Cryptology ePrint Archive: Report 2014/091

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

S. M. Dehnavi and 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.

Category / Keywords: foundations / Symmetric Cryptography, MDS Diffusion Layer, Group, Ring, Sigma-LFSR, Number Generator

Date: received 8 Feb 2014, last revised 14 Feb 2014

Contact author: std_dehnavism at khu ac ir

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Version: 20140214:132415 (All versions of this report)

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