Cryptanalysis of an image encryption algorithm using quantum chaotic map and DNA coding

Recently, an image encryption algorithm using Quantum Chaotic Map and DNA Coding (QCMDC-IEA) has been reported. It consists of two main components: pixel-level permutation and DNA domain substitution. To support its ability to withstand various attacks, several security analyses and experimental simulations were presented. However, after careful cryptanalysis, we found that QCMDC-IEA has inherent fatal security problems. Although formally using complex chaos and DNA encoding, the chaos-based sequences used for encryption in QCMDC-IEA are independent of a plain image such that it suffers from the defect of the existence of an equivalent key. Moreover, the lack of confusion and diffusion in DNA domain encryption makes it vulnerable to cryptographic attacks. DNA domain encryption is then essentially a 2-bit data substitution process, so it can be equivalently simplified. On this basis, we propose an attack method to crack QCMDC-IEA, which first obtains an equivalent permutation key by differential cryptanalysis, and then eliminates the DNA domain substitution based on a chosen-plaintext attack using only four special plain images and their corresponding cipher images, and finally recovers the original plain images. Our attack method takes full advantage of the security defects in QCMDC-IEA and achieves complete decipherment with low complexity, thus better revealing its intrinsic security mechanism. To improve the security performance, some security enhancement suggestions are recommended for similar cryptosystems. Both theoretical analysis and experimental simulation results show that the proposed cryptographic attack method is effective and feasible for QCMDC-IEA with low attack complexity. Therefore, the cryptanalysis work in this paper can provide some theoretical hints for improving the security of a class of image encryption algorithms based on DNA coding and chaos.