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access icon free Construction of resilient S-boxes with higher-dimensional vectorial outputs and strictly almost optimal non-linearity

  • Author(s): WeiGuo Zhang 1, 2 ; LuYang Li 2 ; Enes Pasalic 3
    • View affiliations
    • Affiliations: 1: State Key Laboratory of Cryptology, P.O. Box 5159, Beijing 100878, People's Republic of China ;
      2: ISN Laboratory, Xidian University, Xi'an 710071, People's Republic of China ;
      3: Faculty of Mathematics, Natural Sciences and Information Technologies, University of Primorska & Institute Andrej Marušič, Koper 6000, Slovenia
  • Source: Volume 11, Issue 4, July 2017, p. 199 – 203
    DOI:  10.1049/iet-ifs.2016.0168 , Print ISSN 1751-8709, Online ISSN 1751-8717
© The Institution of Engineering and Technology
Received 01/04/2016, Accepted 21/06/2016, Published 11/08/2016

Resilient substitution boxes (S-boxes) with high non-linearity are important cryptographic primitives in the design of certain encryption algorithms. There are several trade-offs between the most important cryptographic parameters and their simultaneous optimisation is regarded as a difficult task. In this study, the authors provide a construction technique to obtain resilient S-boxes with so-called strictly almost optimal non-linearity for a larger number of output bits m than previously known. This is the first time that the non-linearity bound 2 n−1 − 2 n/2 of resilient (n,m) S-boxes, where n and m denote the number of the input and output bits, respectively, has been exceeded for m>⌊n/4⌋. Thus, resilient S-boxes with extremely high non-linearity and a larger output space compared with other design methods have been obtained.

Inspec keywords: Gaussian processes; cryptography; mixture models; optimisation

Other keywords: cryptographic parameters; strictly almost optimal nonlinearity; resilient S-boxes; resilient substitution boxes; simultaneous optimisation; Gaussian mixture model; encryption algorithms; cryptographic primitives; higher-dimensional vectorial outputs; GMM-type construction

Subjects: Cryptography theory; Cryptography; Other topics in statistics; Other topics in statistics; Optimisation techniques; Optimisation techniques

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