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


Creative Commons License

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

MATHEMATICAL PROBLEMS IN ENGINEERING, 2014 (SCI İndekslerine Giren Dergi) identifier identifier

  • Basım Tarihi: 2014
  • Doi Numarası: 10.1155/2014/540253
  • Dergi Adı: MATHEMATICAL PROBLEMS IN ENGINEERING

Özet

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.