Paper 2021/665 Original: eprint.iacr.org/2021/665 ↗
On the algebraic immunity of direct sum constructions
Abstract
In this paper, we study sufficient conditions to improve the lower bound on the algebraic immunity of a direct sum of Boolean functions. We exhibit three properties on the component functions such that satisfying one of them is sufficient to ensure that the algebraic immunity of their direct sum exceeds the maximum of their algebraic immunities. These properties can be checked while computing the algebraic immunity and they allow to determine better the security provided by functions central in different cryptographic constructions such as stream ciphers, pseudorandom generators, and weak pseudorandom functions. We provide examples for each property and determine the exact algebraic immunity of candidate constructions.
Metadata
- Available format(s)
PDF- Category
- Secret-key cryptography
- Publication info
- Preprint.
- History
- 2021-05-25: last updated
- 2021-05-25: published
- Short URL
- https://ia.cr/2021/665
- License
- https://creativecommons.org/licenses/by/4.0/
BibTeX
@misc{cryptoeprint:2021/665,
author = {Pierrick Méaux},
title = {On the algebraic immunity of direct sum constructions},
howpublished = {Cryptology {ePrint} Archive, Paper 2021/665},
year = {2021},
url = {https://eprint.iacr.org/2021/665}
}