International Association for Cryptologic Research

International Association
for Cryptologic Research


Paper: Balanced Boolean Functions with Nonlinearity > 2^{n-1} - 2^{(n-1)/2}

Selçuk Kavut
Melek D. Yücel
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Abstract: Recently, balanced 15-variable Boolean functions with nonlinearity 16266 were obtained by suitably modifying unbalanced Patterson-Wiedemann (PW) functions, which possess nonlinearity 2^{n-1}-2^{(n-1)/2}+20 = 16276. In this short paper, we present an idempotent interpreted as rotation symmetric Boolean function) with nonlinearity 16268 having 15 many zeroes in the Walsh spectrum, within the neighborhood of PW functions. Clearly this function can be transformed to balanced functions keeping the nonlinearity and autocorrelation distribution unchanged. The nonlinearity value of 16268 is currently the best known for balanced 15-variable Boolean functions. Furthermore, we have attained several balanced 13-variable Boolean functions with nonlinearity 4036, which improves the recent result of 4034.
  title={Balanced Boolean Functions with Nonlinearity > 2^{n-1} - 2^{(n-1)/2}},
  booktitle={IACR Eprint archive},
  keywords={Balanced Boolean functions, Nonlinearity},
  note={ 13763 received 15 Aug 2007, last revised 7 Sep 2007},
  author={Selçuk Kavut and Melek D. Yücel},