Performance of Finite Precision on Discrete Chaotic Map Based on a Feedback Shift Register

Abstract

The scintillating technological improvements have changed the process of communication in all parts of the world. Shopping, banking, instant communication, and so on can be operated online and do not care about the linkage of those Internet communications. Because of simple chaotic structure, discrete nature, less arithmetic computation, and high complexity, low-dimensional chaotic systems such as a logistic map and tent map are more attractive than a high-dimensional chaotic system. To overcome the disadvantages of a low-dimensional chaotic map with a finite precision in chaos-based application, the chaotic map with a feedback shift register (CMFSR) is proposed. The related properties and performance associated with CMFSR are analysed. The relationship among the precision of the system, the architecture, and the performance are discussed. The experiments about new pseudorandom number generator (PRNG) based on CMFSR show that our scheme is simple, secure, and easy to accomplish. Experiments show that the proposed architecture of CMFSR is secure for random number generation.