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Constructing new APN functions from known ones. (English) Zbl 1184.94228
Summary: 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 \(x^3+\text{tr}(x^9)\) over \(\mathbb F_{2^n}\). It is proven that for \(n\geq 7\) 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).

MSC:
94D10 Boolean functions
94A60 Cryptography
11T71 Algebraic coding theory; cryptography (number-theoretic aspects)
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