CAREER: Finite-Field Wavelets for Cryptography and Error Control Coding

Georgia Tech Research Corporation, Atlanta GA

Investigators

Abstract

Finite-Field Wavelets for Cryptography and Error-Control Coding Faramarz Fekri Today's success is increasingly dependent on being able to access, share and use information whenever and wherever needed. The widespread availability and transmission of such information demands new approaches to cryptography and error-control coding. Notions of complexity, scalability, and adaptability are becoming critical challenges for error-control coding and data security. This research explores wavelet transform over finite fields and their applications to convolutional coding and data security. It investigates a rich set of signal processing techniques that can be exploited for the construction of new coding and security schemes. The research is not evolutionary. It defines a new research area on the boundary of three very large research fields; namely digital signal processing, communications, and computer science. It impacts 1. basic science, 2. technology and products, and 3. education and learning. This research explores the intersection of finite-field wavelet transforms, error-control coding and data encryption. The primary focus of this research is to advance the study of wavelets and filter banks over finite fields and their applications to error -control coding and data security. It develops the theory of wavelet transforms over finite fields which provides a general wavelet decomposition of sequences defined over finite fields. This is an approach that has a rich history in signal processing for the representation of real-valued signals, but it has been lacking in the finite-field case. In particular, the research explores multiresolution wavelets and overcomplete filter banks over finite fields. Along with wavelet theory on finite fields, this work investigates the first application of the finite-field wavelet theory to new types of time varying convolutional codes that have unusual trellis structures with reduced complexity. Using multiresolution decomposition of wavelets, the researchers intend to construct rate-compatible wavelet convolutional codes for handheld devices to support flexible data rates (voice, fax, video,...). To address security issues with handheld devices, this research exploits the finite-field wavelet as a unifying framework for effective joint design of data encryption and error control coding. In this framework, the public and secret keys of the user determine the wavelet system and the security is tied to the length of the wavelet basis function. The goal of the research is centered around the development of innovative coding/security protocols for handheld devices.