Cryptanalysis of an Image Encryption Scheme Using Variant Hill Cipher and Chaos

In 2019, a chaotic image encryption scheme based on a variant of the Hill cipher (VHC-CIES) was proposed by the Moroccan scholars. VHC-CIES introduces a Hill cipher variant and three improved one-dimensional chaotic maps to enhance the security. In this paper, we conduct a comprehensive cryptanalysis, and find that VHC-CIES can resist neither chosen-plaintext attack nor chosen-ciphertext attack due to its inherent flaws. When it comes to chosen-plaintext attack, firstly, we select a plaintext with the pixel values are all 0 and its corresponding ciphertext, and then use algebraic analysis to obtain the equivalent key stream for cracking VHC-CIES. Secondly, we select a plaintext which the pixel values are invariably 1 and obtain its corresponding ciphertext to obtain some Hill cipher variant parameters of VHC-CIES. Finally, we use the resulting steps of the first two to recover the original plain image from a given target cipher image. Similarly, a chosen-ciphertext attack method can also break VHC-CIES. Theoretical analysis and experimental results show that both chosen-plaintext attack and chosen-ciphertext attack can effectively crack VHC-CIES with data complexity of only O(2). For color images of size 256×256×3, when our simulation encryption time is 0.3150 s, the time for complete breaking by chosen-plaintext attack and chosen-ciphertext attack is about 0.6020 s and 0.9643 s, respectively. To improve its security, some suggestions for further improvement are also given. The cryptanalysis work in this paper may provide some reference for the security enhancement of chaos-based image cryptosystem design.