#11548: Basic implementation of Harley's point counting for elliptic curve.
-------------------------------+--------------------------------------------
Reporter: jpflori | Owner: cremona
Type: enhancement | Status: new
Priority: major | Milestone: sage-4.7.2
Component: elliptic curves | Keywords: point counting, satoh,
elliptic curve, canonical lift, robert harley
Work_issues: | Upstream: N/A
Reviewer: | Author: Jean-Pierre Flori
Merged: | Dependencies:
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This is a basic implementation of Harley's point counting algorithm in
characteristic 2 as presented in Vercauteren thesis (so with what is
called there Norm Computation I).
It uses Sage's interface to Pari library for computations in Z_q.
It is absolutely not optimized.
A simple optimization would be to cythonize it and use direct calls to
Pari or NTL/GF2X libraries.
It is faster than the basic FGH algo implementation of ticket #11448 :
{{{
sage: from sage.schemes.elliptic_curves.fgh_algo import
compute_trace_char2
sage: from sage.schemes.elliptic_curves.harley_algo import harley_2
sage: K = GF(1<<160,'t')
sage: a = K.random_element(); time print harley_2(a); time print
compute_trace_char2(a);
-735100818784167142776219
Time: CPU 7.37 s, Wall: 7.38 s
-735100818784167142776219
Time: CPU 37.33 s, Wall: 37.36 s
}}}
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Ticket URL: <http://trac.sagemath.org/sage_trac/ticket/11548>
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