Related papers: Nonlinearity of Boolean functions: an algorithmic …
We associate to each Boolean function a polynomial whose evaluations represents the distances from all possible Boolean affine functions. Both determining the coefficients of this polynomial from the truth table of the Boolean function and…
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.…
We study the computational complexity of two Boolean nonlinearity measures: the nonlinearity and the multiplicative complexity. We show that if one-way functions exist, no algorithm can compute the multiplicative complexity in time…
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…
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…
Boolean functions are mathematical objects with numerous applications in domains like coding theory, cryptography, and telecommunications. Finding Boolean functions with specific properties is a complex combinatorial optimization problem…
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…
This paper investigates the learnability of the nonlinearity property of Boolean functions using neural networks. We train encoder style deep neural networks to learn to predict the nonlinearity of Boolean functions from examples of…
We propose a new polynomial-time algorithm for linear programming. We further extend the ideas used in this new linear programming algorithm for nonlinear programming problems. The new algorithm is based on the idea of treating the…
We present new algorithms to compute fundamental properties of a Boolean function given in truth-table form. Specifically, we give an O(N^2.322 log N) algorithm for block sensitivity, an O(N^1.585 log N) algorithm for `tree decomposition,'…
Gr{\"o}bner bases is one the most powerful tools in algorithmic non-linear algebra. Their computation is an intrinsically hard problem with a complexity at least single exponential in the number of variables. However, in most of the cases,…
We consider the multiplicative complexity of Boolean functions with multiple bits of output, studying how large a multiplicative complexity is necessary and sufficient to provide a desired nonlinearity. For so-called $\Sigma\Pi\Sigma$…
This paper depicts an algorithm for solving the Decision Boolean Satisfiability Problem using the binary numerical properties of a Special Decision Satisfiability Problem, parallel execution, object oriented, and short termination. The two…
Polynomial system solving is a classical problem in mathematics with a wide range of applications. This makes its complexity a fundamental problem in computer science. Depending on the context, solving has different meanings. In order to…
Additive Fourier Transform is sdudied. A fast multiplication algorithm for polynomials over the binary field is given. The bit complexity of the algorithm is $O(n(log n)(\log\log n)^2)$.
We propose a quantum algorithm to estimate the Gowers $U_2$ norm of a Boolean function, and extend it into a second algorithm to distinguish between linear Boolean functions and Boolean functions that are $\epsilon$-far from the set 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…
We consider two kinds of problems: the computation of polynomial and rational solutions of linear recurrences with coefficients that are polynomials with integer coefficients; indefinite and definite summation of sequences that are…
In this paper, we suggest a new efficient algorithm in order to compute S-polynomial reduction rapidly in the known algorithm for computing Grobner bases, and compare the complexity with others.
We discuss quantum algorithms, based on the Bernstein-Vazirani algorithm, for finding which variables a Boolean function depends on. There are 2^n possible linear Boolean functions of n variables; given a linear Boolean function, the…