Short cycles in repeated exponentiation modulo a prime | Macquarie University ResearchOnline

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Title: Short cycles in repeated exponentiation modulo a prime
Related: Designs codes and cryptography, Vol. 56, No. 1, (2009), p.1-8
DOI: 10.1007/s10623-009-9339-2
Publisher: Springer
Date: 2009
FoR/RFCD Code(s): 010100 Pure Mathematics 090600 Electrical and Electronic Engineering 080200 Computation Theory and Mathematics
Author/Creator: Glebsky, Lev
Author/Creator: Shparlinski, Igor E
Description: Given a prime p, we consider the dynamical system generated by repeated exponentiations modulo p, that is, by the map u ® fg(u), where f g (u) ≡ 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.
Description: 8 page(s)
Subject Keyword: 010100 Pure Mathematics
Subject Keyword: 090600 Electrical and Electronic Engineering
Subject Keyword: 080200 Computation Theory and Mathematics
Subject Keyword: discrete logarithm
Subject Keyword: cycle
Subject Keyword: dynamical system
Resource Type: journal article
Organisation: Macquarie University. Dept. of Computing

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