LIU Jian, CHEN Lusheng. On Nonlinearity of S-Boxes and Their Related Binary Codes[J]. Chinese Journal of Electronics, 2016, 25(1): 167-173. doi: 10.1049/cje.2016.01.025
Citation: LIU Jian, CHEN Lusheng. On Nonlinearity of S-Boxes and Their Related Binary Codes[J]. Chinese Journal of Electronics, 2016, 25(1): 167-173. doi: 10.1049/cje.2016.01.025

On Nonlinearity of S-Boxes and Their Related Binary Codes

doi: 10.1049/cje.2016.01.025
Funds:  This work is supported by the National Key Basic Research Program of China (973 Pragram) (No.2013CB834204).
  • Received Date: 2014-02-13
  • Rev Recd Date: 2014-04-18
  • Publish Date: 2016-01-10
  • The nonlinearity of S-boxes and their related supercodes of the first order Reed-Muller code are discussed. Based on the properties of multi-output bent functions and almost bent functions, we determine the maximum size of linear supercodes of the first order Reed-Muller code which have optimal or suboptimal minimum distance, and we also give the weight distributions of these supercodes which achieve the best possible size. Furthermore, an upper bound on the minimum distance of a class of binary linear codes is presented, which yields a new upper bound on the nonlinearity of S-boxes. The new bound on nonlinearity improves a bound given by Carlet et al. in 2007.
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