On the security of a class of diffusion mechanisms for image encryption

TL;DR

This paper analyzes the security of a diffusion mechanism used in image encryption, revealing that its vulnerability allows for key recovery with constant data complexity, thus questioning its robustness.

Contribution

It provides a theoretical analysis showing the diffusion mechanism's vulnerability to plaintext attacks, regardless of key scheduling, supported by numerical validation.

Findings

Key recovery complexity is O(1) for the diffusion mechanism.

The mechanism is vulnerable under plaintext attack assumptions.

Numerical examples confirm the theoretical analysis.

Abstract

The need for fast and strong image cryptosystems motivates researchers to develop new techniques to apply traditional cryptographic primitives in order to exploit the intrinsic features of digital images. One of the most popular and mature technique is the use of complex ynamic phenomena, including chaotic orbits and quantum walks, to generate the required key stream. In this paper, under the assumption of plaintext attacks we investigate the security of a classic diffusion mechanism (and of its variants) used as the core cryptographic rimitive in some image cryptosystems based on the aforementioned complex dynamic phenomena. We have theoretically found that regardless of the key schedule process, the data complexity for recovering each element of the equivalent secret key from these diffusion mechanisms is only O(1). The proposed analysis is validated by means of numerical examples. Some additional cryptographic applications of our work are also discussed.