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arXiv · 1607.08602

Fast Jacobian arithmetic for hyperelliptic curves of genus 3

Andrew V. Sutherland
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Abstract

We consider the problem of efficient computation in the Jacobian of a hyperelliptic curve of genus 3 defined over a field whose characteristic is not 2. For curves with a rational Weierstrass point, fast explicit formulas are well known and widely available. Here we address the general case, in which we do not assume the existence of a rational Weierstrass point, using a balanced divisor approach.

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Andrew V. Sutherland. 2016-07-28. Fast Jacobian arithmetic for hyperelliptic curves of genus 3. https://doi.org/10.2140/obs.2019.2.425

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