International Association
for Cryptologic Research

Many modern block ciphers use maximum distance separate

(MDS) matrices as their diffusion layers. In this paper, we propose

a new method to verify a sort of MDS diffusion block matrices whose

blocks are all polynomials in a certain primitive block over the

finite field $\\mathbb F_2$. And then we discover a new kind of

transformations that can retain MDS property of diffusion matrices

and generate a series of new MDS matrices from a given one.

Moreover, we get an equivalence relation from this kind of

transformation. And MDS property is an invariant with respect to

this equivalence relation which can greatly reduce the amount of

computation when we search for MDS matrices. The minimal polynomials

of matrices play an important role in our strategy. To avoid being

too theoretical, we list a series of MDS diffusion matrices obtained

from our method for some specific parameters. Furthermore, we

talk about MDS recursive diffusion layers with our method and extend

the corresponding work of M. Sajadieh et al. published on FSE 2012

and the work of S. Wu published on SAC 2012.