# Implementation of MS Circle Map in Digital Image Encryption
## 1 Introduction
[7] proposed a new image encryption algorithm by constructing a hyperchaotic map called 2D-SQPM and then developed an image encryption algorithm based on 2D-SQPM and a pixel fusion strategy (IEASP). At initialization, an initial secret key is input to 2D-SQPM to generate a keystream, and, then, this keystream is used to encrypt each image. For each image, IEASP completes the encryption through pixel fusion and two rounds of vector-level image filtering, chaotic pixel superposition, and intra-vector quick scrambling. [PERSON], [PERSON] et al. [8] developed a multi-image encryption algorithm based on the new fractional-order 3D Lorenz chaotic system and 2D-SCPM. Other researchers have proposed encryption algorithms using the chaos logistic map and deoxyribonucleic acid (DNA) encoding functions to improve the security level of image encryption algorithms. DNA encoding is used to scramble pixel values into DNA bases and scramble them in DNA addition, DNA complement, and exclusive or (XOR) operations. Meanwhile, the logistic function is used as a keystream generator required in DNA complement and XOR operations [9]. There has been some research on chaos function-based encryption algorithms, such as those using the chaos function logistic map [10], which produces a key space of \(10^{30}\); those using the Maria Suryadi (MS) map [11; 12], which produces a keyspace of \(3.24\times 10^{634}\); those using the Gauss Iterated map [13], which has a Number of Pixel Change Rate (NPCR) value of 93. 6% and Unified Averaged Changed Intensity (UACI) of 27.9%; those using Gauss and Circle [14], which produces a key space of 2.6244 \(\times\)\(10^{1269}\)[15]; and those which develop an image encryption algorithm using the logistic map and Piecewise Linear Chaotic map, which has a key sensitivity value of \(10^{-10}\) resistance to brute force attack. In this study, digital image encryption and decryption were carried out through the composition of MS Map and Circle Map functions. The developed algorithm aims to improve security resilience against various attacks and speed up the process time in digital image encryption. The performance of the proposed algorithm was tested using initial value sensitivity level analysis, key space analysis, histogram, correlation, entropy, NPCR, UACI, Mean Square Error (MSE), and Peak Signal to Noise Ratio (PSNR). In previous studies, image encryption using the Tent map with a key space of 2\({}^{106}\), an entropy value of 7.999876, and correlation coefficients near zero demonstrated strong resistance to brute force and statistical analysis attacks [16]. Similarly, MS Map encryption resulted in a key space of 3.24 \(\times\) 10\({}^{634}\), key sensitivity of 10\({}^{-17}\), and uniform distribution in encrypted images, making it resistant to known-plaintext and brute-force attacks [11]. In comparison, Henon-Tent map encryption achieved a key space of 10\({}^{60}\), entropy of 7.9992, and key sensitivity of 10\({}^{-16}\), with an NPCR of 99.61% and UACI of 33.46%, making it resistant to brute force, chosen-plaintext, and chosen-ciphertext attacks [17]. More recently, a hybrid MS-Tent map encryption algorithm was designed with an even larger key space of 1.05 \(\times\) 10\({}^{959}\), key sensitivity of 10\({}^{-17}\), and near-zero correlation coefficients, proving its robustness against brute-force and statistical attacks [18]. These comparisons highlight that the MS Circle Map encryption algorithm not only offers superior security through a significantly larger key space but also enhances resistance to various cryptanalysis attacks, making it a highly efficient and secure method for digital image encryption. Recent advancements in image encryption have extensively explored pixel scrambling and diffusion techniques to enhance security. An encryption method using Hilbert curve-based pixel scrambling and dynamic DNA coding-based pixel diffusion demonstrated strong security performance [19].