Digital Chaotic Signal Generator Using Robust Chaos in Compound Sinusoidal Maps

Abstract

SUMMARY This paper presents an implementation of a digital chaoticsignal generator based on compound one-dimensional sinusoidal maps.The proposed chaotic map not only offers high chaoticity measured from apositive lyapunov exponent but also provides diverse bifurcation structureswith robust chaos over most regions of parameter spaces. Implementationon FPGA realizes small number of components and offers a highly randomchaotic sequence with no autocorrelation. The proposed chaotic signal gen-erator offers a potential alternative in random test pattern generation or insecured data communication applications. key words: sinusoidal chaotic map, digital chaotic signal generator 1. Introduction A digital chaotic signal generator provides a random digitalsequence for various applications such as in automatic testpattern generation [1], in data encryption [2], or in securecommunications [3]. A search for effective chaotic mapswith hardware implementations for use as a core buildingblock in such digital chaotic signal generators have there-fore been made continuously, involving logistics map [4],tent map [5] and Rossler chaotic model [6]. However, most¨one-dimensional chaotic maps that employ simple nonlin-earity may not provide sufficient complexity. This lettertherefore focuses on a chaotic map using a sinusoidal func-tion with an inherent multi-modal polynomial function de-scribed by Maclaurin series. The compound topology of si-nusoidal maps is proposed for the enhancement of dynami-cal behaviors in terms of a positive lyapunov exponent, bi-furcation structure, and hence randomness entropy of a dig-ital sequence output.