A Class of Quadratic Polynomial Chaotic Maps and its Application in Cryptography

Abstract

At present, the probability density of most chaotic systems is unknown, and the statistical characteristics of chaotic sequences cannot be described by the probability density of chaotic maps. This paper constructs a class of quadratic polynomial chaotic maps with three system parameters, which are topologically conjugated with Tent maps. The probability density functions of this kind of chaotic maps are given. Then, an arcsine function is designed to transform the chaotic sequence generated by the quadratic polynomial chaotic map into a new random sequence, which obeys the uniform distribution on the interval (-0.5, 0.5). In order to show the application of the new uniform random numbers, the applications of it in generating random arrangement, Gaussian measurement matrix of compressed sensing, and pseudo random number generator are discussed.