@inproceedings{921a85621fb54bdab772673154a558bb,

title = "On exponential sums and group generators for elliptic curves over finite fields",

abstract = "In the paper an upper bound is established for certain exponential sums, analogous to Gaussian sums, defined on the points of an elliptic curve over a prime finite field. The bound is applied to prove the existence of group generators for the set of points on an elliptic curve over Fq among certain sets of bounded size. We apply this estimate to obtain a deterministic O(q1/2+ε) algorithm for finding generators of the group in echelon form, and in particular to determine its group structure.",

author = "Kohel, {David R.} and Shparlinski, {Igor E.}",

year = "2000",

language = "English",

isbn = "3540676953",

volume = "1838",

series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",

publisher = "Springer, Springer Nature",

pages = "395--404",

editor = "Wieb Bosma",

booktitle = "Algorithmic Number Theory",

address = "United States",

note = "4th International Symposium on Algorithmic Number Theory, ANTS 2000 ; Conference date: 02-07-2000 Through 07-07-2000",

}