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

Faramarz Fekri今天的成功越来越依赖于能够随时随地访问、共享和使用信息。 此类信息的广泛可用性和传输需要新的密码学和错误控制编码方法。 复杂性、可扩展性和适应性的概念正在成为差错控制编码和数据安全的关键挑战。 本研究探讨有限域上之小波变换及其在卷积编码与资料保全上之应用。 它研究了一组丰富的信号处理技术，可用于构建新的编码和安全方案。 这项研究不是进化的。 它定义了一个新的研究领域的边界上的三个非常大的研究领域，即数字信号处理，通信和计算机科学。 影响1。基础科学2技术和产品，3。教育和学习。 本研究探讨有限域小波变换、错误控制编码与资料加密的交集。 本研究的主要焦点是推进有限域上小波和滤波器组的研究及其在差错控制编码和数据安全中的应用。 它发展了有限域上的小波变换理论，提供了有限域上定义的序列的一般小波分解。 这是一种在信号处理中具有丰富历史的方法，用于表示实值信号，但它在有限域情况下一直缺乏。 特别是，研究探讨了有限域上的多分辨率小波和过完备滤波器组。 沿着有限域上的小波理论，这项工作研究了有限域小波理论的第一个应用程序的新类型的时变卷积码，具有不寻常的网格结构，降低了复杂性。 利用小波的多分辨率分解，研究人员打算为手持设备构建速率兼容的小波卷积码，以支持灵活的数据速率（语音，传真，视频等）。 为了解决手持设备的安全问题，本研究利用有限域小波作为一个统一的框架，有效的联合设计的数据加密和错误控制编码。 在该框架中，用户的公钥和私钥决定了小波系统，安全性与小波基函数的长度有关。 该研究的目标是围绕手持设备的创新编码/安全协议的发展。

Finite-Field Wavelets for Cryptography and Error-Control CodingFaramarz 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.