#4964: [with patch, needs review] Add Weil pairing to Sage
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Reporter: dmhansen | Owner: mollerhansen
Type: enhancement | Status: reopened
Priority: minor | Milestone: sage-3.3
Component: algebraic geometry | Resolution:
Keywords: pairing, elliptic curve |
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Comment (by cremona):
This looks pretty good to me though I have not done any detailed testing,
I only looked at the code.
I have one suggestion which should speed this up whenever the actual
orders of P or Q are strictly less than n: find the orders of P and Q,
say m1 and m2. (The generic function order_from_multiple might be useful
here.) Let d=gcd(m1,m2). Then it is clear that the result is a d'th
root of unity, and it can be computed by taking the pairing of (m1/d)*P
and (m2/d)*Q. [Proof: exercise.] This would save a lot when d is much
less than n.
I also have a question: rather than wait for a division by zero error to
catch dependent input, why not do a discrete log calculation to test this?
Maybe that's much slower for large n; it would be nice to have this
decision justified.
Sorry, that's all I have time for just now.
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Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/4964#comment:6>
Sage <http://sagemath.org/>
Sage - Open Source Mathematical Software: Building the Car Instead of
Reinventing the Wheel
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