Image Encryption & Authentication Using Orthogonal Transformation on Residual Number System

Abstract

In every communication channel or methodology now-a-days, there is a necessity of secure transmission from sender to the authentic receiver. Therefore a number of data encryption techniques have come up in recent years for different information transfer systems. We are mainly concerned with the types of data, which are represented and interpreted as images. Several classical image encryption approaches like discrete cosine transform or Fourier transform have been proposed and being used. We propose a new method for encrypting images using an orthogonal transformation, namely, Walsh transformation with a key matrix which together fulfill our purpose of cipher. Throughout our operations on image data, we use modular arithmetic so that computations with the resulting residue number system will become efficient. In this paper, we state the algorithm design steps to calculate key matrix which plays the most vital role in any encryption technique. We also show that the total number of possible combinations of key generation is so high for a common brute force or a hacker that virtually it will be impossible to find the authentic key. Also the encryption approach considers image in a divided matrix domain and finally combines all independent cryptographic operations as encryption is a one-to-one mapping. This takes care of the possibility that if any pixel value is ill-stored or wrongly received at the receiver end, which will not affect the decryption process and the final recovered image will differ by a negligible amount. Though this technique is a very simple one, it is very efficient in terms of authenticity, privacy and integrity.