Algebraic Properties of Generalized Rijndael-Like Ciphers

Authors

L. Babinkostova, Boise State UniversityFollow
Kevin W. Bombardier, Wichita State University
Matthew M. Cole, University of Notre Dame
Thomas A. Morrell, Washington University
Cory B. Scott, Colorado College

Document Type

Article

Publication Date

5-2014

Abstract

We provide conditions under which the set of Rijndael-like functions considered as permutations of the state space and based on operations of the finite field GF(p^k) (p ≥ 2) is not closed under functional composition. These conditions justify using a sequential multiple encryption to strengthen generalized Rijnadael like ciphers. In R. Sparr and R. Wernsdorf provided conditions under which the group generated by the Rijndael-like round functions based on operations of the finite field GF(2^k) is equal to the alternating group on the state space. In [39], this paper we provide conditions under which the group generated by the Rijndael-like round functions based on operations of the finite field GF(p^k) (p ≥ 2) is equal to the symmetric group or the alternating group on the state space.

Copyright Statement

This document was originally published in Groups Complexity Cryptology by de Gruyter. Copyright restrictions may apply. The final publication is available at doi: 10.1515/gcc-2014-0004

Publication Information

Babinkostova, L.; Bombardier, Kevin W.; Cole, Matthew M.; Morrell, Thomas A.; and Scott, Cory B.. (2014). "Algebraic Properties of Generalized Rijndael-Like Ciphers". Groups Complexity Cryptology, 6(1), 37-54. https://doi.org/10.1515/gcc-2014-0004