**On the Fast Algebraic Immunity of Threshold Functions**

*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.

**Category / Keywords: **secret-key cryptography / Boolean Functions, Fast Algebraic Attacks, Symmetric Functions, Threshold Functions.

**Date: **received 29 Feb 2020

**Contact author: **pierrick meaux at uclouvain be

**Available format(s): **PDF | BibTeX Citation

**Version: **20200304:080931 (All versions of this report)

**Short URL: **ia.cr/2020/273

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