模素数重复幂的短圈
Short Cycles in Repeated Exponentiation Modulo a Prime
摘要：
给定一个素数$p$，我们考虑由模$p$的重复幂运算生成的动力系统，即由映射$u \mapsto f_g(u)$生成的动力系统，其中$f_g(u) \equiv g^u \pmod p$和$0 \le f_g(u) \le p-1$。该映射特别用于密码安全伪随机生成器的许多构造中。我们得到了上述动力系统的不动点和短圈个数的非平凡上界。
英文摘要：
Given a prime $p$, we consider the dynamical system generated by repeated exponentiations modulo $p$, that is, by the map $u \mapsto f_g(u)$, where $f_g(u) \equiv g^u \pmod p$ and $0 \le f_g(u) \le p-1$. This map is in particular used in a number of constructions of cryptographically secure pseudorandom generators. We obtain nontrivial upper bounds on the number of fixed points and short cycles in the above dynamical system.
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。
