An asymmetric phase image encryption technique using Arnold transform, singular value decomposition, Hessenberg decomposition, and fractional Hartley transform

Abstract

In this paper, we perform a cryptanalysis of a previously published symmetric cryptosystem that utilizes the Arnold transform (AT), singular value decomposition (SVD), and the fractional Hartley transform (FrHT) domain. By performing an attack-analysis, it is shown that the symmetric cryptosystem is vulnerable to a Known-Plaintext Attack (KPA). If an attacker knows the cipher-text and the order of the FrHT, attacker can recover the correct combination of SVD and AT parameters used in the image encryption algorithm. To overcome the security weakness of the symmetric cryptosystem, we propose an asymmetric phase image encryption by employing the Arnold transform, Singular value decomposition, and Hessenberg decomposition (HD) in the FrHT domain. The scheme is validated using evaluation metrics; mean-square-error, peak signal-to-noise, entropy, 3D mesh-, correlation-, noise-attack-, occlusion-attack-, and linear-attack analyses. Keys generated by SVD and HD make the cryptosystem asymmetric, making it resistant to Known-Plaintext Attack (KPA) and Chosen-Plaintext Attack (CPA).