@inproceedings{69284fc5766f46dcb954497eeec75e9f,

title = "Orders of points on elliptic curves",

abstract = "We show that a randomly chosen point on a randomly chosen elliptic curve modulo a prime p, with overwhelming probability generates a cyclic subgroup of size close to p. We apply this result to obtain lower bounds for periods of two recently introduced pseudorandom number generators on elliptic curves.",

keywords = "elliptic curves, orders of points, pseudorandom number generators, FINITE-FIELD, CYCLICITY",

author = "IE Shparlinski",

year = "2005",

language = "English",

isbn = "0821834762",

series = "Contemporary Mathematics Series",

publisher = "American Mathematical Society",

pages = "245--251",

editor = "J Gutierrez and Shpilrain and JT Yu",

booktitle = "Affine algebraic geometry",

address = "United States",

note = "1st RSME-AMS Joint Meeting ; Conference date: 19-06-2003 Through 21-06-2003",

}