International Journal of Computer Applications (0975 – 8887) Volume 54– No.2, September 2012 1 A Novel Framework for Image Encryption using Karhunen-Loeve Transform T. Sivakumar Assistant Professor (Senior Grade) Department of Information Technology PSG College of Technology,Tamilnadu-641004,India. R. Venkatesan, Ph.D Professor & Head Department of Computer Science and Engineering PSG College of Technology,Tamilnadu-641004,India. ABSTRACT The Karhunen-Loeve (KL) transform is widely used technique for image compression or clustering analysis. Since KL transform is a reversible linear transform, a novel cryptosystem is developed to provide confidentiality service for images. The original image (x), in the form of square matrix, is given as input to the KL transform which in turn produces the encrypted image (y) and the decryption key (k). Since the key matrix (k) plays a major role for decryption, it is encrypted by the receiver’s public key by using RSA algorithm. The encrypted image (y) and key matrix (k) are transmitted over the public network. On receiving the encrypted image (y) and key matrix (k), the receiver takes the transpose of the decrypted key matrix (k) and multiplies the result with the encrypted image (y) to get the original image (x). The time complexity of the proposed scheme is calculated separately for both encryption, O(n 2 ), and decryption, O(n 3 ). The histograms of the encrypted images are almost uniform and different from that of the original images. This method of image cryptosystem is more suitable for small images. Keywords:Image Encryption, KL Transform, Image Histogram, and Correlation Coefficient 1. INTRODUCTION In this fast growing technical world, where the Internet provides essential communication between tens of millions of people and is being increasingly used as a tool for transmission of digital images, security becomes a tremendously important issue. Most traditional cryptosystems have been designed to protect textual data. Traditional encryption algorithms such as data encryption standard (DES) and RSA, has the weakness of low-level efficiency when the image is large. Use of traditional cryptosystem to encrypt images directly is not good for two reasons [5]: (a) since the image size is much larger than that of text, it needs more time to directly encrypt the images, and (b) the decrypted text must be equal to the original text, but this is not required for images (i.e., small distortion is acceptable due to human perception). The basic function of the KL transform depends on the statistics of input data and the coefficients in the Karhunen– Loève theorem are random variables. It is the best among all linear transforms with respect to energy compaction which means most of the ‘energy’ of the transform coefficients is concentrated within the first few components. The foremost properties of KL Transformare (a) reversible linear transform, (b) exploits the statistical properties, (c) discards redundancy, (d) minimizes the total mean square error, and (e) Gaussian distribution. The following are some major requirements to design any cryptosystem: 1. An encryption scheme is unconditionally secure if the ciphertext generated by the scheme does not contain enough information to determine uniquely the corresponding plaintext. 2. Reversible transformation: A block cipher operates on a plaintext block of n bits to produce a ciphertext block of n bits. There are 2 n possible different plaintext blocks and, for theencryption to be reversible (ie. for decryption to be possible), each must produce a unique ciphertext block. 3. Diffusion: The statistical structure of the plaintext is dissipated into long-range statistics of the ciphertext. This is achieved by having each plaintext digit affect the value of many ciphertext digits. 4. Size of input plaintext message must be equal to the size of output ciphertext message produced by the scheme. Since KL transform satisfies some of the above said properties of cryptosystem, this paper focus on to design and develop a cryptosystem to provide confidentiality service for images. 2. RELATED WORK In Hill cipher algorithm, the inverse of the key matrix used for encrypting the plaintext does not always exist. If the key matrix is not invertible, then encrypted text cannot be decrypted. Bibhudendra et al [1], proposed a novel Advanced Hill (AdvHill) encryption technique, which uses an involutory matrix, to encrypt an image. In the Involutory matrix generation method the key matrix used for the encryption is itself invertible. Thus the computational complexity is reduced by avoiding the process of finding inverse of the matrix at the time of decryption. In [3], the authors have made use of five discrete orthogonal transforms in speech encryption systems. The transforms considered are the Discrete Fourier Transform, Discrete Cosine Transform, Walsh Hadamard Transform, KarhunenLoeve Transform and the Discrete Prolate Spheroidal Transform. First the speech samples converted to a transform domain and the encryption is done in the transform domain. The encrypted transform samples are converted back to the time domain and transmitted. The authors concluded that, the DCT, DFT and DPST can be used in narrow band systems such as speech transmission over public switched telephone network and the KLT and WHT are more suitable where wider bandwidth is available. The transformation is done twice during encryption and twice during decryption. G.A.Sathishkumar et al [4] provided a secure image encryption technique using multiple chaotic based circular mapping. Here, first, a pair of sub keys is given by using chaotic logistic maps. Second, the image is encrypted using