Block ciphers as sets of permutations: indifferentiability, group generating sets, distinguishers.

A block cipher can be seen as a set of permutations acting on the plaintext/ciphertext space. A key chooses one permutation from this set. A good cipher resembles a set of independently and randomly drawn permutations. While numerous results are known on the analysis of separate permutations once a key is fixed, only few analysis techniques have been established for the analysis of block ciphers as sets of permutations. At the same time, a good block cipher requires the set of permutations to behave in an idealized way. With this research project, we aim to bridge this gap by applying advanced mathematical techniques from three different areas. Using techniques from the complexity theory, we will derive proper security notions for the security of block ciphers as permutation sets. Using group theory, we will study new quantitative group-theoretical parameters of round transformations generating permutation sets related to block cipher permutations in the symmetric group. Using combinatorial methods and statistics, we will identify novel distinguishers of block ciphers from sets of randomly drawn permutations as well as corresponding key recovery techniques.

Keywords:Provable security, Related-key attacks, Permutations, Block ciphers, Cryptanalysis, Cryptography, Cryptology