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A Low-Memory Algorithm for Point Counting on Picard Curves

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Abstract

Combining the ideas of Bauer, Teske and Weng, [1] and Gaudry, Schost [3], we give a low memory algorithm for computing the number of points on the Jacobian of a Picard curve. It is efficient enough to handle Picard curves over finite prime fields \({\mathbb F}_{p}\), where p is a prime with 58 bits. We present an example where the Jacobian has a prime group order of size 2174

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References

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Authors and Affiliations

  1. Laboratoire d’Informatique (LIX), École Polytechnique, 91128, Palaiseau CEDEX, France

    Annegret Weng

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  1. Annegret Weng
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Correspondence to Annegret Weng.

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Communicated by: A. Menezes

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Weng, A. A Low-Memory Algorithm for Point Counting on Picard Curves. Des Codes Crypt 38, 383–393 (2006). https://doi.org/10.1007/s10623-005-1598-y

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  • DOI: https://doi.org/10.1007/s10623-005-1598-y

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