Exhaustive search for small dimension recursive MDS diffusion layers for block ciphers and hash functions

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 F
₂
-linear transformations (combinations of XORs and shifts) which are much lighter. Using this algorithm, it was possible to design a 16×16 matrix on a 5-bit alphabet, yielding an efficient 80-bit diffusion layer with maximal branch number.