Design and Test of Pseudorandom Number Generator Using a Star Network of Lorenz Oscillators

Abstract

We have recently developed a chaos-based stream cipher based on augmented Lorenz equations as a star network of Lorenz subsystems. In our method, the augmented Lorenz equations are used as a pseudorandom number generator. In this study, we propose a new method based on the augmented Lorenz equations for generating binary pseudorandom numbers and evaluate its security using the statistical tests of SP800-22 published by the National Institute for Standards and Technology in comparison with the performances of other chaotic dynamical models used as binary pseudorandom number generators. We further propose a faster version of the proposed method and evaluate its security using the statistical tests of TestU01 published by L'Ecuyer and Simard.

Design of the nonlinear look-up table in the chaotic pseudorandom number generator based on augmented Lorenz map

“…The method for generating binary pseudorandom numbers from the chaotic time series of x n,i is as follows [3,6]. We first transform x n,i into the corresponding binary number b n,i using the following equation.…”

“…where 10 α is an amplification factor [3,6], and α is a positive integer. According to [3,6], we use α = 6 in this paper.…”

“…where 10 α is an amplification factor [3,6], and α is a positive integer. According to [3,6], we use α = 6 in this paper. Subsequently, b n,i are concatenated into a binary sequence b [3,6] defined as…”

“…According to [3,6], we use α = 6 in this paper. Subsequently, b n,i are concatenated into a binary sequence b [3,6] defined as…”

“…In order to overcome the problems in conventional chaos-based encryption, a chaotic stream cipher based on the augmented Lorenz equations has been proposed [2]. The pseudorandom number generated from the augmented Lorenz system is shown to be statistically secure [3] in the sense that the generated pseudorandom numbers pass all of the statistical tests in NIST SP 800-22 [4] and TestU01 BigCrush [5]. However, the generating speed of the pseudorandom number through numerical integration of the augmented Lorenz equations is slow compared to modern stream ciphers.…”