We describe several families of efficiently implementable Boolean functions achieving provable trade-offs between resiliency, nonlinearity, and algebraic immunity. In particular, the following statement holds for each of the function families that we propose. Given integers $m_0\geq 0$, $x_0\geq 1$, and $a_0\geq 1$, it is possible to construct an $n$-variable function which has resiliency at least $m_0$, linear bias (which is an equivalent method of expressing nonlinearity) at most $2^{-x_0}$ and algebraic immunity at least $a_0$; further, $n$ is linear in $\max(m_0,x_0,a_0)$, and the function can be implemented using $O(n)$ 2-input gates, which is essentially optimal.

翻译：我们描述了几类高效可实现的布尔函数族，这些函数族在弹性、非线性度和代数免疫之间实现了可证明的折中关系。特别地，对于我们提出的每一类函数族，以下命题均成立：给定整数 $m_0\geq 0$、$x_0\geq 1$ 和 $a_0\geq 1$，可以构造一个 $n$ 元布尔函数，其弹性至少为 $m_0$，线性偏置（这是非线性度的等价表达方式）至多为 $2^{-x_0}$，且代数免疫至少为 $a_0$；此外，$n$ 与 $\max(m_0,x_0,a_0)$ 呈线性关系，且该函数可用 $O(n)$ 个二输入门实现，这本质上是最优的。