Cryptanalysis of a secure image encryption scheme based on a novel 2D sine–cosine cross‑chaotic map

Recently, a new secure image encryption scheme was proposed based on a novel 2D sine–cosine cross‑chaotic map. The authors claimed that the encryption scheme they proposed was secure enough to resist all the existing cryptanalytic attacks. However, the multi-round original cryptosystem with permutation–bit diffusion structure (PBDS) was found to have three security vulnerabilities and was proved to be equivalent to the one-round cryptosystem with PBDS, which would lead to the original cryptosystem being successfully cracked by chosen-plaintext attack (CPA). Subsequently, two efficient and feasible attack schemes were proposed in this paper, and they require $$\left\lceil {\log_{2} W \times H} \right\rceil + 1$$ and $$\left\lceil {\log_{256} W \times H} \right\rceil + 1$$ times of CPA in total, respectively. Simulation and experimental results have verified the effectiveness and feasibility of the two attack schemes.