Breaking an image encryption scheme based on Arnold map and Lucas series

TL;DR

This paper critically analyzes a recent image encryption scheme based on Arnold map and Lucas series, revealing significant vulnerabilities that compromise its security and rendering it unsuitable for cryptographic use.

Contribution

The paper demonstrates that the proposed encryption scheme is breakable due to a reduced key space and weaknesses against known plaintext attacks, challenging prior claims of security.

Findings

Key space is significantly reduced after analysis.

The scheme is vulnerable to brute force, chosen, and known plaintext attacks.

The design flaws make the system insecure for cryptographic purposes.

Abstract

Fairly recently, a novel image encryption based on Arnold scrambling and Lucas series has been proposed in the literature. The scheme design is based on permutation-substitution operations, where Arnold map is used to permute pixels for some T rounds, and Lucas sequence is used to mask the image and substitute pixel's values. The authors of the cryptosystem have claimed, after several statistical analyses, that their system is "with high efficiency" and resists chosen and known plaintext attacks. Negatively, in this paper we showed the opposite. The key space of the scheme under study could be reduced considerably after our equivalent keys analysis, and thus the system is breakable under reasonable brute force attack. After all, the design of the scheme has several weaknesses that make it weak against chosen and known plaintext attacks. Consequently, we do not recommend the use of this system for any cryptographic concern or security purpose.