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In the last few decades, evolutionary algorithms were successfully applied numerous times for creating Boolean functions with good cryptographic properties. Still, the applicability of such approaches was always limited as the cryptographic community ...

Due to the outsourcing of semiconductor design and manufacturing, a number of threats have emerged in recent years, and they are overproduction of integrated circuits (ICs), illegal sale of defective ICs, and piracy of intellectual properties (IPs). ...

The security of cryptographic algorithms (such as block ciphers and hash functions) is often evaluated in terms of their output randomness. This paper presents a novel method for the statistical randomness testing of cryptographic primitives, which is ...

Field-Programmable Gate Arrays (FPGA) implement logic functions using programmable cells, such as K-input lookup-tables (K-LUTs). A K-LUT can implement any Boolean function with K inputs and one output. Methods for mapping into K-LUTs are extensively ...

Semi-bent functions with even number of variables are a class of important Boolean functions whose Hadamard transform takes three values. Semi-bent functions have been extensively studied due to their applications in cryptography and coding theory. In ...

Recently an arithmetic or "with carry" analog of the Walsh-Hadamard transform of Boolean functions was defined. In this paper we compute the arithmetic Walsh transforms of quadratic functions. We find that, as with traditional Walsh-Hadamard transform, ...

The Chow parameters of a Boolean function f: {-1,1}ⁿ -> {-1,1} are its n+1 degree-0 and degree-1 Fourier coefficients. It has been known since 1961 [Cho61, Tan61] that the (exact values of the) Chow parameters of any linear threshold function f uniquely ...

In this paper, we consider a threshold circuit C computing the modulus function MOD_m, and investigate a relationship between two complexity measures, fan-in l and energy e of C, where the fan-in l is defined to be the maximum number of inputs of every ...

A two-dimensional threshold function of $k$-valued logic can be viewed as a coloring of the points of a $k\times k$ square lattice into two colors such that there exists a straight line separating points of different colors. For the number of such ...

Network reliability evaluation is important for the planning, design and control of arbitrary systems. A novel set theory based method for deriving terminal reliability expressions of complex system configurations is described in this paper. The ...

In this paper, we give a lower bound for the optimum distance profiles of the second-order Reed-Muller code in the dictionary order and in the inverse dictionary order. In particular, we investigate the second-order Reed-Muller codes of length ≤256. We ...

Bent functions are maximally nonlinear Boolean functions with an even number of variables. These combinatorial objects, with fascinating properties, are rare. The class of bent functions contains a subclass of functions the so-called hyper-bent ...

Every Boolean function can be presented as a logical formula in conjunctive normal form. Fast algorithm for conjunction plays significant role in overall algorithm for computing arbitrary Boolean function. First, we present a quantum query algorithm for ...

We give the first non-trivial upper bounds on the average sensitivity and noise sensitivity of degree-d polynomial threshold functions (PTFs). These bounds hold both for PTFs over the Boolean hypercube {-1,1}ⁿ and for PTFs over Rⁿ under the standard n-...

The error correction capability of binary linear codes with minimum distance decoding, in particular the number of correctable/uncorrectable errors, is investigated for general linear codes and the first-order Reed-Muller codes. For linear codes, a lower ...

Quantum algorithms can be analyzed in a query model to compute Boolean functions. Function input is provided in a black box, and the aim is to compute the function value using as few queries to the black box as possible. The complexity of the algorithm ...

This paper attempts to utilize the ideas of higher order differential cryptanalysis to investigate Boolean algebra based block ciphers. The theoretical foundation is built for later research, and two kinds of distinguishing attacks are proposed. The ...

This paper presents an encoding scheme for pair sharing. Pair sharing relations and abstract operations required for a pair sharing analysis are encoded as Boolean functions and operations on Boolean functions. Preliminary experimental results with a ...

In the 2nd Annual FOCS (1961), C. K. Chow proved that every Boolean threshold function is uniquely determined by its degree-0 and degree-1 Fourier coefficients. These numbers became known as the Chow Parameters. Providing an algorithmic version of Chow'...

In this paper we present a theoretical construction of Rotation Symmetric Boolean Functions (RSBFs) on odd number of variables with maximum possible algebraic immunity (AI) and further these functions are not symmetric. Our RSBFs are of better ...