Boolean functions play an important role in cryptography. They are elementary building blocks for various cryptographic algorithms – stream ciphers, block ciphers, hash functions, etc. The most common usage for Boolean functions is the construction of larger blocks – substitution boxes [4, 5, 6]. Boolean functions used in these constructions ought to satisfy certain criteria in order to resist ...

In this paper we introduce the study of quantum boolean functions, which are unitary operators f whose square is the identity: f = I. We describe several generalisations of well-known results in the theory of boolean functions, including quantum property testing; a quantum version of the Goldreich-Levin algorithm for finding the large Fourier coefficients of boolean functions; and two quantum v...

Boolean networks are an important model of gene regulatory networks in systems and computational biology. Such networks have been widely studied with respect to their stability and error tolerance. It has turned out that canalizing Boolean functions and their subclass, the nested canalizing functions, appear frequently in such networks. These classes have been shown to have a stabilizing effect...

This paper deals with the number of monochromatic combinatorial rectangles required to approximate a Boolean function on a constant fraction of all inputs, where each rectangle may be defined with respect to its own partition of the input variables. The main result of the paper is that the number of rectangles required for the approximation of Boolean functions in this model is very sensitive t...

This thesis presents two new methods of test-per-clock BIST design for combinational circuits. One of them is based on a transformation of the PRPG code words into test patterns generated by an ATPG tool. This transformation is done by a combinational circuit. For a design of such a circuit two major tasks have to be solved: first, the proper matching between the PRPG code words and the test pa...

In this paper we characterize (octal) bent generalized Boolean functions defined on Z2 with values in Z8. Moreover, we propose several constructions of such generalized bent functions for both n even and n odd.

The notions of perfect nonlinearity and bent functions are closely dependent on the action of the group of translations over IF2 . Extending the idea to more generalized groups of involutions without fixed points gives a larger framework to the previous notions. In this paper we largely develop this concept to define G-perfect nonlinearity and G-bent functions, where G is an Abelian group of in...

It is well known that Exclusive Sum-Of-Products (ESOP) expressions for Boolean functions require on average the smallest number of cubes. Thus, a simple complexity measure for a Boolean function is the number of cubes in its simplest ESOP. It will be shown that this structure-oriented measure of the complexity can be improved by a unique complexity measure which is based on the function. Thus, ...

A Boolean function $g$ is said to be an optimal predictor for another Boolean function $f$, if it minimizes the probability that $f(X^{n})\neq g(Y^{n})$ among all functions, where $X^{n}$ is uniform over the Hamming cube and $Y^{n}$ is obtained from $X^{n}$ by independently flipping each coordinate with probability $\delta$. This paper is about self-predicting functions, which are those that co...