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Searching collisions in hash functions
Joščák, Daniel ; Tůma, Jiří (advisor) ; Holub, Štěpán (referee)
The main interest of this paper is finding collisions in the hash function MD5. We present our new algorithm based on Wangs et al. methods of finding collisions in MD5. While writing this thesis Stevens and Klima published their fast algorithms for finding collisions. We give a description of these algorithms and the calculation of computianal complexity of all three algorithms.
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Mathematical foundations of Steven's algorithm
Štubňa, Ivan ; Tůma, Jiří (advisor) ; Vábek, Jiří (referee)
In the present work we address the issue of nding collisions in MD5 hash function. In this work we focus on Steven's algorithm for nding the di erential paths and solve some problems associated with this algorithm. We solve especially problem of the rotation and selections of parameters within one step of generating di erential path. The aim of this work is to present mathematical solutions of these problems and propose an optimization of Steven's algorithm.
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Cryptanalysis of ciphers used in GSM phones
Barboriková, Jana ; Tůma, Jiří (advisor) ; Kechlibar, Marian (referee)
The aim of this thesis is to introduce the family of A5 algorithm which is used in data encryption and decryption in GSM phones. It is focused on real time cryptanalysis of the stream cipher A5/1. It describes in detail the known plaintext attack published by A. Biryukov, A. Shamir and D. Wagner. Both the attack and the cipher are implemented. The implementation proves that the preprocessing stage of the attack is very time consuming, but the actual attack can be carried out in real time on a single PC. Then the problem of finding a good statistical model for the process of generating tree of predecessors of internal states of A5/1 is studied. We present reasons why the singletype Galton-Watson process is not suitable for the problem and introduce a multitype Galton-Watson process and a macro process. The models are applied to the process of generating predecessors and their predictions are compared with experimental data.
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Application of ACO to simple subsitution ciphers
Turek, Luboš ; Tůma, Jiří (advisor) ; Holub, Štěpán (referee)
Název práce: Použití ACO algoritmu na řešení jednoduché substituční šifry Autor: Luboš Turek Katedra (ústav): Katedra algebry Vedoucí bakalářské práce: doc. RNDr. Jiří Tůma, DrSc. e-mail vedoucího: jiri.tuma@mff.cuni.cz Abstrakt: V předložené práci studujeme kombinatorickou metaheuristiku Ant Colony Optimization a zkoumáme možné způsoby jejího použití k pro- lomení jednoduché substituční šifry. Součástí práce je návrh a implementace programu. Klíčová slova: jednoduchá substituční šifra, ant colony optimization, ACO, kryptologie, kryptografie Title: Application of ACO to simple subsitution ciphers Author: Luboš Turek Department: Department of Algebra Supervisor: doc. RNDr. Jiří Tůma, DrSc. Supervisor's e-mail address: jiri.tuma@mff.cuni.cz Abstract: In the present work we study combinatorial metaheuristic Ant Colony Optimization and we search for its application to the problem of cracking simple subtitution cipher. Functional implementation is a part of the thesis. Keywords: simple substitution cipher, ant colony optimization, ACO, cryp- tology, cryptography 5
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Application of group theory in solving puzzles
Pavlík, Tomáš ; Opršal, Jakub (advisor) ; Tůma, Jiří (referee)
This thesis studies the theory of combinatorical puzzles and its connection to the group theory. The aim of this work is to introduce the concept of puzzle to mathematics and to use group theory to solve it, special attention will be focused on solvable groups. Everything is interspersed with a number of practical examples to better understand the topic.
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