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Formal groups, elliptic curves, and some theorems of Couveignes

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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

The formal group law of an elliptic curve has seen recent applications to computational algebraic geometry in the work of Couveignes to compute the order of an elliptic curve over finite fields of small characteristic ([2], [6]). The purpose of this paper is to explain in an elementary way how to associate a formal group law to an elliptic curve and to expand on some theorems of Couveignes. In addition, the paper serves as background for [1]. We treat curves defined over arbitrary fields, including fields of characteristic two or three. The author wishes to thank Al Laing for a careful reading of an earlier version of the manuscript and for many useful suggestions.

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References

  1. A. W. Bluher, Relations between certain power sums of elliptic modular forms in characteristic two, to appear in J. Number Theory

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  2. J. M. Couveignes, Quelques calculs en theorie des nombres, Ph.D. thesis, Bordeaux, 1995

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Authors and Affiliations

  1. National Security Agency, 9800 Savage Road, 20755-6000, Fort George G. Meade, MD

    Antonia W. Bluher

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  1. Antonia W. Bluher
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Joe P. Buhler

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© 1998 Springer-Verlag Berlin Heidelberg

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Bluher, A.W. (1998). Formal groups, elliptic curves, and some theorems of Couveignes. 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/BFb0054887

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  • DOI: https://doi.org/10.1007/BFb0054887

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-64657-0

  • Online ISBN: 978-3-540-69113-6

  • eBook Packages: Springer Book Archive

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