Paper 2012/093

Recent Results on Balanced Symmetric Boolean Functions

Yingming Guo, Guangpu Gao, and Yaqun Zhao

Abstract

In this paper we prove all balanced symmetric Boolean functions of fixed degree are trivial when the number of variables grows large enough. We also present the nonexistence of trivial balanced elementary symmetric Boolean functions except for $n=l\cdot2^{t+1}-1$ and $d=2^t$, where $t$ and $l$ are any positive integers, which shows Cusick's conjecture for balanced elementary symmetric Boolean functions is exactly the conjecture that all balanced elementary symmetric Boolean functions are trivial balanced. In additional, we obtain an integer $n_0$, which depends only on $d$, that Cusick's conjecture holds for any $n>n_0$.

Metadata
Available format(s)
PDF
Category
Foundations
Publication info
Published elsewhere. Unknown where it was published
Keywords
Boolean functionsBalancednesselementary symmetric functions
Contact author(s)
guoyingming123 @ gmail com
History
2012-04-23: last of 3 revisions
2012-02-24: received
See all versions
Short URL
https://ia.cr/2012/093
License
Creative Commons Attribution
CC BY

BibTeX

@misc{cryptoeprint:2012/093,
      author = {Yingming Guo and Guangpu Gao and Yaqun Zhao},
      title = {Recent Results on Balanced Symmetric Boolean Functions},
      howpublished = {Cryptology ePrint Archive, Paper 2012/093},
      year = {2012},
      note = {\url{https://eprint.iacr.org/2012/093}},
      url = {https://eprint.iacr.org/2012/093}
}
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