Random property enhancement of a 1D chaotic PRNG with finite precision implementation

Abstract

The random-like behavior of chaotic systems make them perfect candidates for the core of numerous pseudo-random number generators. The coupling of two or more chaotic maps has been proven to increase the random property robustness of the generated sequences. However, these properties are also strongly influenced by the datatype implementation of these generators owing to the effect of the sensitivity to initial conditions. Hence, several factors must be considered concerning the hardware implementation of these coupled chaotic map-based generators. This paper first examines the effect of fixed-point precision implementation on the periodicity of a single skew tent map and the extension of this effect on the statistical properties of the generated sequence from coupled skew tent maps. Then, the effect on cross-coupled skew tent maps is discussed. Further, a modification to the cross-coupled scheme is presented; this achieves a reduction in the fixed-point fraction length required for generating a sequence suitable for cryptographic applications while expanding the dependency on the control parameters of the maps. The generated sequences from the proposed modification met all the applied statistical and correlation test requirements, demonstrating that they possess acceptable random properties and are suitable for cryptographic applications.