@inproceedings{83cc4b782ce04cf0ba1073f10cc5dd32,
title = "Schoof{\textquoteright}s algorithm and isogeny cycles",
abstract = "The heart of Schoof{\textquoteright}s algorithm for computing the cardinality m of an elliptic curve over a finite field is the computation of m modulo small primes l. Elkies and Atkin have designed practical improvements to the basic algorithm, that make use of {\textquotedblleft}good{\textquotedblright} primes l. We show how to use powers of good primes in an efficient way. This is done by computing isogenies between curves over the ground field. A new structure appears, called {\textquotedblleft}isogeny cycle{\textquotedblright}. We investigate some properties of this structure.",
author = "Couveignes, \{Jean Marc\} and Fran{\c c}ois Morain",
note = "Publisher Copyright: {\textcopyright} 1994, Springer Verlag. All rights reserved.; 1st Algorithmic Number Thoery Symposium, ANTS-I 1994 ; Conference date: 06-05-1994 Through 09-05-1994",
year = "1994",
month = jan,
day = "1",
doi = "10.1007/3-540-58691-1\_42",
language = "English",
isbn = "9783540586913",
series = "Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)",
publisher = "Springer Verlag",
pages = "43--58",
editor = "Adleman, \{Leonard M.\} and Ming-Deh Huang",
booktitle = "Algorithmic Number Theory - 1st International Symposium, ANTS-I, Proceedings",
}