# Cryptanalysis of Permutation-Diffusion-Based Lightweight Chaotic Image Encryption Scheme Using CPA
## 1 Introduction  
With the development of Internet and information technology, ever-increasing multimedia data is emerging in our daily lives. Among multimedia data, digital image carrying information in a visualized manner has become a widely used data format. Many of these digital images in networks may be involved in personal privacy, military secrets, trade secrets, and even national security. If such digital images are intercepted by some unauthorized users, serious security disasters can occur. Thus, it is essential to protect private images with some effective solutions [1; 2; 3; 4]. Image encryption [5; 6; 7], which aims at preventing unauthorized access by converting the data into an unrecognized form, has been a well-known effective and popular method to secure them. Among different types of image encryption algorithms, the Chaos-based cryptosystem is particularly efficient and popular in image processing fields as it has many significant characteristics such as ergodicity, unpredictability, and initial state sensitivity [8; 9; 10; 11]. In general, the existing chaotic systems can be partitioned into two primary types: one dimension (1D) maps [9] and high dimension (HD) maps [11]. 1D chaotic maps often have simple structures and low computational complexity; thus, it is efficient and easy to generate pseudorandom sequence during image cryptography. However, they face some potential drawbacks like vulnerability and limited chaotic ranges [12; 13]. The demanding for higher level of security of image cryptosystems motivates researchers to extend 1D maps to HD chaotic maps. Generally speaking, HD maps have larger chaotic ranges and at least two variables to acquire better chaotic behaviors. These properties also make their chaotic orbits more unpredictable, and thus lead to a higher security for cryptosystems. However, higher computational overhead and implementation difficulty of these HD chaotic maps make them impractical for resource-limited devises as well [14; 15; 16]. Thus, to balance chaotic behaviors and computational cost, it is necessary and vital to develop such a scheme, which not only ensures larger key space to resist brute attack and key sensitivity to control parameters, but also can be implemented in a low computational overhead. To meet the demanding for practical scenarios, a novel and lightweight chaotic image encryption scheme using 2D dimension Baker's map has been proposed for secure communication [17]. The image cryptography algorithm [17] under study, involves the use of Permutation-Diffusion based on Fridrich's structure. First, based on the two sets of initial settings--\((\alpha,x_{0},y_{0})\) and \((\alpha^{\prime},x_{0}^{\prime},y_{0}^{\prime})\)--of 2D Baker's map, the key matrices **X** and **Y**, both used for the permutation phase, and the diffusion key \(R\) (random number), used for the diffusion phase, are obtained. Then, in the permutation phase, the original plaintext is permuted based on the generated key matrices **X** and **Y**; the permuted plaintext is further diffused by the XOR operation between the matrix **r** and the permuted plaintext **P**. The original cryptosystem can provide good security for image to some degree; nevertheless, the simple XOR operation of the diffusion phase is insecure enough since it can be completely cracked by using only one time of CPA. In turn, the permutation phase can be further broken with the other CPA attack proposed by the state-of-the-art works [18]. Based on the above, the original encryption design may be not suitable for privacy protection with higher level of security requirements. The main contributions of this paper are as follows. 1. We propose a feasible attack strategy that can completely break the original Permutation-Diffusion based image cryptosystem with high security and low computational overhead, which is especially applicable for secure image communication in the resource-constrained modern network environment. 2.