Cryptology ePrint Archive: Report 2007/063

Constructing new APN functions from known ones

Lilya Budaghyan and Claude Carlet and Gregor Leander

Abstract: 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 $x^3+\tr(x^9)$ over $\F_{2^n}$. It is proven that in general this function is CCZ-inequivalent to the Gold functions (and therefore EA-inequivalent to power functions), to the inverse and Dobbertin mappings, and in the case $n=7$ it is CCZ-inequivalent to all power mappings.

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

Publication Info: submitted to FFA

Date: received 19 Feb 2007, last revised 23 May 2007

Contact author: lilya at science unitn it

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

Note: In this version we add new results.

Version: 20070523:155707 (All versions of this report)

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