On Cryptographic Applications of Matrices Acting on Finite Commutative Groups and Rings

S.  M.  Dehnavi; A.  Mahmoodi Rishakani; M.  R.  Mirzaee Shamsabad

Paper 2014/091

On Cryptographic Applications of Matrices Acting on Finite Commutative Groups and Rings

S. M. Dehnavi, A. Mahmoodi Rishakani, and M. R. Mirzaee Shamsabad

Abstract

In this paper, we investigate matrices acting on finite commutative groups and rings; in fact, we study modules on ring of matrices over Z_N and also modules over the ring (F_2^t,\oplus,\land); these new algebraic constructions are a generalization of some of the constructions which were previously presented by the authors of this paper. We present new linearized and nonlinear MDS diffusion layers, based on this mathematical investigation. Then, we study some types of nonlinear number generators over Z_(2^n ) and we present a lower bound on the period of these new nonlinear number generators. As a consequence, we present nonlinear recurrent sequences over Z_(2^n ) with periods which are multiples of the period of the corresponding sigma-LFSR’s.

Metadata

Available format(s): PDF
Category: Foundations
Publication info: Preprint. MAJOR revision.
Keywords: Symmetric Cryptography MDS Diffusion Layer Group Ring Sigma-LFSR Number Generator
Contact author(s): std_dehnavism @ khu ac ir
History: 2014-12-11: last of 6 revisions; 2014-02-10: received; See all versions
Short URL: https://ia.cr/2014/091
License: CC BY

BibTeX

@misc{cryptoeprint:2014/091,
      author = {S.  M.  Dehnavi and A.  Mahmoodi Rishakani and M.  R.  Mirzaee Shamsabad},
      title = {On Cryptographic Applications of Matrices Acting on Finite Commutative Groups and Rings},
      howpublished = {Cryptology {ePrint} Archive, Paper 2014/091},
      year = {2014},
      url = {https://eprint.iacr.org/2014/091}
}