A Novel Chaotic Image Encryption Algorithm Based on Latin Square and Random Shift

Abstract

To realize the safe transmission of images, a chaotic image encryption algorithm based on Latin square and random shift is proposed. The algorithm consists of four parts: key generation, pixel scrambling, pixel replacement, and bit scrambling. Firstly, the key is generated from the plain image to improve the sensitivity of the encryption method. Secondly, each pixel in each row of the image matrix is moved cyclically to the right, in turn, to change the position of the image pixel and realize pixel position scrambling. Then, a 256-order Latin square matrix composed of a chaotic sequence is used as a lookup table, and the replacement coordinates are calculated based on the image pixel value and the chaotic sequence value, replacing the corresponding coordinate elements in the image matrix. Finally, decompose the bitplane of the image matrix and combine it into two-bit matrices, scramble the two bit matrices, respectively, with the Latin square matrix, recombine the scrambled two-bit matrices, and convert them into decimal to obtain the ciphertext image. In the proposed encryption method, all the Latin square matrices used are generated by chaotic sequences, further enhancing the complexity of the generated Latin square matrix and improving the algorithm’s security. Experimental results and security analysis show that the proposed algorithm has good security performance and is suitable for image encryption.

A new chaotic image encryption algorithm based on transversals in a Latin square

“…We conducted simulation experiments and listed all the results in this section. In order to reflect the advantages of this algorithm, we compared this algorithm with some representative algorithms [4,12,33,34,[42][43][44].…”

“…Although the value of Lena in this article is inferior to Refs. [42], it is better than other six Refs [4,12,33,34,43,44]. .…”

“…Meanwhile chaotic systems also have some disadvantages, such as being defined on a set of real numbers, accompanied by short period phenomena, local linearity and uneven distribution, and requiring discretization when used [8], therefore it's easy to be damaged by chosen plaintext attacks or known plaintext attacks. In addition, many algorithms often use high-dimensional chaotic systems [9][10][11][12][13], increasing the complexity and unpredictability. The higher the dimension of the system, the more computations are required.…”

“…Recently, many combinatorial design structures have been applied in cryptography, such as Latin square [12,[31][32][33][34][35][36], Latin cube [11,13,17], Hadamard matrix [37], etc. Using simple chaotic system and these uniform combinatorial design structure as auxiliary, better encryption effect can also be achieved.…”

“…The same as algorithm in [17], it fully utilized the orthogonality of 3D Latin cube. In 2021, Zhang et al proposed an encryption algorithm based on Latin square and random shift [12]. Wang et al also put forward an image encryption algorithm based on Latin square array [34], utilizing the orthogonality and uniformity of Latin square.…”