SEARCH-BASED CHAOTIC PSEUDORANDOM BIT GENERATOR

Abstract

This paper proposes the construction of a new chaotic pseudorandom bit generator, which forms the main building block of a chaotic stream cipher. The design of the algorithm is based on a single chaotic map whose numerical orbit indirectly contributes towards the generation of the keystream. The latter is produced from the numerical orbit by applying a technique that searches for iterates in specific intervals [a,b], for some real numbers a and b, and outputs 0 or 1 based on the iterate preceding the targeted iterate. The generator suggested here is built up from a quadratic map. We analyze the cycle length of the keystreams and investigate the resistance of the generator to well-known cryptanalytic attacks. Furthermore, the statistic characteristics of the keystreams are examined numerically using the NIST statistical test suite. The numerical and theoretical results demonstrate that the proposed technique results in generating keystreams possessing very good cryptographic properties and high level of security against existing cryptanalytic attacks. Empirical results show that the search technique leads to the generation of keystreams possessing good randomness properties when applied to any chaotic map whose orbits have good randomness properties such as the quadratic map, tent map and sawtooth map.