Sub-categories of mathematical topology, like the mathematical theory of chaos, offer interesting applications devoted to information security. In this research work, we have introduced a new chaos-based pseudorandom number generator implemented in FPGA, which is mainly based on the deletion of a Hamilton cycle within the n-cube (or on the vectorial negation), plus one single permutation. By do...

The optical transfer function (OTF) is used in describing imaging systems in the Fourier domain. So far the calculation of the OTF of a large-aperture imaging system has been difficult because the vectorial nature of light breaks the cylindrical symmetry of the pupil function. We derive a simple line integral solution for calculating the vectorial three-dimensional OTF. We further extend this a...

The Forward Problem (FB) of Boolean equations consists of finding solutions of a system of Boolean equations, or equivalently, a single Boolean equation of the form f(X) = 0 where f(X): B n → B and B is an arbitrary Boolean algebra. By contrast, the Inverse Problem (IB) of Boolean equations aims to reconstruct the equation f (X) = 0 given the set of solutions and hence to verify the correctness...

We identify a new restriction on Boolean circuits called bijectivity and prove that bijective Boolean circuits require exponential size to compute the Boolean permanent function. As consequences of this lower bound, we show exponential size lower bounds for: (a) computing the Boolean permanent using monotone multilinear circuits ; (b) computing the 0-1 permanent function using monotone arithmet...

New criteria of extended resiliency and extended immunity of vectorial Boolean functions, such as S-boxes for stream or block ciphers, were recently introduced. They are related to a divide-and-conquer approach to algebraic attacks by conditional or unconditional equations. Classical resiliency turns out to be a special case of extended resiliency and as such requires more conditions to be sati...

We study the length of polynomials over nite simple non-Abelian groups needed to realize Boolean functions. We apply the results for bounding the length of 5-permutation branching programs recognizing a Boolean set. Moreover, for Boolean and general functions on these groups, we present upper bounds on the length of shortest polynomials computing an arbitrary nary Boolean or general function, o...

The conceptions of χ-value and K-rotation symmetric Boolean functions are introduced by Cusick. K-rotation symmetric Boolean functions are a special rotation symmetric functions, which are invariant under the k − th power of ρ. In this paper, we discuss cubic 2-value 2-rotation symmetric Boolean function with 2n variables, which denoted by F2n(x2n). We give the recursive formula of weight of F2...

This paper describes a stochastic hill climbing algorithm named SHCLVND to optimize arbitrary vectorial < n ! < functions. It needs less parameters. It uses normal (Gaussian) distributions to represent probabilities which are used for generating more and more better argument vectors. The-parameters of the normal distributions are changed by a kind of Hebbian learning. Kvasnicka et al. KPP95] us...