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Primality proving using elliptic curves: An update

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Book cover Algorithmic Number Theory (ANTS 1998)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 1423))

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Abstract

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.

The author is on leave from the French Department of Defense, Délégation Générale pour l'Armement.

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  1. Laboratoire d'Informatique de l'école polytechnique (LIX - CNRS UMR 7650), F-91128, Palaiseau Cedex, France

    F. Morain

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  1. F. Morain
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Joe P. Buhler

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© 1998 Springer-Verlag Berlin Heidelberg

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Morain, F. (1998). Primality proving using elliptic curves: An update. In: Buhler, J.P. (eds) Algorithmic Number Theory. ANTS 1998. Lecture Notes in Computer Science, vol 1423. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0054855

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  • DOI: https://doi.org/10.1007/BFb0054855

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  • Print ISBN: 978-3-540-64657-0

  • Online ISBN: 978-3-540-69113-6

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