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 ⋅ 2^m or 3 ⋅ 2^m + 1 variables.

受快速代​​数攻击对流密码的影响，以及最近使用阈值函数作为过滤函数主要部分的构造，我们研究了阈值函数的快速代数免疫。作为第一个结果，我们准确地确定了超过 8 个变量中所有多数函数的快速代数免疫。然后，对于所有n ≥ 8 和 1 和n之间的所有阈值，我们对大多数阈值表现出快速代数免疫，并且我们为与少数剩余案例相关的值确定了一个小范围。最后，如果m ≥ 2，我们可以准确地确定 3 ⋅ 2 ^m或 3 ⋅ 2 ^m + 1 变量中所有阈值函数的快速代数免疫。