This chapter proposes a multiple image encryption method based on multi-dimensional chaotic equations. Four-dimensional differential chaotic equations of Lorenz attractor have been used to generate the initial security key, and alternate logistic maps have been used for encryption. Initially, three input images are used in a matrix form, where size of each image is M×N, and a composite image is derived by combining the one dimensional matrix of the input images, where size of the composite image matrix is 3×(M×N). Secondly, Lorenz attractor (LA) generates the security key using the composite matrix, and then alternate logistic map is applied with one-dimensional and two-dimensional logistic maps to confuse the matrix. In every iteration of logistic maps, XOR operation is used to encrypt the composite image, and at last, transformation is applied to diffuse the matrix. Finally, the encrypted composite image is obtained in the form of a confused matrix. The proposed algorithm reduces the correlation, increases entropy, and enhances performance of encryption.
TopIntroduction
Nowadays, data security is a significant problem in computer networks and mobile device technology (Sankpal & Vijaya, 2014). The rapid advancement and evolution in transmission technologies have increased the security concerns about multimedia data as lots of data is being stored and transmitted in various patterns over the network. Thus the security of the digital data against eavesdropping and attackers is an important concern. Hence, the security algorithms have emerged as a vital research issues (KN, 2011)(Patel & Parikh, 2018). The digital data is of many types like audio, video, text and image. The digital image data has specific instinctive trait such as huge data size, high correlation between neighbouring pixels and strong redundancy etc. (Mohammad et al., 2017). The image data requires the high real-time tract in conversation. Hence, an encryption algorithm with high security is required (Bakhshandeh & Eslami, 2013). Due to these characteristics, the classic encryption algorithms such as Advanced Encryption Standard (AES)(Çavuşoğlu et al., 2017), Data Encryption Standard (DES) (Qian et al., 2009), Two Fish cipher (Agath et al., 2018), IDEA (Xu et al., 2016)etc. These algorithms are not effective and intact for real time digital image encryption.
Since last three decades, many researchers are using chaos based techniques for encrypting an image. The chaos and cryptography share many common characteristics that make chaos theory suitable for cryptography (Guan et al., 2005). The chaotic maps are an imperative part of the chaos theory and play a valuable role in image encryption (Özkaynak, 2018). The cryptography algorithms use the encryption key, rounds of chaotic maps for permutation and diffusion process for encryption. Moreover, phase space in such algorithms consists of finite set of integer numbers [9]. However, in chaotic maps, phase space consists of set of real number and these use iteration for encryption. The specialties of chaotic maps have encouraged researcher to invent many new and secure encryption algorithms (Suri & Vijay, n.d.a). The chaotic maps have many peculiarities such as sensitive to initial conditions, nonlinear dynamic behaviour, ergodicity, high speed and good computational power. The chaotic system works into two steps, generating security key and encryption is done by using this security key. These can be divided into two categories: one dimensional chaotic map and multi dimensional chaotic map (Li et al., 2018; Pak & Huang, 2017; Wang et al., 2018).
Recently, many image encryption algorithms have been proposed using the one dimensional chaotic map, two dimensional chaotic map, three dimensional chaotic map, four dimensional chaotic map and modified one dimensional chaotic map (Marotto, 1978). The one dimensional chaotic maps have simple structure, low computation cost and easy implementation. One dimensional chaotic map provides the limited range of dynamic chaotic behaviour and also uses less parameter for encryption (Pareek et al., 2005). However, one dimensional chaotic maps are easily cracked by using many methods like phase regression or nonlinear prediction methods (Baldovin & Robledo, 2002). Therefore, the multi dimensional technologies have been proposed.Multi dimensional chaotic map enhance the security in image encryption because of its complicated structure. Multi dimensional maps are more secure and effective than the low dimensional chaotic maps. These maps provide the large range of dynamic chaotic behaviour and good performance compared to one dimensional chaotic map (Murillo-Escobar et al., 2017). The proposed algorithm use non linear four dimensional differential equations and these equations are used the traditional three dimensional differential equation. These equations enumerate large range of dynamic chaotic state. Four dimensional differential equations generate pseudo random bit sequences (PRBS) and this method increases the speed and randomness of the key generation and an effect on the security of the image encryption (Murillo-Escobar et al., 2017; Tong et al., 2015).