On the Construction of 20×20 and 24×24 Binary Matrices with Good Implementation Properties for Lightweight Block Ciphers and Hash Functions

We present an algebraic construction based on state transform matrix (companion matrix) for n×n (where n≠2k, k being a positive integer) binary matrices with high branch number and low number of fixed points. We also provide examples for 20×20 and 24×24 binary matrices having advantages on implement...

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Main Authors:	Muharrem Tolga Sakallı, Sedat Akleylek, Bora Aslan, Ercan Buluş, Fatma Büyüksaraçoğlu Sakallı
Format:	Article
Language:	English
Published:	Hindawi Limited 2014-01-01
Series:	Mathematical Problems in Engineering
Online Access:	http://dx.doi.org/10.1155/2014/540253

id	doaj-2b29a816853a4a718f6c0cc807c342a3
record_format	Article
spelling	doaj-2b29a816853a4a718f6c0cc807c342a32020-11-24T20:50:54ZengHindawi LimitedMathematical Problems in Engineering1024-123X1563-51472014-01-01201410.1155/2014/540253540253On the Construction of 20×20 and 24×24 Binary Matrices with Good Implementation Properties for Lightweight Block Ciphers and Hash FunctionsMuharrem Tolga Sakallı0Sedat Akleylek1Bora Aslan2Ercan Buluş3Fatma Büyüksaraçoğlu Sakallı4Department of Computer Engineering, Trakya University, 22030 Edirne, TurkeyDepartment of Computer Engineering, Ondokuz Mayis University, 55139 Samsun, TurkeySoftware Engineering Department, Kirklareli University, 39000 Kırklareli, TurkeyDepartment of Computer Engineering, Namık Kemal University, 59860 Çorlu, TurkeyDepartment of Computer Engineering, Trakya University, 22030 Edirne, TurkeyWe present an algebraic construction based on state transform matrix (companion matrix) for n×n (where n≠2k, k being a positive integer) binary matrices with high branch number and low number of fixed points. We also provide examples for 20×20 and 24×24 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 GF(2) with degree 5 and 4 are used in finite field Hadamard or circulant manner to construct 20×20 and 24×24 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 n×n (where n≠2k, k being a positive integer) binary matrices with high branch number and low number of fixed points.http://dx.doi.org/10.1155/2014/540253
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Muharrem Tolga Sakallı Sedat Akleylek Bora Aslan Ercan Buluş Fatma Büyüksaraçoğlu Sakallı
spellingShingle	Muharrem Tolga Sakallı Sedat Akleylek Bora Aslan Ercan Buluş Fatma Büyüksaraçoğlu Sakallı On the Construction of 20×20 and 24×24 Binary Matrices with Good Implementation Properties for Lightweight Block Ciphers and Hash Functions Mathematical Problems in Engineering
author_facet	Muharrem Tolga Sakallı Sedat Akleylek Bora Aslan Ercan Buluş Fatma Büyüksaraçoğlu Sakallı
author_sort	Muharrem Tolga Sakallı
title	On the Construction of 20×20 and 24×24 Binary Matrices with Good Implementation Properties for Lightweight Block Ciphers and Hash Functions
title_short	On the Construction of 20×20 and 24×24 Binary Matrices with Good Implementation Properties for Lightweight Block Ciphers and Hash Functions
title_full	On the Construction of 20×20 and 24×24 Binary Matrices with Good Implementation Properties for Lightweight Block Ciphers and Hash Functions
title_fullStr	On the Construction of 20×20 and 24×24 Binary Matrices with Good Implementation Properties for Lightweight Block Ciphers and Hash Functions
title_full_unstemmed	On the Construction of 20×20 and 24×24 Binary Matrices with Good Implementation Properties for Lightweight Block Ciphers and Hash Functions
title_sort	on the construction of 20×20 and 24×24 binary matrices with good implementation properties for lightweight block ciphers and hash functions
publisher	Hindawi Limited
series	Mathematical Problems in Engineering
issn	1024-123X 1563-5147
publishDate	2014-01-01
description	We present an algebraic construction based on state transform matrix (companion matrix) for n×n (where n≠2k, k being a positive integer) binary matrices with high branch number and low number of fixed points. We also provide examples for 20×20 and 24×24 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 GF(2) with degree 5 and 4 are used in finite field Hadamard or circulant manner to construct 20×20 and 24×24 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 n×n (where n≠2k, k being a positive integer) binary matrices with high branch number and low number of fixed points.
url	http://dx.doi.org/10.1155/2014/540253
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On the Construction of 20×20 and 24×24 Binary Matrices with Good Implementation Properties for Lightweight Block Ciphers and Hash Functions

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