Probabilistic encryption

Quantum mechanics

Algorithm

Histogram

Pixel

Chaotic

Deterministic encryption

Entropy (arrow of time)

Theoretical computer science

Encryption

Operating system

Computer science

Physics

Mathematics

Image (mathematics)

Lyapunov exponent

Watermarking attack

Key space

Artificial intelligence

Cryptography

Information Sciences

A chaotic map generally employed to generate chaotic sequence is key element for an image encryption algorithm (IEA). In this study, an IEA using novel 2D chaotic map, which is based on Euler and Pi numbers so-called eπ-map, is presented. eπ-map exploits infinity diversity attribute of these numbers. Moreover, a diffusion operation referred to as “bit reversion” in which the bits of the pixels are symmetrically reverted is proposed for manipulating the pixel value. eπ-map is exhaustively examined through bifurcation and trajectory diagrams, Lyapunov exponent (LE), sample entropy (SE), permutation entropy (PE) and 0-1 test. The encryption performance of the IEA is then investigated across various cryptanalysis such as key-space, key sensitivity, histogram, information entropy, correlation coefficient, differential attack, cropping attack, noise attack and encryption execution time. Furthermore, the results are compared with the most recent literature. It is demonstrated that eπ-map has superior hyperchaotic performance in views of ergodicity, complexity and randomness. The IEA based on eπ-map and bit reversion is a secure and reliable algorithm thanks to its outperforming cryptanalysis results.

2D eπ-map for image encryption