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Negligible

negligible,可以忽略的,指一个函数小于任何关于其自变量的多项式的倒数,一般记为 negl。

A function $f(n)$ is negligible if for every positive polynomial $p$ there is an $N$ such that for all integers $n > N$ it holds that $f(n) < \frac{1}{p(n)}$ .

An equivalent formulation of the above is to require that for all constants $c$ there exists an $N$ such that for all $n > N$ it holds that $f(n) < n^{−c}$ .

—- J. Katz and Y. Lindell. Introduction to modern cryptography 2nd. CRC Press, 2014. p48.

基于上述定义,我们可以得出下列常用结论:

  • $negl_1(n) + negl_2(n)$ 是 negligible 的。
  • 对任何多项式 $p$,$p(n) \cdot negl(n)$ 同样是 negligible 的。