Simplet and its Application in Signal Encryption

Abstract

We propose here a transform which is a new kind of multi-level subband signal decomposition and reconstruction scheme. It is called Simplet which stands for Simple transform and is simple, easy to understand and perfectly reconstructible. No decomposition or reconstruction filter is explicitly required in Simplet. Another advantage of this transform is that the length of the decomposed components in each level of decomposition is equal to the length of the input signal. Computationally, Simplet can be made a constant time transform. There are various forms of Simplet that can be used in various applications of signal and image processing. Simplet is of two types. One is useful for multiresolution signal analysis and the other for signal distortion. We use the later type here for an encryption scheme. In the existing transforms, even when there is noise in the decomposed components, the reconstructed signal is perceptually intelligible. However, in Simplet the reconstructed signal is perceptually unintelligible when the decomposed components have noise in them. This property is made use of in our encryption scheme which first uses Simplet to protect the distinguishable features of the signal by decomposing it into two or more distorted components and then encrypts them by using a special sequence of numbers. This sequence is called Meitei Lock Sequence (MLS) and is generated from a non-zero key vector of an arbitrary length. An MLS is unique for a key vector. Once a signal is encrypted with an MLS, it can be decrypted only with that particular MLS. As an MLS is generated from an arbitrary vector, the search space for finding a particular MLS is very large and hence gives very tight security in our encryption scheme. We have found that the empirical correlation coefficient between an original signal and a decrypted signal using any decryption key that is different from (even if very close to) the actual key, is sufficiently small. The encryption scheme is fast as both the Simplet and MLS are fast algorithms.