(IJCSIS) International Journal of Computer Science and Information Security, Vol. 12, No. 3, March 2014 Chaotic Scheme for Image Encryption Based on Arnold Cat's Map Ansam Osama Abdul-Majeed Department of Software Engineering College of Computer Science and Mathematics / University of Mosul Mosul, Iraq Abstract— Digital images are widely used media over the Internet for different purpose. Therefore, security becomes important in the transmission. This paper presents spatial domain multilevel image encryption algorithm based on Arnold cat's map. The algorithm divides the image into different size overlapping blocks along the levels of encryption. The block at level 1 begins at the center of the image and this block is iteratively enlarged in the next levels. In each level of the proposed algorithm, Arnold cat's map is implemented in each level on the block's pixels. Also, zigzag scan is applied on the whole image to further reducing the correlation between adjacent pixels. In order to achieve the diffusion, the pixel values are xored with different xor values begin at a value, which is generated randomly, beside control parameters and iteration number of Arnold cat's map, by using mid-product algorithm with the secret key as an initial seed. The results of experiments indicated that the proposed algorithm is highly decorrelated the adjacent pixels and it resists the statistical attacks. The values of ciphered image entropy are close to the ideal value. Furthermore, the proposed algorithm is very sensitive to key. It was concluded that the use of zigzag scan beside Arnold cat's map in spatial domain was very efficient to hide the statistical characteristics of the image. Keywords-Image encryption; Arnold cat's map; Zigzag scan; mid-product. I. INTRODUCTION Today, huge amount of different information has been transmitted over Internet. Thus, information security become very important issue in order to preserve the transmission of private and critical information[1]. Cryptography is the process of transforming original media from significative to ambiguous form to protect it from unauthorized persons. In recent years, the chaotic encryption played an important role in image encryption because one of the most important properties of chaotic is the sensitiveness to the initial condition and control parameters that makes it resists the statistical attacks [2]. Compared with the traditional algorithms; the chaotic algorithms are susceptible to the control parameters, while traditional algorithms are susceptible to key. In addition, diffusion and confusion are performed in traditional encryption by rounds, while they are performed by iteration in chaotic encryption [3]. Anyway, the higher security image encryption algorithm needs to fulfill the concepts of confusion and diffusion. Confusion and diffusion mean shuffling the pixels, as well as modifying the values to hide the statistical properties of the image [4]. In the past few years, many image encryption schemes using Arnold cat's map has been proposed. G. Chen, Y. Mao, and C. K. Chui, (2004), extend the 2D Arnold cat's map to 3D map. In between the adjacent round, the algorithm applied "xor plus mod" operation on each pixel to achieve the diffusion.The key is schemed by using Chen's chaotic system [3]. M. Ahmad, O. Farooq, and J. Blackledge, (2010), proposed a novel scheme that divided the image into 8×8 macroblock, computed the DCT coefficients for that block, and partitioned the block into non-overlapping blocks of coefficients. At each level, the block size reduced into the half, iteratively. The scheme shuffled the coefficients by using Arnold cat's map, and the Logistic map used to produce the control parameters and to mask the value of image pixels [1]. S. Keshari, and S. G. Modani, (2011), suggested method uses chaotic map to convert image pixels to corresponding map variable that used as initial condition to iterate other map. The algorithm then scrambled the position of pixel using Arnold cat's map [2]. S. Kashyap, and K. Karthik, (2011), divided the image into blocks, applied DCT, and then applied Arnold transform individually on each block using control parameters and number of iterations as a key. The algorithm generated a hash function by using the mean and variance of the blocks [4]. Z. Tang, and X. Zhang, (2011), proposed an image encryption algorithm by dividing the image into number of overlapping squared blocks. For each block, the algorithm generated a pseudo-random number as iterative number of Arnold transform for that block. After that, the Arnold cat's map applied in random order on each of these blocks [5]. This paper was aimed to propose multilevel image encryption algorithm in the spatial domain based on chaotic Arnold cat's map which is implemented on the pixels of overlapping blocks. In the proposed algorithm, the first block begins at the center of the image, and it is enlarged iteratively in hierarchical manner along the levels of encryption. The proposed algorithm used zigzag scan beside the Arnold cat's map to further reducing the correlation between adjacent pixels. In order to fulfill the concept of diffusion, the pixels values are xored with incremented values, depending on another random generated xor value. The control parameters and the iteration number of Arnold cat's map as well as the xor 26 http://sites.google.com/site/ijcsis/ ISSN 1947-5500