FINITE-FIELD WAVELET TRANSFORMS 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.