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Cryptanalysis of AES
Botka, Michal ; Tůma, Jiří (advisor) ; Drápal, Aleš (referee)
In the present work we study a security of the AES cipher. We concern in a mathematical representation of a block cipher and how to use it to algebraic attacks. We show a summary of known algorithms which are useful for these attacks. We show how to convert problem of solving the system of polynomial equations to SAT problem and we describe how SAT solvers work.
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Rotational cryptanalysis of ARX ciphers
Töpfer, Jakub ; Hojsík, Michal (advisor) ; Tůma, Jiří (referee)
We investigate functions which can be realized using only addition, XOR and rotation (ARX). Sometimes we admit operations with constants as well (ARX+C). We start our research from a theoretical point of view. We prove that every function can by written using only ARX+C operations and that we can even omit XOR. On the other hand, other combinations of these operations do not generate all functions. We also present an algorithm determining whether a function can be realised only by addition and XOR. After that we present a rotational cryptanalysis, which is designed especially for ARX ciphers. We demonstrate this method on reduced variants of Threefish, TEA and XTEA ciphers and discuss for which ciphers it is suitable. The last part of this thesis deals with a modification of rotational cryptanalysis called rotational rebound attack and shows its application on Threefish.
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PSO-algorithms and possibilities for their use in cryptanalysis.
Svetlíková, Lenka ; Tůma, Jiří (advisor) ; Hojsík, Michal (referee)
The aim of the thesis was to investigate the usage of PSO algorithm in the area of cryptanalysis. We applied PSO to the problem of simple substitution and to DES attack. By a modified version of PSO algorithm we achieved better or comparable results as by the usage of other biologically motivated algorithms. We suggested a method how to use PSO to attack DES and we were able to break it with the knowledge of only 20 plain texts and corresponding cipher texts. We have analyzed the reasons of failure to break more than a 4 rounds of DES and provided explanation for it. At the end we described the basic principles of differential cryptanalysis for DES and presented a specific mo- dification of PSO for searching optimal differential characteristics for DES. For simple ciphers, PSO is working efficiently but for sophisticated ciphers like DES, without in- corporating deep internal knowledge about the process into the algorithm, we could not expect significant outcomes. 1
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New proposals for hash functions
Sušil, Petr ; Tůma, Jiří (advisor) ; Holub, Štěpán (referee)
Hash functions are an important cryptographic primitive. They are used as message authentication codes, manipulation detection codes and in many cryptograhic protocols. This thesis gives an explanation of the recent generic attacks against hash functions. It also explains the attack against authentication hash function COMP128, which was being used til 2002 in GSM network. The thesis also discusses possible flaws in a new authentication hash function SQUASH designed for an RFID chip.
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Security and usability of standard has hfunctions, in particular MD-5, SHA-1 and SHA-2
Galaczová, Barbora ; Tůma, Jiří (advisor) ; Joščák, Daniel (referee)
Title: Security and usability of standard hash functions, in particular MD-5, SHA-1 and SHA-2 Author: Galaczová Barbora Department: Department of Algebra Supervisor: Doc. RNDr. Tůma Jiří, DrSc., Department of Algebra Consultant: Ing. Budiš Petr, Ph.D. Abstract: In the present work we try to digestedly describe standard hash functions, in particular MD-5, SHA-1 and SHA-2. We describe resume of existing attacks on these hash functions. We closely focused on MD-5 collision attacks, because the other hash function collision attacks result from these. Next we describe posibilities of practical usage of hash function collisions, in particular into the qualified certificates area and possible threats. At the end to the present work we describe new hash functions, which could replace current hash functions. This work also contains software to calculate MD-5 hash and search it`s collisions. The software is based on method invented by Czech cryptoanalytist Vlastimil Klíma. Keywords: hash function, collision, qualified certificate, security.
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