True pseudo-random number generation using chaotic maps

Abstract

Generating a very high-quality random data is crucial for simulations using the Monte Carlo-method, secure cryptographic applications, and data security. There are two main methods in generating random data. The first method is called the hardware random number generator where it measures physical phenomenon that are expected to be random such as atmospheric noise. However, they are limited by the number of random bits per second it can produce. The second method is called the pseudo-random number generator where it uses computational algorithm to generate long sequence of random data. Chaotic discrete dynamic systems such as logistic map have been used to generate pseudo-random number. However, chaos theory states that within the apparent randomness in a chaotic system, there are underlying patterns, repetition, and interconnectedness which are not desirable for most real-world applications. In order to further randomise the data and remove such order within apparent randomness, a new premium Pseudo-Random Number Generator based on Modulized Chaotic System Dynamics (PRNG-MCSD) is proposed. Modulo operation provides the strongest discontinuity and time-varying nonlinearity which generates very high-quality data through its repeated geometrical folding operations. The principle and the dynamic characteristics of the PRNG-MCSD would be discussed. Results based on statistical analyses such as Diehard and NIST test shows that the proposed PRNG-MCSD can generate very high-quality random data for simulations using the Monte Carlo-method, secure cryptographic applications, and data security.