Abstract
We discuss arithmetic in the Jacobian of a hyperelliptic curve C of genus g. The traditional approach is to fix a point P ∞ ∈ C and represent divisor classes in the form E − d(P ∞ ) where E is effective and 0 ≤ d ≤ g. We propose a different representation which is balanced at infinity. The resulting arithmetic is more efficient than previous approaches when there are 2 points at infinity.
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Galbraith, S.D., Harrison, M., Mireles Morales, D.J. (2008). Efficient Hyperelliptic Arithmetic Using Balanced Representation for Divisors. In: van der Poorten, A.J., Stein, A. (eds) Algorithmic Number Theory. ANTS 2008. Lecture Notes in Computer Science, vol 5011. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-79456-1_23
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DOI: https://doi.org/10.1007/978-3-540-79456-1_23
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-79455-4
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