There is a bug somewhere in the point counting code for elliptic
curves. Checked both on Linux/4.2.x and OSX-PowerPC/4.2.1. The bug
appears to be either in the PARI ellsea routine or in the SAGE
interface to it. With some more time I plan to look further and look
for an easy fix (unless someone else is already doing the work). The
problem shows up with moderate sized curves over prime fields - a good
example being the NIST p-384 cryptographic curve:
sage: p384 = 2^384 - 2^128 - 2^96 + 2^32 -1
sage: b384 =
0xB3312FA7E23EE7E4988E056BE3F82D19181D9C6EFE8141120314088F5013875AC656398D8A2ED19D2A85C8EDD3EC2AEF
sage: E = EllipticCurve(GF(p384),[-3,b384])
sage: E.cardinality()
/Applications/sage/sage-4.2.1/local/lib/python2.6/site-packages/sage/
schemes/elliptic_curves/sea.pyc
in ellsea(E, p, early_abort)
45 gp.eval('E = ellinit(%s*Mod(1,%s));'%(E,p))
46 N = gp.eval("ellsea(E,%s,0,%s)"%(p,int(early_abort)))
47 if N.find("*") != -1:
---> 48 raise RuntimeError, "Error: '%s'"%N
49 return Integer(N)
RuntimeError: Error: ' *** vector: length (lg) overflow'
--
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