Paper 2012/093 Original: eprint.iacr.org/2012/093 ↗
Recent Results on Balanced Symmetric Boolean Functions
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
- Preprint.
- History
- 2012-04-23: last updated
- 2012-02-24: published
- Short URL
- https://ia.cr/2012/093
- License
- https://creativecommons.org/licenses/by/4.0/
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},
url = {https://eprint.iacr.org/2012/093}
}