Abstract
In this paper, we propose three ideas to speed up the computation of the group operation in the Jacobian of a hyperelliptic curve:
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1
Division of polynomials without inversions in the base field, and an extended gcd algorithm which uses only one inversion in the base field.
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2
The omission of superfluous calculations in the reduction part.
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3
Expressing points on the Jacobian in a slightly different form.
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Nagao, Ki. (2000). Improving Group Law Algorithms for Jacobians of Hyperelliptic Curves. In: Bosma, W. (eds) Algorithmic Number Theory. ANTS 2000. Lecture Notes in Computer Science, vol 1838. Springer, Berlin, Heidelberg. https://doi.org/10.1007/10722028_28
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DOI: https://doi.org/10.1007/10722028_28
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-67695-9
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