Fwd: [sage-gsoc] Wanted: Mentor for Project with Hyperelliptic Curves

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Vincent Delecroix

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Apr 8, 2021, 2:42:10 AM4/8/21
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Dear Simon, dear all,

@all: forwarding from sage-gsoc

@Simon: your project seems great for a GSoc project. I am
unsure about SageMath capabilities to deal with hyperellitpic
curves but it has some features

https://doc.sagemath.org/html/en/reference/arithmetic_curves/sage/schemes/hyperelliptic_curves/hyperelliptic_finite_field.html

Since your project not listed on the wiki
https://wiki.sagemath.org/GSoC/2021 the possible candidates
for mentors might not be around. I forward your message to the
sage-nt group.

Best
Vincent

-------- Message transféré --------
Sujet : [sage-gsoc] Wanted: Mentor for Project with Hyperelliptic Curves
Date : Wed, 7 Apr 2021 05:46:11 -0700 (PDT)
De : Simon Schwarz <simonsc...@gmail.com>
Répondre à : sage...@googlegroups.com
Pour : sage-gsoc <sage...@googlegroups.com>

Hello all,

my name is Simon and I am currently a postgraduate student in Computer
Science at the University of Cambridge.

As a GSoC 2021 project, I would be interested in extending SageMath's
implementation of Jacobians of hyperelliptic curves. In particular, I'd
like to add point counting methods over finite fields (relevant paper
<https://hal.inria.fr/inria-00512403/document>) and implement the Weil
pairing (and possibly additional pairings) on hyperelliptic curves
(relevant paper
<http://cacr.uwaterloo.ca/techreports/2009/cacr2009-30.pdf>).
Note that SageMath already supports those over elliptic curves, but
currently lacks support for hyperelliptic curves. In contrast, Magma
already includes those methods (see Magma documentation here
<https://magma.maths.usyd.edu.au/magma/handbook/text/1557>), so I think
it would be a great addition if this functionality is also supported by
SageMath.

If anybody can imagine being a mentor for this project please get in
touch with me so we can discuss this project a bit further. Likewise, if
you have any other questions do not hesitate to contact me.

Best regards,
Simon

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Kiran Kedlaya

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Apr 9, 2021, 1:19:24 PM4/9/21
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I should point out that we have some point-counting available already for hyperelliptic curves courtesy from PARI, but of the p-adic sort (small characteristic) rather than the Schoof-Pila sort (larger characteristic).

What I think is needed to go further is to implement the group law in the Jacobian. This has been long overdue and would be a great topic for a GSoC project!

Kiran

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