Direct construction of quasi-involutory recursive-like MDS matrices from 2-cyclic codes

  • Victor Cauchois Direction générale de l'armement - Maîtrise de l'information (DGA-MI) and Institut de Recherche Mathématique de Rennes (IRMAR), Université de Rennes 1, Rennes, France
  • Pierre Loidreau Direction générale de l'armement - Maîtrise de l'information (DGA-MI) and Institut de Recherche Mathématique de Rennes (IRMAR), Université de Rennes 1, Rennes, France
  • Nabil Merkiche Direction générale de l'armement (DGA IP) and Sorbonne University, University of Pierre and Marie Curie (UPMC) Paris University 06, The French National Centre for Scientific Research (CNRS), Laboratoire d'informatique de Paris 6 (LIP6) – UMR 7606, Paris, France
Keywords: diffusion layers, MDS matrices, involutions, cyclic codes

Abstract

A good linear diffusion layer is a prerequisite in the design of block ciphers. Usually it is obtained by combining matrices with optimal diffusion property over the Sbox alphabet. These matrices are constructed either directly using some algebraic properties or by enumerating a search space, testing the optimal diffusion property for every element. For implementation purposes, two types of structures are considered: Structures where all the rows derive from the first row and recursive structures built from powers of companion matrices. In this paper, we propose a direct construction for new recursive-like MDS matrices. We show they are quasi-involutory in the sense that the matrix-vector product with the matrix or with its inverse can be implemented by clocking a same LFSR-like architecture. As a direct construction, performances do not outperform the best constructions found with exhaustive search. However, as a new type of construction, it offers alternatives for MDS matrices design.
Published
2017-02-03
How to Cite
Cauchois, V., Loidreau, P., & Merkiche, N. (2017). Direct construction of quasi-involutory recursive-like MDS matrices from 2-cyclic codes. IACR Transactions on Symmetric Cryptology, 2016(2), 80-98. https://doi.org/10.13154/tosc.v2016.i2.80-98
Section
Articles