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Mathematical Problems in Engineering
Volume 2014, Article ID 540253, 12 pages
http://dx.doi.org/10.1155/2014/540253
Research Article

On the Construction of and Binary Matrices with Good Implementation Properties for Lightweight Block Ciphers and Hash Functions

1Department of Computer Engineering, Trakya University, 22030 Edirne, Turkey
2Department of Computer Engineering, Ondokuz Mayis University, 55139 Samsun, Turkey
3Institute of Applied Mathematics, Middle East Technical University, 06531 Ankara, Turkey
4Software Engineering Department, Kirklareli University, 39000 Kırklareli, Turkey
5Department of Computer Engineering, Namık Kemal University, 59860 Çorlu, Turkey

Received 16 June 2014; Revised 9 October 2014; Accepted 13 October 2014; Published 2 November 2014

Academic Editor: Kwok-Wo Wong

Copyright © 2014 Muharrem Tolga Sakallı et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We present an algebraic construction based on state transform matrix (companion matrix) for (where , being a positive integer) binary matrices with high branch number and low number of fixed points. We also provide examples for and binary matrices having advantages on implementation issues in lightweight block ciphers and hash functions. The powers of the companion matrix for an irreducible polynomial over with degree 5 and 4 are used in finite field Hadamard or circulant manner to construct and binary matrices, respectively. Moreover, the binary matrices are constructed to have good software and hardware implementation properties. To the best of our knowledge, this is the first study for (where , being a positive integer) binary matrices with high branch number and low number of fixed points.