Paper 2007/370 Original: eprint.iacr.org/2007/370 ↗
FURTHER PROPERTIES OF SEVERAL CLASSES OF BOOLEAN FUNCTIONS WITH OPTIMUM ALGEBRAIC IMMUNITY
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.
Metadata
- Available format(s)
PDF- Category
- Foundations
- Publication info
- Preprint.
- History
- 2007-09-19: last updated
- 2007-09-19: published
- Short URL
- https://ia.cr/2007/370
- License
- https://creativecommons.org/licenses/by/4.0/
BibTeX
@misc{cryptoeprint:2007/370,
author = {Claude Carlet and Xiangyong Zeng and Chunlei Li and Lei Hu},
title = {FURTHER PROPERTIES OF SEVERAL CLASSES OF BOOLEAN FUNCTIONS WITH OPTIMUM ALGEBRAIC IMMUNITY},
howpublished = {Cryptology {ePrint} Archive, Paper 2007/370},
year = {2007},
url = {https://eprint.iacr.org/2007/370}
}