Finite-Field Wavelets with Applications in Cryptography and Coding

For graduate students, research engineers, practicing professionals.

This text explores wavelets and filter banks over finite fields and their intersection with error control coding and data encryption. It develops the “theory of wavelet transforms over finite fields,” which provides a general wavelet decomposition of sequences defined over finite fields. Along with wavelet theory on finite fields, this work introduces the first application of this theory to error correcting codes and data security. It also introduces a finite-field wavelet based public key encryption technique.