Cryptology ePrint Archive: Report 2005/359

An infinite class of quadratic APN functions which are not equivalent to power mappings

L. Budaghyan and C. Carlet and P. Felke and G. Leander

Abstract: We exhibit an infinite class of almost perfect nonlinear quadratic polynomials from $\mathbb{F}_{2^n}$ to $\mathbb{F}_{2^n}$ ($n\geq 12$, $n$ divisible by 3 but not by 9). We prove that these functions are EA-inequivalent to any power function. In the forthcoming version of the present paper we will proof that these functions are CCZ-inequivalent to any Gold function and to any Kasami function, in particular for $n=12$, they are therefore CCZ-inequivalent to power functions.

Category / Keywords: foundations / Vectorial Boolean function, S-box, Nonlinearity, Differential uniformity, Almost perfect nonlinear, Almost bent, Affine equivalence, CCZ-equivalence

Date: received 6 Oct 2005, last revised 17 Oct 2005

Contact author: Gregor Leander at rub de

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Version: 20051017:152710 (All versions of this report)

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