Paper 2012/335 Original: eprint.iacr.org/2012/335 ↗
Constructing Vectorial Boolean Functions with High Algebraic Immunity Based on Group Decomposition
Abstract
In this paper, we construct a class of vectorial Boolean functions over $\mathbb{F}_{2^{n}}$ with high algebraic immunity based on the decomposition of the multiplicative group of $\mathbb{F}_{2^n}$. By viewing $\mathbb{F}_{2^{n}}$ as $G_1G_2\bigcup \{0\} $ (where $G_1$ and $G_2$ are subgroups of $\mathbb{F}_{2^{n}}^{*},~(\#G_1,\#G_2)=1$ and $\#G_1\times \#G_2=2^{2k}-1$), we give a generalized description for constructing vectorial Boolean functions with high algebraic immunity. Moreover, when $n$ is even, we provide two special classes of vectorial Boolean functions with high(sometimes optimal) algebraic immunity, one is hyper-bent, and the other is of balancedness and optimal algebraic degree .
Metadata
- Available format(s)
PDF- Category
- Foundations
- Publication info
- Preprint.
- History
- 2012-06-22: last updated
- 2012-06-22: published
- Short URL
- https://ia.cr/2012/335
- License
- https://creativecommons.org/licenses/by/4.0/
BibTeX
@misc{cryptoeprint:2012/335,
author = {Yu Lou and Huiting Han and Chunming Tang and Maozhi Xu},
title = {Constructing Vectorial Boolean Functions with High Algebraic Immunity Based on Group Decomposition},
howpublished = {Cryptology {ePrint} Archive, Paper 2012/335},
year = {2012},
url = {https://eprint.iacr.org/2012/335}
}