A new construction of highly nonlinear S-boxes

Peter Beelen, Gregor Leander

    Research output: Contribution to journalJournal articleResearchpeer-review


    In this paper we give a new construction of highly nonlinear vectorial Boolean functions. This construction is based on coding theory, more precisely we use concatenation to construct Boolean functions from codes over $\mathbb{F}_q$ containing a first-order generalized Reed–Muller code. As it turns out this construction has a very compact description in terms of Boolean functions, which is of independent interest. The construction allows one to design functions with better nonlinearities than known before.
    Original languageEnglish
    JournalCryptography and Communications
    Issue number1
    Pages (from-to)65-77
    Publication statusPublished - 2012


    • Concatenation
    • Reed–Muller codes
    • Linear codes
    • Boolean functions
    • Nonlinearity

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