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Construction of highly nonlinear resilient S-boxes with given degree

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Abstract

We provide two new construction methods for nonlinear resilient S-boxes with given degree. The first method is based on the use of linear error correcting codes together with highly nonlinear S-boxes. Given a [u, m, t + 1] linear code where u = n−d−1, d > m, we show that it is possible to construct (n, m, t, d) resilient S-boxes which have currently best known nonlinearity. Our second construction provides highly nonlinear (n, m, t, d) resilient S-boxes which do not have linear structure, then an improved version of this construction is given.

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Authors and Affiliations

  1. College of Computer, National University of Defense Technology, Changsha, 410073, People’s Republic of China

    Shaojing Fu

  2. Institute of Industrial Science, University of Tokyo, 4-6-1 Komaba, Meguro-ku, Tokyo, 153-8505, Japan

    Shaojing Fu & Kanta Matsuura

  3. College of Science, National University of Defense Technology, Changsha, 410073, People’s Republic of China

    Chao Li & Longjiang Qu

Authors
  1. Shaojing Fu
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  2. Kanta Matsuura
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  3. Chao Li
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  4. Longjiang Qu
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Correspondence to Shaojing Fu.

Additional information

Communicated by R. Steinwandt.

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Fu, S., Matsuura, K., Li, C. et al. Construction of highly nonlinear resilient S-boxes with given degree. Des. Codes Cryptogr. 64, 241–253 (2012). https://doi.org/10.1007/s10623-011-9568-z

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  • DOI: https://doi.org/10.1007/s10623-011-9568-z

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