Paper 2020/273
On the Fast Algebraic Immunity of Threshold Functions
Pierrick Méaux
Abstract
Motivated by the impact of fast algebraic attacks on stream ciphers, and recent constructions using a threshold function as part of the filtering function, we study the fast algebraic immunity of threshold functions. As a first result, we determine exactly the fast algebraic immunity of all majority functions in more than $8$ variables. Then, For all $n\geq 8$ and all threshold value between $1$ and $n$ we exhibit the fast algebraic immunity for most of the thresholds, and we determine a small range for the value related to the few remaining cases. Finally, provided $m\geq 2$, we determine exactly the fast algebraic immunity of all threshold functions in $3\cdot 2^m$ or $3\cdot 2^m +1$ variables.
Note: minor modifications
Metadata
- Available format(s)
-
PDF
- Category
- Secret-key cryptography
- Publication info
- Preprint. MINOR revision.
- Keywords
- Boolean FunctionsFast Algebraic AttacksSymmetric FunctionsThreshold Functions.
- Contact author(s)
- pierrick meaux @ uclouvain be
- History
- 2021-05-06: revised
- 2020-03-04: received
- See all versions
- Short URL
- https://ia.cr/2020/273
- License
-
CC BY
BibTeX
@misc{cryptoeprint:2020/273,
author = {Pierrick Méaux},
title = {On the Fast Algebraic Immunity of Threshold Functions},
howpublished = {Cryptology {ePrint} Archive, Paper 2020/273},
year = {2020},
url = {https://eprint.iacr.org/2020/273}
}
