Cryptology ePrint Archive: Report 2016/143

On upper bounds for algebraic degrees of APN functions

Lilya Budaghyan, Claude Carlet, Tor Helleseth, Nian Li, Bo Sun

Abstract: We study the problem of existence of APN functions of algebraic degree $n$ over $\ftwon$. We characterize such functions by means of derivatives and power moments of the Walsh transform. We deduce some non-existence results which mean, in particular, that for most of the known APN functions $F$ over $\ftwon$ the function $x^{2^n-1}+F(x)$ is not APN, and changing a value of $F$ in a single point results in non-APN functions.

Category / Keywords: foundations / almost perfect nonlinear, almost bent, Boolean function, differential uniformity, nonlinearity

Date: received 16 Feb 2016, last revised 8 Jul 2016

Contact author: lilia b at mail ru

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Note: This is an improved version of the paper.

Version: 20160708:115846 (All versions of this report)

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