Short cycles in repeated exponentiation modulo a prime

Lev Glebsky, Igor E. Shparlinski

Research output: Contribution to journalArticlepeer-review

5 Citations (Scopus)

Abstract

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.

Original languageEnglish
Pages (from-to)35-42
Number of pages8
JournalDesigns, Codes and Cryptography
Volume56
Issue number1
DOIs
Publication statusPublished - Jul 2010

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