Section: New Results
Diffusion layers for block ciphers
MDS matrices allow the construction of optimal linear diffusion layers in block ciphers. However, MDS matrices usually have a large description (for example, they can never be sparse), and this results in costly software/hardware implementations. We can solve this problem using recursive MDS matrices, which can be computed as a power of a simple companion matrix—and thus have a compact description suitable for constrained environments. Until now, finding recursive MDS matrices required an exhaustive search on families of companion matrices; this clearly limited the size of MDS matrices that one could look for. We have found a new direct construction, based on shortened BCH codes, which allows us to efficiently construct these matrices for arbitrary parameter sizes  . D. Augot and M. Finiasz received the best paper award at FSE 2014, and were invited to submit an extended journal version to Journal of Cryptology.
P. Karpman started to study sub-optimal diffusion layers, which can be built using algebraic geometry codes with a large automorphism group. Preliminary work has been done, leading to promising results  . To properly assert the cryptanalytic properties of these codes, V. Ducet is starting to implement a method for computing efficiently the weight distribution of AG codes.