On Circulant Involutory MDS Matrices

Victor Cauchois (1) , Pierre Loidreau (2)

1 DGA.MI - DGA Maîtrise de l'information
2 IRMAR - Institut de Recherche Mathématique de Rennes

We give a new algebraic proof of the non-existence of circulant involutory MDS matrices with coefficients in fields of characteristic 2. In odd characteristics we give parameters for the potential existence. If we relax circulancy to θ-circulancy, then there is no restriction to the existence of θ-circulant involutory MDS matrices even for fields of characteristic 2. Finally, we relax further the involutory definition and propose a new direct construction of almost involutory θ-circulant MDS matrices. We show that they can be interesting in hardware implementations.

Domaines: Cryptographie et sécurité [cs.CR]; Théorie de l'information et codage [math.IT]

Victor Cauchois, Pierre Loidreau. On Circulant Involutory MDS Matrices. Designs, Codes and Cryptography, 2019. ⟨hal-02387814⟩