Entropy analysis with lyapunov exponents for random number generators

Abstract

Many applications require random numbers. Generating high quality random numbers is a very serious problem. It is quite easy to design a random number generator that will pass the statistical tests, but it is much more difficult to know where the randomness comes from and how much true randomness is there. Chaotic system is regarded as an important entropy source in the design of random number generator. The relationship between random number generator and chaotic dynamical systems is studied in this paper. The main contribution of this paper is that it gives an analysis method for entropy source in random number generators. Entropy describes the unpredictability of random number generators. In practice, calculation of entropy is hard, so Lyapunov exponent has been used as an unpredictability measure of entropy source. Proposed analysis method has been verified on a chaos based random number generator design, and fits to analysis of other RNG designs. © 2015 ISAST.