# Joint Image Compression and Encryption Using IWT with SPIHT, Kd-Tree and Chaotic Maps
## 1 Introduction  
In the current era, with the availability of inexpensive capturing devices with high resolution, the rapid growth of image transmission over public networks has raised substantial concern in the fields of secure transmission and the compression of images [1; 2]. The compression of data is the main thrust in multimedia applications due to high redundancy. Without compression, storage and communication resources are used inefficiently. In particular, low-bandwidth communication channels and power-limited devices require low-bit-rate compression due to bandwidth and power constraints. In addition, encryption is required for confidentiality and integrity of the information, particularly for open-access networks. Encryption algorithms are typically optimized for a specific type of data due to several factors, such as encryption speed, processing power and sensitivity to bit changes. Encryption algorithms that are specially designed for text data encryptions, such as data encryption standard (DES), advance encryption standard (AES), and Blowfish, are not suitable for image data encryption. Image data have various built-in features, such as redundancy and strong correlationamong adjacent pixels. Therefore, specific encryption techniques are required for such a bulky data. In comparison to traditional encryption techniques, chaotic map cryptosystems are considered more suitable for image encryption [3; 4; 5; 6; 7; 8; 9; 10; 11; 12]. However, some chaotic cryptosystems have well-known weaknesses such as relatively small key size, short-length chaotic orbits and lack of the confusion property [4; 13]. A joint compression and encryption scheme are a promising method for transmitting image data securely and efficiently over public networks. By combining the compression and encryption operations, more uncertainty is achieved in the size of the encrypted image. Due to this uncertainty, the difficulty level that would be faced by attackers is increased. Currently, there exist three approaches in this field: The first method is to achieve compression via encryption algorithms [1]. In this method, compression capability is embedded in an encryption algorithm. However, this method is not suitable for image data because image compression capability is compromised. The second method is based on a compression algorithm and encryption is an additional capability that is realized via entropy coding techniques [1; 2]. However, this method is based on a compression algorithm and encryption is embedded as an additional functionality. Therefore, the security levels are not appropriate. The third scheme is based on compression and encryption serially [1; 14; 15; 16]. Unlike the former two methods, the compression and encryption serially are considered equally important. However, by separating these two operations, we cannot achieve high uncertainty in the length of the cipher image. In this paper, a joint image compression and encryption scheme that is based on IWT with SPIHT, Kd-tree and multiple chaotic maps is proposed. The main contribution of this work is to use high dimensional kd-tree for the diffusion and permutations of integer wavelet coefficients and SPIHT output in such a way that maximum compression is achieved. In the proposed three stage scheme, joint compression and encryption was performed at first two stages. At third stage only encryption was performed through multiple chaotic maps. The proposed method provides high security and much more compression than the existing joint image compression and encryption techniques. The experimental results that are presented in this paper demonstrate the effectiveness of the proposed joint image encryption and compression scheme. This research evaluates the Kd-tree compact data structure for permutation and substitution of wavelet coefficients and SPIHT bit stream for the compression and encryption simultaneously. Kd-tree is used here to find the homogenous regions of zeros and ones in the bit stream for the further compression of SPIHT output.