Abstract---Image compression is an important task in the field of image processing and it is an essential process in digital world to reduce the memory for storage and processing of the images. Many practical applications need compression and security. Encryption is a security control and widely used in many computer applications to provide protection for data. The images are encrypted before compression to give high level security and drawn much attention in several applications like data transferring, medical, navy and military operations. This paper has proposed an efficient image Encryption and Then Compression system (ETC) using Asymmetric Numeral Method (ANM) for compressing the images. The proposed ANM coder is compared with the existing Huffman and Arithmetic coder. The comparative analysis will be carried out for different size of images and results are illustrated that the proposed system is efficient in terms of compression ratio (Bits per Pixel) and computation time. Keywords -Image Encryption, Lossless Compression, Security, Asymmetric Numerical Method and Prediction Error Clustering.I. INTRODUCTION In this digital era, huge amount of data is transferred every second and the use of digital images are also increased. Digital images require more time for transmission because of their larger size. Hence, it is important to compress the images in order to improve the processing. An important goal of image compression is to reduce the bit rate for storage without altering the image quality. Image compression is the process of minimizing the size without degrading the quality of the image. The reduction in file size allows more images to be stored in a given memory space. It also reduces the time required for images to be sent over the Internet.Image compression is of two types: lossy and lossless. In lossy compression, original image is not identical to decompressed image that means there is some loss. Lossy compression is generally used for natural and photography images. Block Truncation Coding and Transform Coding are lossy compression technique. In lossless compression original image and decompressed image are equal, that means there is no loss. Lossless compression provides better compression for highly sensitive applications. Run Length Coding, Huffman Coding, Lempel Ziv Coding and Arithmetic Coding are lossless compression technique. A lossless compression technique is preferred for all purposes and especially for medical imaging and technical drawings. Encryption before compression brings more attention in recent years due to secure transmission in many applications. In Encryption-Then-Compression (ETC) technique, compression has to be conducted after encryption to enhance secure transmission. For fast transmission and protection of information, ETC is carried out in two steps [5]. The first step is an operation of encryption to modify the information and make them unreadable format [10]. The second step is an operation of compression in which the size of information to be transmitted is reduced ...