Conceptos Básicos
This paper introduces direct construction methods for both recursive and nonrecursive MDS and NMDS matrices, which are crucial components in the design of secure and efficient cryptographic primitives.
Resumen
The paper focuses on the construction of linear diffusion layers in symmetric-key cryptography, specifically exploring the direct construction of Maximum Distance Separable (MDS) and Near-MDS (NMDS) matrices.
Key highlights:
Presents direct construction methods for nonrecursive MDS and NMDS matrices using generalized Vandermonde matrices.
Introduces direct construction methods for recursive MDS and NMDS matrices, addressing the lack of such methods for recursive NMDS matrices in the literature.
Proposes a method for constructing involutory MDS and NMDS matrices.
Provides formal proofs for some commonly referenced folklore results in the literature of NMDS codes.
The paper is structured as follows:
Section 2 provides necessary notations and presents fundamental results, including useful results on NMDS codes.
Section 3 describes several direct construction methods for nonrecursive MDS and NMDS matrices.
Section 4 presents direct construction methods for recursive MDS and NMDS matrices.
Section 5 concludes the paper.