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

Author

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  • Muharrem Tolga Sakallı
  • Sedat Akleylek
  • Bora Aslan
  • Ercan Buluş
  • Fatma Büyüksaraçoğlu Sakallı

Abstract

We present an algebraic construction based on state transform matrix (companion matrix) for (where , being a positive integer) binary matrices with high branch number and low number of fixed points. We also provide examples for and 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 with degree 5 and 4 are used in finite field Hadamard or circulant manner to construct and 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 (where , being a positive integer) binary matrices with high branch number and low number of fixed points.

Suggested Citation

  • Muharrem Tolga Sakallı & Sedat Akleylek & Bora Aslan & Ercan Buluş & Fatma Büyüksaraçoğlu Sakallı, 2014. "On the Construction of and Binary Matrices with Good Implementation Properties for Lightweight Block Ciphers and Hash Functions," Mathematical Problems in Engineering, Hindawi, vol. 2014, pages 1-12, November.
    • Handle: RePEc:hin:jnlmpe:540253
    DOI: 10.1155/2014/540253
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