Reflection Ciphers (Extended abstract)

Christina Boura (1) , Anne Canteaut (2) , Lars R. Knudsen (3) , Gregor Leander (3)

1 PRISM - Parallélisme, Réseaux, Systèmes, Modélisation
2 SECRET - Security, Cryptology and Transmissions
3 DTU - Danmarks Tekniske Universitet = Technical University of Denmark

This paper investigates ciphers where the set of encryption functions is identical to the set of decryption functions, which we call reflection ciphers. Equivalently, there exists a permutation P , named the coupling permutation, such that decryption under k corresponds to en-cryption under P (k). We show that this coupling permutation must be an involution without fixed points. Special care has to be taken of some related-key distinguishers since, in the context of reflection ciphers, they may provide attacks in the single-key setting. We then derive some criteria for constructing secure reflection ciphers and analyze the security properties of different families of coupling permutations. In particular, we show that, for affine coupling permutations, the resistance to related-key distinguishers is given by some trade-off between the dimension and the covering-radius of some linear codes. Finally, as an illustration, we provide new variants of the block cipher PRINCE with key schedules corresponding to several coupling permutations.

Mots clés: Reflection ciphers; Involutions; Related-key distinguishers; PRINCE

Domaines: Cryptographie et sécurité [cs.CR]

Christina Boura, Anne Canteaut, Lars R. Knudsen, Gregor Leander. Reflection Ciphers (Extended abstract). Workshop on Coding and Cryptography - WCC 2015, Apr 2015, Paris, France. ⟨hal-01237291⟩