                  1 5 . 0 , 51 . 0 1 . 1 31 . 0 5 . 0 0 , 51 . 0 31 . 0 ) , ( 67 . 1 67 . 1 x e x e x SEM x x    Abstract—This paper proposes a robust image encryption algorithm via Smooth Exponential Map (SEM) to meet the demand for fast and highly secure image transmission. The proposed algorithm consists of two phases; image-diffusion and image-fusion. In the image diffusion phase, pixel locations of the original image are shuffled in the spatial domain while pixel values are modified in the image fusion phase. Investigating the chaotic map characteristics of proposed SEM indicates a full chaotic behavior. Results of testing the proposed algorithm show that the proposed algorithm has a large key space with complete obscuring of the original image, secured against brute-force attack as it is achieved a large complexity of order   90 2 O , and requires 343ms to encrypt 200x200 pixels image. Index Terms—Chaotic map, image encryption, lyapunov exponent, image fusion, image diffusion. I. INTRODUCTION Different digital image encryption algorithms have been proposed in the literature [1-4]. The main concern of such algorithms is to meet the demand for fast and highly secure image transmission. There are two major groups of digital image encryption algorithms: non-chaos selective methods (i.e., traditional algorithms) and Chaos-based selective or non-selective methods [5]. Unfortunately, traditional image encryption algorithms were reported with low-level efficiency [2]. On the other hand, the chaos-based image encryption scheme provides an efficient encryption solution [6]. In this paper, a robust image encryption algorithm based on Smooth-Exponential-Map (SEM) is proposed to meet the demand for fast and highly secure image transmission. The proposed algorithm consists of two phases; image-diffusion and image-fusion. In the image diffusion phase, pixel locations of the original image are shuffled in the spatial domain while pixel values are modified in the image fusion phase. The rest of this paper is organized as follows. Section 2 presents the proposed SEM. Section 3 discusses and analyzes the chaotic map characteristics of proposed SEM. The two implementation phases; diffusion and fusion, of the proposed SEM-based image encryption algorithm are explored in Section 4. Experimental results and evaluation of the proposed algorithm are illustrated in Section 5 while Section 6 concludes the paper. Manuscript received April 05, 2012; revised May 5, 2012 The authors are with the Department of Computer Engineering, Al- Hussein Bin Talal University, Ma’an, Tel: +962799128884 (e-mail: Jordan, fadiabuamara@ahu.edu.jo, shorman@ahu.edu.jo). II. SMOOTH-EXPONENTIAL MAP (SEM) The proposed Smooth-Exponential-Map is characterized by (1) where ) , ( 1  n n x SEM x   is the iteration function such that ] 1 , 0 [ ] 1 , 0 [ :  SEM . The initial value 0 x and the parameter  compromise the initial condition and the control parameter of the SEM, respectively. The parameter  has the range of ] 468 . 1 , 3324 . 1 [   while the sequence of real values     , , , , 1 0 n x x x forms the system orbit. III. SEM CHARACTERISTICS INVESTIGATION The following chaotic-map characteristics of the SEM algorithm are investigated in this section: return maps, bifurcation diagram within an interval, high sensitivity to initial conditions and control parameters, and Lyapunov exponents. Fig. 1. (A) The iteration function associated with SEM map for 338 . 1   . (B) time series plot for two sequences of 100 iterates generated by the SEM. The solid-blue and red-dashed lines stand for 0.2287 and 0.2287001, respectively. Fadi Abu-Amara and Ahmed Musa Robust Chaos via Smooth Exponential Map International Journal of Future Computer and Communication, Vol. 1, No. 2, August 2012 196