Abstract
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 \(\theta \)-circulancy, then there is no restriction to the existence of \(\theta \)-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 \(\theta \)-circulant MDS matrices. We show that they can be interesting in hardware implementations.
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This is one of several papers published in Designs, Codes and Cryptography comprising the “Special Issue on Coding and Cryptography”.
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Cauchois, V., Loidreau, P. On circulant involutory MDS matrices. Des. Codes Cryptogr. 87, 249–260 (2019). https://doi.org/10.1007/s10623-018-0520-3
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DOI: https://doi.org/10.1007/s10623-018-0520-3