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Paper: Correlation Immune Boolean Functions with Very High Nonlinearity

Authors:
Subhamoy Maitra
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URL: http://eprint.iacr.org/2000/054
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Abstract: Here we provide a construction method for unbalanced, first order correlation immune Boolean functions on even number of variables $n \geq 6$. These functions achieve the currently best known nonlinearity $2^{n-1} - 2^{\frac{n}{2}} + 2^{\frac{n}{2} - 2}$ . Then we provide a simple modification of these functions to get unbalanced correlation immune Boolean functions on even number of variables $n$, with nonlinearity $2^{n-1} - 2^{\frac{n}{2}} + 2^{\frac{n}{2} - 2} - 2$ and maximum possible algebraic degree $n-1$. Moreover, we present a detailed study on the Walsh spectra of these functions.
BibTeX
@misc{eprint-2000-11398,
  title={Correlation Immune Boolean Functions with Very High Nonlinearity},
  booktitle={IACR Eprint archive},
  keywords={secret-key cryptography / Boolean Function, Stream Cipher},
  url={http://eprint.iacr.org/2000/054},
  note={ subho@isical.ac.in 11257 received 27 Oct 2000},
  author={Subhamoy Maitra},
  year=2000
}