Paper 2016/751

Feistel Like Construction of Involutory Binary Matrices With High Branch Number

Adnan Baysal, Mustafa Çoban, and Mehmet Özen

Abstract

In this paper, we propose a generic method to construct involutory binary matrices from a three round Feistel scheme with a linear round function. We prove bounds on the maximum achievable branch number (BN) and the number of fixed points of our construction. We also define two families of efficiently implementable round functions to be used in our method. The usage of these families in the proposed method produces matrices achieving the proven bounds on branch numbers and fixed points. Moreover, we show that BN of the transpose matrix is the same with the original matrix for the function families we defined. Some of the generated matrices are \emph{Maximum Distance Binary Linear} (MDBL), i.e. matrices with the highest achievable BN. The number of fixed points of the generated matrices are close to the expected value for a random involution. Generated matrices are especially suitable for utilising in bitslice block ciphers and hash functions. They can be implemented efficiently in many platforms, from low cost CPUs to dedicated hardware.

Metadata
Available format(s)
PDF
Category
Secret-key cryptography
Publication info
Preprint. MINOR revision.
Keywords
Diffusion layerbitslice cipherhash functioninvolutionMDBL matricesFixed points
Contact author(s)
adnan baysal @ tubitak gov tr
History
2016-08-08: received
Short URL
https://ia.cr/2016/751
License
Creative Commons Attribution
CC BY

BibTeX

@misc{cryptoeprint:2016/751,
      author = {Adnan Baysal and Mustafa Çoban and Mehmet Özen},
      title = {Feistel Like Construction of Involutory Binary Matrices With High Branch Number},
      howpublished = {Cryptology ePrint Archive, Paper 2016/751},
      year = {2016},
      note = {\url{https://eprint.iacr.org/2016/751}},
      url = {https://eprint.iacr.org/2016/751}
}
Note: In order to protect the privacy of readers, eprint.iacr.org does not use cookies or embedded third party content.