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

TL;DR

This paper introduces a new recursive algorithm to efficiently find small-dimension MDS matrices for lightweight block ciphers, enabling compact, lightweight diffusion layers with maximal security properties.

Contribution

It presents a novel recursive construction method for MDS matrices that simplifies implementation and enhances efficiency in lightweight cryptographic primitives.

Findings

Designed a 16x16 MDS matrix on a 5-bit alphabet

Achieved an 80-bit diffusion layer with maximal branch number

Replaced classical field multiplications with simple F2-linear transformations

Abstract

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.