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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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Date
2014-01-01
Author
SAKALLI, MUHARREM TOLGA
AKLEYLEK, SEDAT
ASLAN, BORA
BULUŞ, ERCAN
Sakalli, Fatma Buyuksaracoglu
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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.
Subject Keywords
Algebraic construction
URI
https://hdl.handle.net/11511/67958
Journal
MATHEMATICAL PROBLEMS IN ENGINEERING
DOI
https://doi.org/10.1155/2014/540253
Collections
Graduate School of Applied Mathematics, Article
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M. T. SAKALLI, S. AKLEYLEK, B. ASLAN, E. BULUŞ, and F. B. Sakalli, “On the Construction of 20 x 20 and 24 x 24 Binary Matrices with Good Implementation Properties for Lightweight Block Ciphers and Hash Functions,”
MATHEMATICAL PROBLEMS IN ENGINEERING
, pp. 0–0, 2014, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/67958.