Paper 2007/370

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

Claude Carlet, Xiangyong Zeng, Chunlei Li, and Lei Hu

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
Published elsewhere. Unknown where it was published
Keywords
boolean functions
Contact author(s)
xzeng @ hubu edu cn
History
2007-09-19: received
Short URL
https://ia.cr/2007/370
License
Creative Commons Attribution
CC BY

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},
      note = {\url{https://eprint.iacr.org/2007/370}},
      url = {https://eprint.iacr.org/2007/370}
}
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