@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",

}