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Comparing real and imaginary arithmetics for divisor class groups of hyperelliptic curves

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Algorithmic Number Theory (ANTS 1998)

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

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Abstract

We compare optimized arithmetics with ideals in real resp. imaginary quadratic function fields for divisor class groups of hyperelliptic curves. Our analysis shows that the new real quadratic arithmetic presented by Rück and the first author in [6] and an appropriate modification of the algorithm of Cantor both require a number of operations which is O(g 2) in the field of constants, where g is the genus of a hyperelliptic curve.

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References

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Author information

Authors and Affiliations

  1. Institute of Theoretical Computer Science, Darmstadt University of Technology, 64283, Darmstadt, Germany

    Sachar Paulus

  2. Department of Computer Science, University of Manitoba, R3T 2N2, Winnipeg, Manitoba, Canada

    Andreas Stein

Authors
  1. Sachar Paulus
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  2. Andreas Stein
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Joe P. Buhler

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© 1998 Springer-Verlag Berlin Heidelberg

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Paulus, S., Stein, A. (1998). Comparing real and imaginary arithmetics for divisor class groups of hyperelliptic curves. 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/BFb0054894

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  • DOI: https://doi.org/10.1007/BFb0054894

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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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