Abstract:

The cyclic matrix is generated by its first row of elements, and then each row is shifted by the first row. Therefore, the cyclic matrix can not only maximize the utilization of the hardware circuit, but also save the storage space and have high computational efficiency. Constructing a reversible cyclic matrix conforming to the requirements of secure communication systems is a problem worthy of study. This paper corrects the erroneous application of the reversible matrix in secure communication in some documents, and gives the correct application examples and standards. Firstly, a necessary and sufficient condition for constructing the reversible cyclic matrix is obtained by studying the relation between the van Vandermonde Matrix and the cyclic matrix. Secondly, according to the finite field G(2⁸) characteristics, the necessary and sufficient conditions for constructing the reversible cyclic matrix on the real field are extended to the finite field, and a fast generation algorithm of the reversible cyclic matrix is proposed. Finally, a sufficient condition for constructing the cyclic matrix with optimal diffusion performance is proposed.

Key words: secure communication, the optimal diffusion matrix, reversible matrix, encryption, cyclic matrix