Exploring the Feasibility of Meeting the MDS Criterion in Random Matrices and Searching for Efficient Random Involutory Hadamard MDS Matrices

  • Trần Thị Lượng Academy of cryptography techniques of Viet Nam Government Information Security Commission, Hanoi
Keywords: MDS matrix, random matrices, Hadamard MDS matrix, Circulant-like MDS matrix.

Abstract

Maximum distance separable codes (MDS codes) have been studied for a long time in error correcting code theory and have important applications in cryptography. There are many different methods have been studied to build MDS matrices such as: from MDS codes, Cauchy matrices, Hadamard matrices, Vandermonde matrices, circulant and circulant-like matrices etc. In this paper, the construction of MDS matrix from random matrices is studied, and the possibility of satisfying the MDS condition of any random matrix is presented. Then, the method of random search of MDS matrices will be given. In addition, we propose algorithms to randomly search for efficient involutory Hadamard MDS matrices of size 4, and 8. These results will be meaningful to determine the possibility that MDS matrices can be obtained from random matrices and diversify the methods of searching for MDS matrices. The involutory Hadamard MDS matrices make the encryption and decryption processes identical, which makes them very efficient for both hardware and software implementation.

Author Biography

Trần Thị Lượng, Academy of cryptography techniques of Viet Nam Government Information Security Commission, Hanoi
Chủ nhiệm Bộ môn, Khoa An toàn thông tin

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Published
2024-01-22