Slovak University of Technology, Bratislava
Faculty of Electrical Engineering and Information Technology
Degree Course: INFORMATICS
Author: Bc. Marek Martinkovič
Diploma thesis: Factorisation of large integers
Supervisor: prof. RNDr. Otokar Grošek, CSc.
This work is focused on design and implementation of library, that consists of functions working with big numbers and on implementation of factorization algorithms. Suitable structure of big number is based on known structures used in existing projects. Designed structure is implemented in C++ language. Library consists as well from basic arithmetical operations, that work with implemented structere of big number. Big number is implemented as class and arithmetical operations are methods of this class. Factorization methods are implemented using methods of big number. Project is focused on three factorization methods. They are ECM method, based on eliptic curve, (P-1) method, based on Fermat's Theorem and quadratic sieve method. These methods are described and implemented. Implemented methods were used for factorization of numbers. Factorization of these numbers was known. Corretness of implementation was verified in this way. Character of quadratic sieve method allows parallel solution of processing. In this work is designed distributed solution in an internet environment. Implementation runs in various working mods. These mods gives to user information about the state of processing.