This paper analyzes the security of an image encryption algorithm based on a two-dimensional hyperchaotic map. This encryption algorithm generated chaotic sequences through a combination of two one-dimensional chaotic maps and used them as the permutation and diffusion key. Then, the image was encrypted by using the structure of row-column permutation, forward-diffusion, and backward-diffusion. The proposer claimed that the above algorithm was secure. However, it was found through cryptanalysis that the algorithm cannot withstand the chosen plaintext attack. Although the forward-diffusion and backward-diffusion of the original algorithm use two different diffusion keys and there is a ciphertext feedback mechanism, the analysis of the diffusion by iterative optimization showed that it can be equivalent to global diffusion. In addition, the generation of chaotic sequences in the encryption process is independent of the plaintext image, so the equivalent diffusion and permutation key stream can be obtained by adjusting the individual pixel values of the chosen plaintexts. Aiming at the security loopholes in the encryption algorithm, the theoretical and experimental results are presented to support the efficiency of the proposed attack and suggestions for improvement are given. Finally, compared with the performance analysis of the existing cracking algorithm, our cryptanalysis greatly improved the cracking efficiency without increasing the complexity of the data.
Keywords: chosen plaintext attack; cryptanalysis; hyperchaotic map; image encryption.