### 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)
Category
Foundations
Publication info
Preprint. MAJOR revision.
Keywords
Symmetric CryptographyMDS Diffusion LayerGroupRingSigma-LFSRNumber 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},
note = {\url{https://eprint.iacr.org/2014/091}},
url = {https://eprint.iacr.org/2014/091}
}

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