codes and the…
Extending previous analyses on function classes like linear functions, we analyze how the simple (1+1) evolutionary algorithm optimizes pseudo-Boolean functions that are strictly monotone. Contrary to what one would expect, not all of these…
The nonlinearity of a Boolean function is a key property in deciding its suitability for cryptographic purposes, e.g. as a combining function in stream ciphers, and so the nonlinearity computation is an important problem for applications.…
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…
We consider a probability distribution on the set of Boolean functions in n variables which is induced by random Boolean expressions. Such an expression is a random rooted plane tree where the internal vertices are labelled with connectives…
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 logarithm of the number of binary n-variable bent functions is asymptotically less than $11(2^n)/32$ as n tends to infinity. Keywords: boolean function, Walsh--Hadamard transform, plateaued function, bent function, upper bound
We address a sequential decision problem that arises in the computation of symmetric Boolean functions of distributed data. We consider a collocated network, where each node's transmissions can be heard by every other node. Each node has a…
An algorithm for computing the nonlinearity of a Boolean function from its algebraic normal form (ANF) is proposed. By generalizing the expression of the weight of a Boolean function in terms of its ANF coefficients, a formulation of the…
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…
Non-linearity of a Boolean function indicates how far it is from any linear function. Despite there being several strong results about identifying a linear function and distinguishing one from a sufficiently non-linear function, we found a…
In this paper, we focus on the links between Boolean function theory and quantum computing. In particular, we study the notion of what we call fully-balanced functions and analyse the Fourier--Hadamard and Walsh supports of those 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 compute the nonlinearity of Boolean functions with Groebner basis techniques, providing two algorithms: one over the binary field and the other over the rationals. We also estimate their complexity. Then we show how to improve our…
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…
Regularization plays a key role in a variety of optimization formulations of inverse problems. A recurring theme in regularization approaches is the selection of regularization parameters, and their effect on the solution and on the optimal…
Relations between the decision tree complexity and various other complexity measures of Boolean functions is a thriving topic of research in computational complexity. It is known that decision tree complexity is bounded above by the cube of…
We study parity decision trees for Boolean functions. The motivation of our study is the log-rank conjecture for XOR functions and its connection to Fourier analysis and parity decision tree complexity. Let f be a Boolean function with…