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Paper: FURTHER PROPERTIES OF SEVERAL CLASSES OF BOOLEAN FUNCTIONS WITH OPTIMUM ALGEBRAIC IMMUNITY

Authors:
Claude Carlet
Xiangyong Zeng
Chunlei Li
Lei Hu
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URL: http://eprint.iacr.org/2007/370
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Abstract: Thanks to a method proposed by Carlet, several classes of balanced Boolean functions with optimum algebraic immunity are obtained. By choosing suitable parameters, for even $n\geq 8$, the balanced $n$-variable functions can have nonlinearity $2^{n-1}-{n-1\choose\frac{n}{2}-1}+2{n-2\choose\frac{n}{2}-2}/(n-2)$, and for odd $n$, the functions can have nonlinearity $2^{n-1}-{n-1\choose\frac{n-1}{2}}+\Delta(n)$, where the function $\Delta(n)$ is describled in Theorem 4.4. The algebraic degree of some constructed functions is also discussed.
BibTeX
@misc{eprint-2007-13650,
  title={FURTHER PROPERTIES OF SEVERAL CLASSES OF BOOLEAN FUNCTIONS WITH OPTIMUM ALGEBRAIC IMMUNITY},
  booktitle={IACR Eprint archive},
  keywords={foundations / boolean functions},
  url={http://eprint.iacr.org/2007/370},
  note={ xzeng@hubu.edu.cn 13770 received 14 Sep 2007},
  author={Claude Carlet and Xiangyong Zeng and Chunlei Li and Lei Hu},
  year=2007
}