TY - GEN
T1 - Primality proving using elliptic curves
T2 - 3rd International Symposium on Algorithmic Number Theory, ANTS 1998
AU - Morain, F.
N1 - Publisher Copyright:
© Springer-Verlag Berlin Heidelberg 1998.
PY - 1998/1/1
Y1 - 1998/1/1
N2 - In 1986, following the work of Schoof on counting points on elliptic curves over finite fields, new algorithms for primality proving emerged, due to Goldwasser and Kilian on the one hand, and Atkin on the other. The latter algorithm uses the theory of complex multiplication. The algorithm, now called ECPP, has been used for nearly ten years. The purpose of this paper is to give an account of the recent theoretical and practical improvements of ECPP, as well as new benchmarks for integers of various sizes and a new primality record.
AB - In 1986, following the work of Schoof on counting points on elliptic curves over finite fields, new algorithms for primality proving emerged, due to Goldwasser and Kilian on the one hand, and Atkin on the other. The latter algorithm uses the theory of complex multiplication. The algorithm, now called ECPP, has been used for nearly ten years. The purpose of this paper is to give an account of the recent theoretical and practical improvements of ECPP, as well as new benchmarks for integers of various sizes and a new primality record.
UR - https://www.scopus.com/pages/publications/84947787924
U2 - 10.1007/bfb0054855
DO - 10.1007/bfb0054855
M3 - Conference contribution
AN - SCOPUS:84947787924
SN - 3540646574
SN - 9783540646570
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 111
EP - 127
BT - Algorithmic Number Theory - 3rd International Symposium, ANTS-III 1998, Proceedings
A2 - Buhler, Joe P.
PB - Springer Verlag
Y2 - 21 June 1998 through 25 June 1998
ER -