Cryptoanalysis of multiple-image encryption scheme based on amplitude- and phase-truncation in the Fourier domain

This paper presents a comprehensive cryptoanalysis of a multiple-image encryption scheme based on amplitude truncation (AT) and phase truncation (PT) in the Fourier domain. In contrast to the conventional single-image cryptosystem based on phase-truncated Fourier transform (PTFT), the enhanced PTFT-based cryptosystem was proposed to encode multiple images efficiently and to augment the security strength by expanding the key space. Nevertheless, we found that the amplitude key exhibits low sensitivity, which has a restricted impact on the security enhancement and makes the scheme vulnerable. Moreover, the two random phase masks (RPMs) employed as private keys are uncorrelated with the plaintexts, which can be recovered through a devised known-plaintext attack (KPA). Once these additional private keys are recovered, the number of unknown keys is reduced to two, making it possible to recover plaintext information encrypted by this advanced PTFT-based cryptosystem using an iterative attack without any knowledge of the private keys. Based on these findings, a hybrid attack consisting of two cascaded KPAs and chosen-ciphertext attacks (CCAs) is proposed to successfully crack the improved PTFT-based cryptosystem. Numerical simulations have been performed to validate the feasibility and effectiveness of the proposed hybrid attack.