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Propriétés Différentielles des Permutations et Application en Cryptographie Symétrique

Abstract : The work I have carried out during this thesis lies between discrete mathematics, finite fields theory and symmetric cryptography. Symmetric cryptography consists in every function and protocol that permits a secure communication between people sharing the same secret key. In block ciphers, as well as in hash functions, SBoxes are small non-linear and necessary functions playing the role of the confusion layer.In the first part of this thesis, we focus on the design of bijective SBoxes that have the best resistance against differential cryptanalysis. First, we study the compositional inverse of the so-called Almost Perfect Nonlinear (APN) power functions. Then, we extensively study a class of permutation polynomials with low differential uniformity which admit efficient implementations in hardware and software. Finally, we build APN functions over finite fields from their discrete derivatives.In the second part, we realize an automatic study of a certain type of differential cryptanalysis: Impossible Differential Cryptanalysis. This known plaintexts attack has been shown to be very efficient against iterative block ciphers. It exploits the knowledge of a differential with probability zero to occur. However, this cryptanalysis remains very technical and many flaws have been discovered, invalidating thus many attacks realized in the past. Our goal is to formalize, to improve and to automatize the complexity evaluation in order to optimize the results one can obtain. We also propose new techniques that aim at reducing the necessary data and time complexities. We finally prove the efficiency of our method by providing the best impossible differential cryptanalysis against the Feistel oriented block ciphers CLEFIA, Camellia, LBlock and Simon.
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Contributor : Valentin Suder <>
Submitted on : Wednesday, December 10, 2014 - 4:36:46 AM
Last modification on : Tuesday, November 5, 2019 - 1:18:05 AM
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  • HAL Id : tel-01093026, version 1



Valentin Suder. Propriétés Différentielles des Permutations et Application en Cryptographie Symétrique. Cryptographie et sécurité [cs.CR]. Université Pierre et Marie Curie, 2014. Français. ⟨tel-01093026⟩



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