Stable Image Encryption Algorithm Based on Expanded One-Dimensional Chaotic Jumping and Parallel Encoding Operation Grouping

Abstract

The current algorithm of encrypting images uses low-dimensional chaotic systems with a limited key space and poor security, while high-dimensional chaotic systems are difficult to implement and inefficient. Additionally, if image encryption algorithms use fixed DNA encoding rules, they could be cracked; dynamic coding can easily deviate from optimal solutions, thus causing algorithm instability. Based on this, a novel technique for image encryption is presented in this article. It is possible to avoid linear correlation of the chaotic sequence by randomly jumping on two uncorrelated one-dimensional chaoses. Meanwhile, numerous encryption results are generated in parallel by randomly grouping DNA encoding groups and encoding operations, and the optimal solution is then selected based on the encryption results, thereby minimizing ciphertext image instability to some extent. According to the experimental results, this algorithm produces high-security, plaintext-sensitive, and non-cracking encrypted images. Furthermore, this algorithm produces excellent encryption results both on color and sized images, and is applicable to a wide variety of applications.

Fractal-Based Hybrid Cryptosystem: Enhancing Image Encryption with RSA, Homomorphic Encryption, and Chaotic Maps

“…A smooth and uniform distribution is typically expected for the histogram of an encrypted image, indicating a high level of randomness and security. Compared to Zhang and Ma [47] and Zhoe et al [51], in Figure 14, we present the histograms for both the plain and cipher images of Baboon and Pepper, showcasing the results of the proposed technique. As depicted in Figure 14, the histograms for the cipher images exhibit a uniform distribution, validating the effectiveness of the proposed technique in securely transferring information through images.…”

“…Additionally, Table 4 provides a comparison with other strategies in the same field, highlighting that this proposed scheme features a robust security algorithm and is more resilient to statistical attacks than other methods. The mean correlation coefficient in the positive direction for images is 0.0008. correlation coefficient should be sufficiently low, as suggested by Zhang and Ma [47].…”

“…A positive sign signifies a positive association, while a negative sign indicates a negative relationship. To meet the image security requirements, the correlation coefficient should be sufficiently low, as suggested by Zhang and Ma [47]. Mathematically, the correlation coefficient between two adjacent pixels can be represented with Equation (17), where x and y represent image pixels, E(x) represents the mean of variable x, and E(y) represents the mean variable of y.…”

“…, The findings reveal a range of correlation coefficients between −1 and +1. Figure 13 illustrates the pixel correlations along three directions [47]: horizontal, vertical, and diagonal of the 512 512  Baboon colour image for both the plain image and the encrypted image. In Table 2, the correlation coefficients between adjacent pixel values are presented for both grayscale and colour images of varying sizes.…”

“…Proposed Lena −0.0041 0.0062 0.0091 Hue et al [48] 0.0004 0.0012 0.0009 Zhang et al [47] −0.00058 0.01091 −0.012076 Setiadi et al [49] −0.0011 0.0005 0.0007 Proposed Pepper 0.0021 0.0006 0.0018 Hue et al [48] 0.0027 0.0020 −0.0042 Alexian et al [50] −0.00021 0.00027 0.00128 Proposed Baboon −0.0003 −0.0011 0.0008 Hue et al [48] −0.0070 0.0021 −0.0077…”