@techreport{TR-IC-PFG-21-43,
   number = {IC-PFG-21-43},
   author = {Tomás S. R. Silva and Ricardo Dahab},
   title = {{MDS Matrices for Cryptography}},
   month = {December},
   year = {2021},
   institution = {Institute of Computing, University of Campinas},
   note = {In English, 43 pages.
    \par\selectlanguage{english}\textbf{Abstract}
       Maximum  distance  separable (MDS) matrices are a key component
       in several cryptoschemes. One of the most interesting features,
       from a cryptographic point of view, of MDS matrices is the fact
       that  these  provide  perfect diffusion for linear layers. \par
       Thus,  this  work  will  not only explore the characteristic of
       perfect diffusion in MDS layers, but will also demonstrate that
       the  use  of MDS matrices is a necessary (but not a sufficient)
       condition  in  order  to  achieve resistance against infinitely
       long  invariant subspace trails attacks in P-SPN linear layers.
       Moreover,   it   will  also  be  presented  some  MDS  matrices 
       construction techniques.
  }
}