Exhaustive Search for Small Dimension Recursive MDS Diffusion Layers for Block Ciphers and Hash Functions
This addresses the need for lightweight cryptographic components in resource-constrained devices, though it is incremental as it builds on existing recursive MDS constructions.
The paper tackled the problem of designing efficient diffusion layers for lightweight block ciphers by developing a new algorithm to find MDS matrices with compact descriptions, resulting in a 16x16 matrix on a 5-bit alphabet that provides an 80-bit diffusion layer with maximal branch number.
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.