高效可实现布尔函数的构造及其非线性/抗冲激/代数免疫性折衷研究
Constructions of Efficiently Implementable Boolean Functions with Provable Nonlinearity/Resiliency/Algebraic Immunity Trade-Offs
AI总结：
本文提出了一种高效可实现的布尔函数构造方法，实现了抗冲激性、非线性性和代数免疫性之间的可证明折衷，且在变量数和门数上达到最优性能。
摘要：
我们描述了几种高效可实现的布尔函数族，这些函数在抗冲激性、非线性性和代数免疫性之间实现了可证明的折衷。具体而言，对于每个我们提出的函数族，给定整数m0≥0，x0≥1，a0≥1，可以构造一个n变量函数，其抗冲激性至少为m0，线性偏差（非线性性的等效表达方法）至多为2^{-x0}，代数免疫性至少为a0；进一步，n与max(m0,x0,a0)成线性关系，且该函数可以用O(n)个2输入门实现，这在本质上是最佳的。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
