Nonlinear Boolean permutations

Abdurashid Mamadolimov, Herman Isa, Miza Mumtaz Ahmad, Moesfa Soeheila Mohamad

Research output: Contribution to journalArticle

Abstract

A Boolean permutation is called nonlinear if it has at least one nonlinear component function. All nonlinear Boolean permutations and their complements are called non-affine Boolean permutations. Any non-affine Boolean permutation is a potential candidate for bijective S-Box of block ciphers. In this paper, we find the number of n-variable non-affine Boolean permutations up to multiplicative n and show a simple method of construction of non-affine Boolean permutations. However, non-affinity property is not sufficient for S-Boxes. Nonlinearity is one of the basic properties of an S-Box. The nonlinearity of Boolean permutation is a distance between set of all non-constant linear combinations of component functions and set of all non-affine Boolean functions. The cryptographically strong S-Boxes have high nonlinearity. In this paper, we show a method of construction of 8-variable highly nonlinear Boolean permutations. Our construction is based on analytically design (8, 1), (8, 2), and (8, 3) highly nonlinear vectorial balanced functions and random permutation for other component functions.

Original languageEnglish
Pages (from-to)1-9
Number of pages9
JournalPertanika Journal of Science and Technology
Volume19
Issue numberSPEC. ISSUE
Publication statusPublished - Oct 2011

Fingerprint

nonlinearity
complement
Boolean functions
methodology
method

Keywords

  • Block cipher
  • Boolean permutation
  • Nonlinearity
  • S-Box

ASJC Scopus subject areas

  • Agricultural and Biological Sciences(all)
  • Chemical Engineering(all)
  • Computer Science(all)
  • Environmental Science(all)

Cite this

Mamadolimov, A., Isa, H., Ahmad, M. M., & Mohamad, M. S. (2011). Nonlinear Boolean permutations. Pertanika Journal of Science and Technology, 19(SPEC. ISSUE), 1-9.

Nonlinear Boolean permutations. / Mamadolimov, Abdurashid; Isa, Herman; Ahmad, Miza Mumtaz; Mohamad, Moesfa Soeheila.

In: Pertanika Journal of Science and Technology, Vol. 19, No. SPEC. ISSUE, 10.2011, p. 1-9.

Research output: Contribution to journalArticle

Mamadolimov, A, Isa, H, Ahmad, MM & Mohamad, MS 2011, 'Nonlinear Boolean permutations', Pertanika Journal of Science and Technology, vol. 19, no. SPEC. ISSUE, pp. 1-9.
Mamadolimov A, Isa H, Ahmad MM, Mohamad MS. Nonlinear Boolean permutations. Pertanika Journal of Science and Technology. 2011 Oct;19(SPEC. ISSUE):1-9.
Mamadolimov, Abdurashid ; Isa, Herman ; Ahmad, Miza Mumtaz ; Mohamad, Moesfa Soeheila. / Nonlinear Boolean permutations. In: Pertanika Journal of Science and Technology. 2011 ; Vol. 19, No. SPEC. ISSUE. pp. 1-9.
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