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Relationship between higher order attacks and CCZ-equivalence
Deptová, Lucie ; Göloglu, Faruk (advisor) ; Hojsík, Michal (referee)
In this thesis, we explain the term CCZ-equivalence in more detail to- gether with an analysis of a special type of matrices of this equivalence. We also clarify the higher order differential cryptanalysis and its generalized ver- sion. To demonstrate this method we present several attacks on a simple five round Feistel cipher, two of these attacks are our own. We have implemented the most important attacks and results of these experiments can be found in the text. We also explore how to use a decomposition F = F2 ◦F−1 1 (where F1 and F2 are permutations) to construct a generalized higher order differential attack to a block cipher with an S-box F. This construction may be used while searching for an attack to F using the CCZ-equivalence which is gener- ally a hard question. The result of our research is a theorem which presents a necessary condition on a degree of F which is needed for an existence of such a decomposition. 1
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Algebraic-differential analysis of Keccak
Seidlová, Monika ; Göloglu, Faruk (advisor) ; Hojsík, Michal (referee)
In this thesis, we analyze the cryptographic sponge function family Keccak - the winner of the SHA-3 Cryptographic Hash Standard competition. Firstly, we explore how higher order differentials can be used to forge a tag in a parallelizable MAC function. We introduce new terms and theory studying what affine spaces remain affine after one round of Keccak's underlying permutation Keccak-f. This allows us to improve the forgery. Secondly, collisions in Keccak could be generated from pairs of values, that follow particular differential trails in Keccak-f. We tested finding pairs for a given differential trail in reduced-round Keccak-f using algebraic techniques with the mathematics software SAGE. We found a pair in a 4-round trail in Keccak-f[50] in under 5 minutes and a 3-round trail in Keccak-f[100] in 80 seconds on a regular PC. Powered by TCPDF (www.tcpdf.org)
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Links Between Differential and Linear Cryptanalysis
Töpfer, Jakub ; Hojsík, Michal (advisor) ; Göloglu, Faruk (referee)
This thesis concerns the relations between correlation matrix, difference propagation matrix and other matrices used in the block cipher cryptanalysis. We show that some relations between these matrices can be seen just as a change of basis provided by the discrete Fourier transform. This can be used for an easier proof of a well-known theorem. We also study properties of difference propagation matrix, describe a class of vectorial Boolean functions which have the same difference propagation matrix and state a numerically justified hypothesis that this class contains all such functions.
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