Exhaustive Search for Small Dimension Recursive MDS Diffusion Layers for Block Ciphers and Hash Functions

Daniel Augot (1, 2) , Matthieu Finiasz (3)

1 LIX - Laboratoire d'informatique de l'École polytechnique [Palaiseau]
2 GRACE - Geometry, arithmetic, algorithms, codes and encryption
3 CryptoExperts

This article presents a new algorithm to find MDS matrices that are well suited for use as a diffusion layer in lightweight block ciphers. Using an recursive construction, it is possible to obtain matrices with a very compact description. Classical field multiplications can also be replaced by simple F2-linear transformations (combinations of XORs and shifts) which are much lighter. Using this algorithm, it was possible to design a 16x16 matrix on a 5-bit alphabet, yielding an efficient 80-bit diffusion layer with maximal branch number.

Domaines: Cryptographie et sécurité [cs.CR]

Daniel Augot, Matthieu Finiasz. Exhaustive Search for Small Dimension Recursive MDS Diffusion Layers for Block Ciphers and Hash Functions. International Symposium on Information Theory (ISIT), 2013, Istambul, Turkey. ⟨hal-00823082⟩