On the fast algebraic immunity of threshold functions
(2021) Cryptography and Communications — Vol. 13, n° 5, p. 741-762 (2021)
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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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Citations
Méaux, P. (2021). On the fast algebraic immunity of threshold functions. Cryptography and Communications, 13(5), 741-762. https://doi.org/10.1007/s12095-021-00505-y (Original work published 2021)