Lightweight MDS Generalized Circulant Matrices

Abstract. In this article, we analyze the circulant structure of generalized circulant matrices to reduce the search space for finding lightweight MDS matrices. We first show that the implementation of circulant matrices can be serialized and can achieve similar area requirement and clock cycle performance as a serial-based implementation. By proving many new properties and equivalence classes for circulant matrices, we greatly reduce the search space for finding lightweight maximum distance separable (MDS) circulant matrices. We also generalize the circulant structure and propose a new class of matrices, called cyclic matrices, which preserve the benefits of circulant matrices and, in addition, have the potential of being self-invertible. In this new class of matrices, we obtain not only the MDS matrices with the least XOR gates requirement for dimensions from 3 × 3 to 8 × 8 in GF(24 ) and GF(28 ), but also involutory MDS matrices which was proven to be non-existence in the clas...

• Type: Journal
• Year: 2016
• Where: IACR
• Authors: Meicheng Liu, Siang Meng Sim
• Keywords: Biometrics, IACR 2016