ÐConsider a hypercube of 2 points described by n Boolean variables and a subcube of 2 points, m n. As is well-known, the Boolean function with value 1 in the points of the subcube can be expressed as the product (AND) of nÿm variables. The standard synthesis of arbitrary functions exploits this property. We extend the concept of subcube to the more powerful pseudocube. The basic set is still co...

SHA-3 Cryptographic Hash Algorithm Competition is a competition raised by NIST in response to recent advances of cryptanalysis, aiming at selecting new hash algorithm instead of SHA-2 like AES selection. The compression function of a hash function could be written in the form of multivariate boolean function. In this paper, we introduce our algorithms of evaluating boolean function and applied ...

In this paper, we develop a theory of covers for funct ions defined over boolean str ings. Given a function , a cover is a decomposition , though not necessarily a partition, of the bits into subproblems that can be solved in parallel. In the paper , we formulat e th e notion of cover size , which equals the size of the largest subproblem in a decomposition for a parti cular function. Cover siz...

We present new algorithms to compute fundamental properties of a Boolean function given in truth-table form. Specifically, we give an O(N logN) algorithm for block sensitivity, an O(N logN) algorithm for ‘tree decomposition,’ and an O(N) algorithm for ‘quasisymmetry.’ These algorithms are based on new insights into the structure of Boolean functions that may be of independent interest. We also ...

In this paper we present a new data structure for representing Boolean functions and an associated set of manipulation algorithms. Functions are represented by directed, acyclic graphs in a manner similar to the representations introduced by Lee [1] and Akers [2], but with further restrictions on the ordering of decision variables in the graph. Although a function requires, in the worst case, a...

In this paper, we construct generalized bent Boolean functions in n + 2 variables from 4 generalized Boolean functions in n variables. We also show that the direct sum of two generalized bent Boolean functions is generalized bent. Finally, we identify a set of affine functions in which every function is generalized bent.

-. In this paper an algorithm is designed which generates in-equivalent Boolean functions of any number of variables from the four Boolean functions of single variable. The grammar for such set of Boolean function is provided. The Turing Machine that accepts such set is constructed.

The problem of finding an extension of a partially defined Boolean function (pdBf) is the problem of finding a Boolean function, which correctly classifies given data. That means that in general we are given two sets of Boolean vectors truepoints and falsepoints and we want to decide if there exists an extension a Boolean function, that on all given truepoints has function value true and on all...

Abductive reasoning involves determining a parsimonious set of explanations that can account for a set of observations. In the Boolean minimization problem, the designer attempts to express a Boolean formula as a sum of products or product of sums expression of the smallest size that satisfies the desired function. In this paper, we show that independent abduction problem can be encoded as an i...

We consider the Fourier Entropy-Influence (FEI) conjecture in the context of cryptographic Boolean functions. We show that the FEI conjecture is true for the functions satisfying the strict avalanche criterion, which forms a subset of asymptotic log–density 1 in the set of all Boolean functions. Further, we prove that the FEI conjecture is satisfied for plateaued Boolean functions, monomial alg...