On the algebraic immunity of direct sum constructions

Pierrick Méaux

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 Functions Algebraic Immunity Direct Sum
Contact author(s): pierrick meaux @ uclouvain be
History: 2021-05-25: received
Short URL: https://ia.cr/2021/665
License: 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},
      url = {https://eprint.iacr.org/2021/665}
}