Slovak University of Technology, Bratislava
Faculty of Electrical Engineering and Information Technology
Degree Course: INFORMATICS
Author: Bc. Peter Slížik
Diploma thesis: Ternary Cyclotomic Generators
Supervisor: RNDr. Hana Lichardová, PhD.
2002, December

The basic principle of stream ciphers is addition of random values to the individual characters of message. Because of simplicity of enciphering algorithm, cipher security depends mainly on design of pseudorandom sequences generator. The basic rule is to produce sequences with long period. Resistance of keystream sequence against replication or imitation by linear functions is expressed by its linear complexity and sphere complexity. An effective attack on stream ciphers is differential cryptanalysis. Its objective is to find relationship between several consecutive members of sequence. The ability of sequence to resist cryptanalysis is indicated by its differential properties.

The aim of this work is to create program performing differential analysis of ciphers with long period. In this work fast cyclotomic pseudorandom numbers generator with good cryptographic properties was designed. An effective method of working with sets of potential keys was applied. The designed software was used to analyse the strength of relationship between cryptographic properties of cipher and its ability to resist the analisys.

A practical application of ternary sequences are arithmetic codes. The arithmetic codes are error-correcting codes designed to correct errors in arithmetical and logical operations. In this work is designed a code which corrects single errors and realised an algorithm for encryption of code words.