Smooth orders and cryptographic applications

Carl Pomerance, Igor E. Shparlinski

Research output: Chapter in Book/Report/Conference proceedingConference proceeding contributionpeer-review

13 Citations (Scopus)

Abstract

We obtain rigorous upper bounds on the number of primes p ≤ x for which p−1 is smooth or has a large smooth factor. Conjecturally these bounds are nearly tight. As a corollary, we show that for almost all primes p the multiplicative order of 2 modulo p is not smooth, and we prove a similar but weaker result for almost all odd numbers n. We also discuss some cryptographic applications.

Original languageEnglish
Title of host publicationAlgorithmic Number Theory
Subtitle of host publication5th International Symposium, ANTS-V Sydney, Australia, July 7–12, 2002 proceedings
EditorsClaus Fieker, David Kohel
Place of PublicationBerlin
PublisherSpringer, Springer Nature
Pages338-348
Number of pages11
ISBN (Print)3540438637
DOIs
Publication statusPublished - 2002
Event5th International Algorithmic Number Theory Symposium, ANTS 2002 - Sydney, Australia
Duration: 7 Jul 200212 Jul 2002

Publication series

NameLecture Notes in Computer Science
PublisherSpringer
Volume2369
ISSN (Print)0302-9743

Other

Other5th International Algorithmic Number Theory Symposium, ANTS 2002
CountryAustralia
CitySydney
Period7/07/0212/07/02

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