Generation of Pseudo-Random Numbers by Chaos-Type Function and Its Application to Cryptosystems

Abstract

The logistic map is known to be one of nonlinear difference equations as a chaos map, and to generate pseudo-random numbers. However, since the chaos has a high sensitive dependency on initial conditions and accumulates inevitable round-off errors caused by iterating the map, the numerical generation of exact chaotic time series is said to be impossible. The aim of this paper is, first, to propose the algorithm to generate exact chaotic time series of a chaos-type function derived from the exact chaos solution. Next, the pseudo-random numbers are evaluated by the four tests and the accumulation of chi-square values. Also, an application to cryptosystems, which do not need the synchronization in usual computer environment, is considered.