Short cycles in repeated exponentiation modulo a prime

被引：3
|
作者：
Glebsky, Lev [2 ]
Shparlinski, Igor E. [1 ]
机构：
[1] Macquarie Univ, Dept Comp, Sydney, NSW 2109, Australia
[2] Univ Autonoma San Luis Potosi, Inst Invest Comunicac Opt, San Luis Potosi 78210, Mexico
来源：
DESIGNS CODES AND CRYPTOGRAPHY | 2010年 / 56卷 / 01期
关键词：
Discrete logarithm; Cycle; Dynamical system;
D O I：
10.1007/s10623-009-9339-2
中图分类号：
TP301 [理论、方法];
学科分类号：
081202 ;
摘要：
Given a prime p, we consider the dynamical system generated by repeated exponentiations modulo p, that is, by the map u bar right arrow f(g)(u), where f(g)(u) equivalent to g(u) (mod p) and 0 <= f(g) (u) <= 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.
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页码：35 / 42
页数：8
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