Slovak University of Technology, Bratislava
Faculty of Informatics and Information Technologies
Degree Course: INFORMATICS
Author: Bc. JŠn Simon
Diploma thesis: Pseudorandom binary number generators based on permutations
Supervisor: RNDr. Hana LichardovŠ, PhD.
2004, May

The objective of this work is to analyze and to design a pseudorandom binary sequence generator based on permutations, and to implement a software product, which uses this generator in practice.

We analyzed the cryptographic properties of binary sequences and proved which permutations are suitable to generate sequences with good characteristics.

We designed a generator based on permutation x-3 over GF(p), where p is a prime period derived from Sophie-Germain prime number, and we proved its good cryptographic properties.

Suitability of sequences generated by our generator for cryptographic purposes was proved by applying statistical tests of FIPS 140-2 and DIEHARD. Results of these tests showed that our designed and implemented generator satisfies all requirements of pseudorandomness.

In the following, we designed and implemented a software product, which encodes and decodes text messages, also generates pseudorandom numbers of various formats. Program offers user interface implemented in Java Swing as well as interface for other programs through protocol SOAP.

Product was successfully implemented in programming languages C++ and Java using mathematical library GMP for large integer support.