## CryptoDB

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

Authors: Claude Carlet Xiangyong Zeng Chunlei Li Lei Hu URL: http://eprint.iacr.org/2007/370 Search ePrint Search Google 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
}