Studying the Properties of Pixels Permutations Based on Discretized Standard Map

Abstract

In this article, we described specifics of pixels permutations based on the discretized, two-dimensional Chirikov standard map. Some properties of the discretized Chirikov map can be used by an attacker to recover the original images that are studied. For images with dimensions N ´ N the vulnerability of permutations allows for brute force attacks, and shown is the ability of an intruder to restore the original image without setting the value of keys permutations. Presented is also, successful cryptographic attack on the encrypted image through permutation of pixels. It is found that for images with dimension N ´ N the maximum number of combinations is equal to NN-1. A modified Chirikov map was proposed with improved permutation properties, due to the use of two nonlinearities, that increase the keys space to N2!.