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On the fast algebraic immunity of threshold functions

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Abstract

Motivated by the impact of fast algebraic attacks on stream ciphers, and recent constructions using a threshold function as main 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 ≥ 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 ≥ 2, we determine exactly the fast algebraic immunity of all threshold functions in 3 ⋅ 2m or 3 ⋅ 2m + 1 variables.

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Funding

The author is a beneficiary of a FSR (“Fonds spécial de recherche”, Belgium) incoming post-doctoral fellowship.

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  1. ICTEAM/ELEN/Crypto Group, Université catholique de Louvain, Louvain-la-Neuve, Belgium

    Pierrick Méaux

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  1. Pierrick Méaux
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Correspondence to Pierrick Méaux.

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Méaux, P. On the fast algebraic immunity of threshold functions. Cryptogr. Commun. 13, 741–762 (2021). https://doi.org/10.1007/s12095-021-00505-y

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