Short cycles in repeated exponentiation modulo a prime

Lev Glebsky, Igor E. Shparlinski

Research output: Contribution to journalArticlepeer-review

5 Citations (Scopus)


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
Issue number1
Publication statusPublished - Jul 2010


Dive into the research topics of 'Short cycles in repeated exponentiation modulo a prime'. Together they form a unique fingerprint.

Cite this