A fast pseudo stochastic sequence quantification algorithm based on Chebyshev map and its application in data encryption

Abstract

Chaos theory has been widely used in cryptography fields in recent years and the performance of the pseudo stochastic sequence quantified from chaos map has great influence on the efficiency and security of an encryption system. In this paper, an improved stochastic middle multi-bits quantification algorithm based on Chebyshev map is proposed to enhance the ability of anti reconstruction a chaos system through reverse iteration and improve the performance of the generated sequence under precision restricted condition. The balance and correlation properties of the generated sequence are analyzed. The sequence is proved to be a binary Bernoulli sequence and the distribution of the differences between the amounts of 0 and 1 is analyzed. The side lobes of auto correlation and values of cross correlation are proved to obey normal distribution N (0, 1/N). © Springer-Verlag Berlin Heidelberg 2006.