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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2014-01-01
SAKALLI, MUHARREM TOLGA
AKLEYLEK, SEDAT
ASLAN, BORA
BULUŞ, ERCAN
Sakalli, Fatma Buyuksaracoglu
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.
MATHEMATICAL PROBLEMS IN ENGINEERING

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Citation Formats
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.