In this paper, we obtain a characterization of generalized Boolean functions based on spectral analysis. We investigate a relationship between the Walsh-Hadamard spectrum and σ f , the sum-of-squares-modulus indicator (SSMI) of the generalized Boolean function. It is demonstrated that σ f = 22n+s for every s-plateaued generalized Boolean function in n variables. Two classes of generalized semi-...

Usually, important parameters in the design and implementation of combinational logic circuits are the number of gates, transistors, and the levels used in the design of the circuit. In this regard, various evolutionary paradigms with different competency have recently been introduced. However, while being advantageous, evolutionary paradigms also have some limitations including: a) lack of con...

INTRODUCTION In an important class of stream ciphers, called combination generators, the key stream is produced by combining the outputs of several independent Linear Feedback Shift Register (LFSR) sequences with a nonlinear Boolean function. Siegenthaler [12] was the first to point out that the combining function should possess certain properties in order to resist divide-and-conquer attacks.A...

Many practical information authentication techniques are based on such cryptographic means as data encryption algorithms and one-way hash functions. A core component of such algorithms and functions are nonlinear functions. In this paper, we reveal a relationship between nonlinearity and propagation characteristic, two critical indicators of the cryptographic strength of a Boolean function. We ...

In view of the construction requirements of Boolean functions with many good cryptography properties, through the analysis of the relationship between the function values on the vectors with weight not more than d and the algebraic immunity, a method to determine the higher order algebraic immunity function is given. Meanwhile, a method that appropriate change in the function value without redu...

Card-based protocols that are based on a deck of physical cards achieve secure multi-party computation with information-theoretic secrecy. Using existing AND, XOR, NOT, and copy protocols, one can naively construct a secure computation protocol for any given (multivariable) Boolean function as long as there are plenty of additional cards. However, an explicit sufficient number of cards for comp...

Manipulation of Boolean functions has important applications in such fields as hardware verification, non-monotonic reasoning, and decision support. Most often, in such applications, the set of prime implicates/implicants of a large formula must be computed. Many algorithms have been proposed to compute the prime implicates of propositionalBoolean formulas, e.g. [4, 5]. Most of them assume that...

We study the probability of making an error if, by querying an oracle a fixed number of times, we declare constant a randomly chosen n-bit Boolean function. We compare the classical and the quantum case, and we determine for how many oracle-queries k and for how many bits n one querying procedure is more efficient than the other.

We construct trace codes over Z4 by using Boolean functions and skew sets, respectively. Their Lee weight distribution is studied by using a Galois ring version of the Walsh-Hadamard transform and exponential sums. We obtain a new family of optimal two-weight codes over Z4.

A new neural network (NN) approach is proposed in this paper to estimate the Boolean function (BF) complexity. Large number of randomly generated single output BFs has been used and experimental results show good correlation between the theoretical results and those predicted by the NN model. The proposed model is capable of predicting the number of product terms (NPT) in the BF that gives an i...