Image encryption with dynamic chaotic Look-Up Table

📝 Abstract

In this paper we propose a novel image encryption scheme. The proposed method is based on the chaos theory. Our cryptosystem uses the chaos theory to define a dynamic chaotic Look-Up Table (LUT) to compute the new value of the current pixel to cipher. Applying this process on each pixel of the plain image, we generate the encrypted image. The results of different experimental tests, such as Key space analysis, Information Entropy and Histogram analysis, show that the proposed encryption image scheme seems to be protected against various attacks. A comparison between the plain and encrypted image, in terms of correlation coefficient, proves that the plain image is very different from the encrypted one.

💡 Analysis

In this paper we propose a novel image encryption scheme. The proposed method is based on the chaos theory. Our cryptosystem uses the chaos theory to define a dynamic chaotic Look-Up Table (LUT) to compute the new value of the current pixel to cipher. Applying this process on each pixel of the plain image, we generate the encrypted image. The results of different experimental tests, such as Key space analysis, Information Entropy and Histogram analysis, show that the proposed encryption image scheme seems to be protected against various attacks. A comparison between the plain and encrypted image, in terms of correlation coefficient, proves that the plain image is very different from the encrypted one.

📄 Content

Image Encryption with Dynamic Chaotic Look-Up Table

Med Karim ABDMOULEH, Ali KHALFALLAH and Med Salim BOUHLEL Research Unit: Sciences and Technologies of Image and Telecommunications Higher Institute of Biotechnology Sfax, Tunisia medkarim.abdmouleh@isggb.rnu.tn; khalfallah.ali@laposte.net; medsalim.bouhlel@enis.rnu.tn

Abstract—In this paper we propose a novel image encryption scheme. The proposed method is based on the chaos theory. Our cryptosystem uses the chaos theory to define a dynamic chaotic Look-Up Table (LUT) to compute the new value of the current pixel to cipher. Applying this process on each pixel of the plain image, we generate the encrypted image.
The results of different experimental tests, such as Key space analysis, Information Entropy and Histogram analysis, show that the proposed encryption image scheme seems to be protected against various attacks. A comparison between the plain and encrypted image, in terms of correlation coefficient, proves that the plain image is very different from the encrypted one. Keywords- Chaos; Image encryption; Logistic-map; Look-Up Table. I. INTRODUCTION Nowadays, in the digital world, the security of transmitted digital images/videos becomes more and more vital, against the web attacks which become important [1]. So, cryptography is used to confirm security in open networks [2].
Cryptography is the science that uses mathematics to offer encryption algorithms to protect information. Many cryptographic methods have been proposed. These techniques are classified into three categories: • Symmetric cryptography: in this class the same key is used for encryption and decryption. Data Encryption Standard (DES) and Advanced Encryption Standard (AES) are the best known examples of symmetric encryption [3] [4]. • Asymmetric cryptography: two different keys are used. The first realization of a public key algorithm called RSA [5] according to its inventors Rivest, Shamir and Adelman, is the most used algorithm in asymmetric encryption. • Hybrid cryptography: it is based on combination of the best features of symmetric cryptography and asymmetric [6]. Security has become a key issue in the world of electronic communication. An efficient cryptosystem should not be broken by hackers. In this research we have tried to propose a secure and simple method of image encryption based on chaotic function. This paper is organized as follows: section II describes the relation between chaos and cryptography and presents the Logistic Map function. The proposed method is introduced in section III. In section IV, we discuss the experimental results and test the efficiency of the algorithm. Finally, section V is devoted to the conclusion. II. CHAOTIC SYSTEM Since the 1990’s, Chaotic Systems (CS) have attracted researchers to use them in secure communication [7] [8]. Most CS proposed in literature are characterized by certain properties [9] that facilitate their use in the design of modern cryptographic systems. These properties are essentially the ergodicity, sensitivity to the initial values and to the controlling parameters. In modern cryptography, the CS have been used extensively in the development of cryptosystems. The CS are among the best known and most widely used in cryptography, they cite the Logistic Map (LM). The Logistic Map [10] is one of the most famous and simplest one-dimensional map. Therefore this function has been studied recently for cryptography applications. The LM is widely used in image encryption [11] [12]. The Logistic Map function is expressed by the following formula:

1 (1 ) n n n X X X µ

• = −

     (1) 
  

Where x is a floating number, which takes values in the interval [0, 1], n = 0, 1, 2, … and µ is the control parameter
0 < µ ≤ 4. If parameter µ takes a value between 0 and 3, the Logistic Map, which is defined by equation (1), is seen to converge to a particular value after some iteration. As parameter µ is further increased, the curves bifurcations become faster and faster. µ should be greater than 3.5784257 (known as the “point of accumulation”) in order to have a chaotic system. Finally for µ=3.9 to 4, the chaos values are generated in the complete range of 0 to 1 [13]. III. PROPOSED METHOD In this section, we present our new image cryptosystem. The architecture of the proposed method is shown in “Fig. 1- 3”. In the first step, we generate a chaotic matrix using the Logistic Map function LM1 (x0XOR and µ0XOR). We mix this chaotic matrix with the plain image using the logical function XOR to obtain the initial encrypted image I1.

Figure 1. XOR Chaotic encryption For each pixel P1 from I1, we generate a chaotic LUT using the Logistic Map function (LM2) having as parameters µ0 and x0(Pc). Where Pc is the value of the previous encrypted pixel by our cryptosystem. The initial condition x0(Pc) depends

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