A New Statement about Direct Exponent of an MDS Matrix in Block Ciphers

MDS code has been studied for a long time in the theory of error-correcting code and has been applied widely in cryptography. Some authors studied and proposed some methods for constructing MDS matrices which do not based on MDS code. Some MDS matrix transformations have been studied and direct exponent is such a transformation. In this paper we present some new results on direct exponent transformation to show the k* number (cycle) that direct p exponent of the MDS matrix fork times results in the original MDS matrix. In addition, the results are shown to have important applications in block ciphers.