Paper 2021/665

On the algebraic immunity of direct sum constructions

Pierrick Méaux

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. Minor revision.
Keywords
Boolean FunctionsAlgebraic ImmunityDirect Sum
Contact author(s)
pierrick meaux @ uclouvain be
History
2021-05-25: received
Short URL
https://ia.cr/2021/665
License
Creative Commons Attribution
CC BY

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},
      note = {\url{https://eprint.iacr.org/2021/665}},
      url = {https://eprint.iacr.org/2021/665}
}
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