Generating pseudo-random numbers with a Brownian system

Abstract

We use a deterministic dynamical system that simulates a Brownian movement over time to produce pseudo-random sequences of binary numbers. We show that the used Brownian system has two positive Lyapunov exponents, this characteristic is different of a chaotic system that has only one maximum positive Lyapunov exponent. The implementation of the random number generator uses fixed point arithmetic with numbers with 5 bits for the integer part and 58 bits for the fractional part. The eight least significant bits for each variable of the 3rd order Brownian system are concatenated to form the sequences of random bits. The generated sequences pass all the NIST and TestU01 statistical randomness tests. Furthermore, a hardware design in FPGA of the proposed pseudo-random generator is presented with a throughput equal to 1085.16 Mb/s. For the best of our knowledge, this is the first time a Brownian system is used as the core of a PRNG.