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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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##### References:
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