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**2020/273**

**Title:**

On the Fast Algebraic Immunity of Threshold Functions

**Authors:**
Pierrick Méaux

**Abstract:**

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

**ePrint:**
https://eprint.iacr.org/2020/273

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