Makhmali S. Methods for increase the efficiency of data protection and transmission error correction by using of polynomial multiplication algebra

Thesis is dedicated to a problem of increasing of efficiency of data protection in computer system and correcting of errors which appearances during data transmission between of system components by accelerating of calculation necessitates for data protection and transmission errors correction implementation. The lack of necessity of carry processing make possible to simplify and speed up software and hardware implementation. Based on a study of polynomial squaring properties the new method of shortcut exponentiation on Galois fields is proposed. The approach to speed up of zero-knowledge identification of abonents by using of multiplication without carry on Galois fields is proposed. Base on ones modifications of FFSIS, Schnorr and Guillou-Quisquater identification schemes are worked out. It was proved that approach allows to speed up of identification. The techniques of keys generation, forming and verification of signature based of finite fields arithmetic are worked out. The method for burst error correction in spectral modulation channels is proposed, feature of one is use of mathematical operations without carry. It has been shown that proposed method provides a significant acceleration bust errors coding, detection and correction and simplifies hardware implementation.