## Cryptology ePrint Archive: Report 2006/445

A class of quadratic APN binomials inequivalent to power functions

Lilya Budaghyan and Claude Carlet and Gregor Leander

Abstract: We exhibit an infinite class of almost perfect nonlinear quadratic binomials 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 and that they are CCZ-inequivalent to any Gold function and to any Kasami function. It means that for $n$ even they are CCZ-inequivalent to any known APN function, and in particular for $n=12,24$, they are therefore CCZ-inequivalent to any power function.

It is also proven that, except in particular cases, the Gold mappings are CCZ-inequivalent to the Kasami and Welch functions.

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

Publication Info: Part of this paper was presented at ISIT 2006

Date: received 27 Nov 2006, last revised 30 Nov 2006

Contact author: lilya at science unitn it

Available format(s): Postscript (PS) | Compressed Postscript (PS.GZ) | PDF | BibTeX Citation

Short URL: ia.cr/2006/445

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