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

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SAKALLI M. T., AKLEYLEK S., ASLAN B., BULUŞ E., Sakalli F. B.

MATHEMATICAL PROBLEMS IN ENGINEERING, 2014 (SCI-Expanded)

• Publication Type: Article / Article
• Publication Date: 2014
• Doi Number: 10.1155/2014/540253
• Journal Name: MATHEMATICAL PROBLEMS IN ENGINEERING
• Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
• Middle East Technical University Affiliated: No

Abstract

We present an algebraic construction based on state transform matrix (companion matrix) for n x n (where n + 2(k), k being a positive integer) binary matrices with high branch number and low number of fixed points. We also provide examples for 20 x 20 and 24 x 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 x 20 and 24 x 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 x n (where n not equal 2(k), k being a positive integer) binary matrices with high branch number and low number of fixed points.