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1.1 INTRODUCTION
Encryption of the image and audio data using the conventional methods of cryptography has certain limitations in the cryptographic strength and large computational effort due to huge amount of data and high correlation among pixels. Some of the popular public key encryption methods, such as RSA, El Gamal are not suitable for encryption of large data files and images, because their encryption rate is slow. Moreover, the security of such public key cryptographic schemes relies on the inability to perform factorization of large numbers or to solve the discrete logarithm problem in a fast, efficient manner. Private key encryption algorithms, such as DES, 2DES, 3DES, AES, IDEA etc. are based on several iterative steps consisting of substitution and permutation. The security is mostly guaranteed by substitution, while the permutation part is somewhat neglected. It is general belief that utilization of complicated permutations might significantly increase the security of the whole cipher.
Chaos-based image-encryption approaches have shown some exceptional properties in the aspects concerning security, complexity, speed, computing power, computational overhead etc [1]. It is not a very new idea and many researchers have proposed different types of such encryption. In chaotic key-based algorithm, image pixels are rearranged based on the time series [2]. This method is very simple, but is weak to the chosen/known-plaintext attack using only one plain image [3]. Scharinger proposed chaotic Kolmogorov flow based image encryption [4]. The whole image is taken as a single block in this scheme, and permuted through a key-controlled chaotic system based on Kolmogorov flow. In order to confuse the data, substitution is applied, which alters the statistical property of the cipher-image. The scheme is computationally secure and superior to contemporary block encryption systems for image and video data encryption. For advancing the quality of encryption effectively, the method of position scrambling can be used before encryption. Some classical scrambling algorithms are Cat map [5-8], baker map [1,9], affine transformation [10], magic-square transformation [11], knight-tour transformation [12], standard map, tent map etc. Among these maps, Cat map and baker map attract much attention. Cat map is a two-dimensional chaotic map introduced by Arnold and Avez. Baker map is another two-dimensional chaotic map based on which Pichler and Scharinger first introduced their encryption schemes. In [1], a symmetric image encryption scheme based on 3-D chaotic Cat map was proposed. The 2-D chaotic Cat map was generalized to 3-D for designing a real-time secure symmetric encryption scheme, which employed 3-D Cat map to shuffle the positions of image pixels and used another chaotic map to confuse the relationship between the cipher-image and the plain-image. In [13], baker map was further extended to 3-D. An alternative chaotic image encryption based on baker map that supports a variable-size image and includes other functions such as password binding and pixel shifting to further strengthen the security of the cipher-image was proposed [14]. In [15], Baptista proposed a chaotic encryption based on partitioning the visiting interval of chaotic orbits of the logistic map.
1.2 MOTIVATION OF THE PRESENT WORK
Though public key algorithms, such as RSA, El Gamal and private key algorithms, such as DES, 2DES, 3DES, AES, IDEA are popular encryption schemes, these methods are not suitable for encryption of large data files and images, because their encryption rate is slow, On the other hand, chaotic map algorithms are appropriate for image encryption, in which speed is an essential criterion. We propose an encryption scheme for images that uses combination of chaotic Cat map and simplified data encryption standard (S-DES). The proposed scheme takes the advantages of Cat map particularly suitable for image encryption at high speed and S-DES for realization of DES with smaller key size. In this scheme, the key of S-DES can be changed in real-time.
1.3 ORGANISATION OF THE DISSERTATION
The organization of our dissertation is as follows.
In Chapter 2, we introduce the background and earlier works of the research containing the chaos, the concepts of cryptography, describes the main features of chaotic Cat map and simplified data encryption standard, the relationship between chaos and cryptography and historical review of chaotic image encryption.
In Chapter 3, we describe our proposed new scheme of chaotic image encryption involving the image encryption algorithm and experimental results.
In Chapter 4 is on conclusions and future works.