@inproceedings{0f53b014a974461ab57b90e8c54ee040,
title = "Smooth orders and cryptographic applications",
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.",
author = "Carl Pomerance and Shparlinski, {Igor E.}",
year = "2002",
doi = "10.1007/3-540-45455-1_27",
language = "English",
isbn = "3540438637",
series = "Lecture Notes in Computer Science",
publisher = "Springer, Springer Nature",
pages = "338--348",
editor = "Claus Fieker and David Kohel",
booktitle = "Algorithmic Number Theory",
address = "United States",
note = "5th International Algorithmic Number Theory Symposium, ANTS 2002 ; Conference date: 07-07-2002 Through 12-07-2002",
}