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

Claude Carlet; Xiangyong Zeng; Chunlei Li; Lei Hu

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