Cryptology ePrint Archive: Report 2006/428

Another class of quadratic APN binomials over $\F_{2^n}$: the case $n$ divisible by 4

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 $\mathbb{F}_{2^{n}}$ with $n=4k$ and $k$ odd. We prove that these functions are CCZ-inequivalent to known APN power functions when $k\ne 1$. In particular it means that for $n=12,20,28$, they are CCZ-inequivalent to any power function.

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

Date: received 17 Nov 2006, last revised 27 Nov 2006

Contact author: lilya at science unitn it

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Version: 20061127:113721 (All versions of this report)

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