International Association for Cryptologic Research

International Association
for Cryptologic Research


Paper: Constructing new APN functions from known ones

Lilya Budaghyan
Claude Carlet
Gregor Leander
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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.
  title={Constructing new APN functions from known ones},
  booktitle={IACR Eprint archive},
  keywords={Affine equivalence, Almost bent, Almost perfect nonlinear, CCZ-equivalence, Differential uniformity, Nonlinearity, S-box, Vectorial Boolean function},
  note={submitted to FFA 13656 received 19 Feb 2007, last revised 23 May 2007},
  author={Lilya Budaghyan and Claude Carlet and Gregor Leander},