Proving the primality of very large numbers with fastECPP

J. Franke; T. Kleinjung; F. Morain; T. Wirth

doi:10.1007/978-3-540-24847-7_14

Proving the primality of very large numbers with fastECPP

J. Franke
, T. Kleinjung
, F. Morain
, T. Wirth

University Bonn

Research output: Chapter in Book/Report/Conference proceeding › Chapter › peer-review

Abstract

The elliptic curve primality proving algorithm is one of the fastest practical algorithms for proving the primality of large numbers. Its fastest version, fastECPP, runs in heuristic time Ō((log N)⁴). The aim of this article is to describe new ideas used when dealing with very large numbers. We illustrate these with the primality proofs of some numbers with more than 10,000 decimal digits.

Original language	English
Title of host publication	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Editors	Duncan Buell
Publisher	Springer Verlag
Pages	194-207
Number of pages	14
ISBN (Print)	3540221565, 9783540221562
DOIs	https://doi.org/10.1007/978-3-540-24847-7_14
Publication status	Published - 1 Jan 2004

Publication series

Name	Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume	3076
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Access to Document

10.1007/978-3-540-24847-7_14

Cite this

Franke, J., Kleinjung, T., Morain, F., & Wirth, T. (2004). Proving the primality of very large numbers with fastECPP. In D. Buell (Ed.), Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (pp. 194-207). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 3076). Springer Verlag. https://doi.org/10.1007/978-3-540-24847-7_14

Franke, J. ; Kleinjung, T. ; Morain, F. et al. / Proving the primality of very large numbers with fastECPP. Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). editor / Duncan Buell. Springer Verlag, 2004. pp. 194-207 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)).

@inbook{b615a961bcf84a6798318aeb4faa028f,

title = "Proving the primality of very large numbers with fastECPP",

abstract = "The elliptic curve primality proving algorithm is one of the fastest practical algorithms for proving the primality of large numbers. Its fastest version, fastECPP, runs in heuristic time Ō((log N)4). The aim of this article is to describe new ideas used when dealing with very large numbers. We illustrate these with the primality proofs of some numbers with more than 10,000 decimal digits.",

author = "J. Franke and T. Kleinjung and F. Morain and T. Wirth",

year = "2004",

month = jan,

day = "1",

doi = "10.1007/978-3-540-24847-7\_14",

language = "English",

isbn = "3540221565",

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

publisher = "Springer Verlag",

pages = "194--207",

editor = "Duncan Buell",

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

}

Franke, J, Kleinjung, T, Morain, F & Wirth, T 2004, Proving the primality of very large numbers with fastECPP. in D Buell (ed.), Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), vol. 3076, Springer Verlag, pp. 194-207. https://doi.org/10.1007/978-3-540-24847-7_14

Proving the primality of very large numbers with fastECPP. / Franke, J.; Kleinjung, T.; Morain, F. et al.
Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). ed. / Duncan Buell. Springer Verlag, 2004. p. 194-207 (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 3076).

Research output: Chapter in Book/Report/Conference proceeding › Chapter › peer-review

TY - CHAP

T1 - Proving the primality of very large numbers with fastECPP

AU - Franke, J.

AU - Kleinjung, T.

AU - Morain, F.

AU - Wirth, T.

PY - 2004/1/1

Y1 - 2004/1/1

N2 - The elliptic curve primality proving algorithm is one of the fastest practical algorithms for proving the primality of large numbers. Its fastest version, fastECPP, runs in heuristic time Ō((log N)4). The aim of this article is to describe new ideas used when dealing with very large numbers. We illustrate these with the primality proofs of some numbers with more than 10,000 decimal digits.

AB - The elliptic curve primality proving algorithm is one of the fastest practical algorithms for proving the primality of large numbers. Its fastest version, fastECPP, runs in heuristic time Ō((log N)4). The aim of this article is to describe new ideas used when dealing with very large numbers. We illustrate these with the primality proofs of some numbers with more than 10,000 decimal digits.

U2 - 10.1007/978-3-540-24847-7_14

DO - 10.1007/978-3-540-24847-7_14

M3 - Chapter

AN - SCOPUS:24144482085

SN - 3540221565

SN - 9783540221562

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 194

EP - 207

BT - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

A2 - Buell, Duncan

PB - Springer Verlag

ER -

Franke J, Kleinjung T, Morain F, Wirth T. Proving the primality of very large numbers with fastECPP. In Buell D, editor, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics). Springer Verlag. 2004. p. 194-207. (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)). doi: 10.1007/978-3-540-24847-7_14

Proving the primality of very large numbers with fastECPP

Abstract

Publication series

Access to Document

Fingerprint

Cite this