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Jan. 2003 Elliptic curve point counting over finite fields with Gaussian normal basis
Sang Geun Hahn, Je Hong Park, Jung Youl Park
Proc. Japan Acad. Ser. A Math. Sci. 79(1): 5-8 (Jan. 2003). DOI: 10.3792/pjaa.79.5

Abstract

In this paper, we present the GNB-aided MSST algorithm for the curves over finite fields that have a Gaussian normal basis of type $t \le 2$. It is based on the MSST algorithm proposed by P. Gaudry [3] at ASIACRYPT 2002. For those fields, we combine the lifting phase of the MSST algorithm and the norm computation algorithm in [6]. So the time complexity of the MSST is reduced from $O(N^{2\mu + 0.5})$ to $O(N^{2\mu + 1/ (\mu + 1)})$ and it runs faster than any other algorithms in our case.

Citation

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Sang Geun Hahn. Je Hong Park. Jung Youl Park. "Elliptic curve point counting over finite fields with Gaussian normal basis." Proc. Japan Acad. Ser. A Math. Sci. 79 (1) 5 - 8, Jan. 2003. https://doi.org/10.3792/pjaa.79.5

Information

Published: Jan. 2003
First available in Project Euclid: 18 May 2005

zbMATH: 1114.11057
MathSciNet: MR1953975
Digital Object Identifier: 10.3792/pjaa.79.5

Subjects:
Primary: 11G20
Secondary: 11G07, 11T71

Rights: Copyright © 2003 The Japan Academy

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Vol.79 • No. 1 • Jan. 2003
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