A Novel Framework for Image Encryption using Karhunen-Loeve Transform

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), and decryption, O(n). 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.