Constructing new APN functions from known ones

L. Budaghyan, C. Carlet, Gregor Leander

    Research output: Contribution to journalJournal articleResearchpeer-review


    We present a method for constructing new quadratic APN functions from known ones. Applying this method to the Gold power functions we construct an APN function x(3) + tr(x(9)) over F2(n). It is proven that for n >= 7 this function is CCZ-inequivalent to the Gold functions, and in the case n = 7 it is CCZ-inequivalent to any power mapping (and, therefore, to any APN function belonging to one of the families of APN functions known so far).
    Original languageEnglish
    JournalFinite Fields and Their Applications
    Issue number2
    Pages (from-to)150-159
    Publication statusPublished - 2009


    • S-box
    • Almost perfect nonlinear
    • Almost bent
    • Differential uniformity
    • CCZ-equivalence
    • Nonlinearity
    • Vectorial Boolean function


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