Analysis of Pi Series and Its Application to Image Encryption

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Abstract

Whether constant π (i.e., pi) is normal is a confusing problem without any strict theoretical demonstration except for some statistical proof. A new concept of pi series is introduced to seek for the possible quasi-chaotic characteristics of pi by the studies of the basic elements such as power spectral density, phase space construction, maximal Lyapunov exponents and correlation dimension in the field of nonlinear time series. In this paper, we propose a new image encryption algorithm with position diffusion and pixel confusion based on pi series. After this algorithm is applied to a still image, the encrypted image demonstrates strong resistance towards exterior attacks such as statistical attacks and differential attacks.