Tóm tắt:

MDS (maximum distance separable) matrices are ones that come from MDS codes that have been studied for a long time in error correcting code theory and have many applications in block ciphers. To improve the security of block ciphers, dynamic block ciphers can be created. Using MDS matrix transformations is a method used to make block ciphers dynamic. Direct exponentiation is a transformation that can be used to generate dynamic MDS matrices to create a dynamic diffusion layer of the block ciphers. However, for cryptographic algorithms that use an MDS matrix as a component of them, the implementation of matrix multiplication is quite expensive, especially when the matrix has a large size. In this paper, the mathematical basis for quick calculation of direct exponentiation of an MDS matrix will be presented. On that basis, it is to suggest how to apply that fast calculation to dynamic algorithms using the direct exponentiation. This result is very meaningful in software implementation for MDS matrices, especially when implementing dynamic block ciphers to increase execution speed.