SLSIA.  I’m working on an introductory survey of ECC (the one suggested in the 
“Climbing the elliptic learning curve” thread a few weeks back) and I’m making 
good progress but I’m stuck on this issue.  I have, of course, found Shoof’s 
algorithm for counting curve points, but that only gets you so far.  With that 
as a baseline, I can kind of imagine an algorithm for finding a base point: 
compute the number of curve points, factor the result, pick the largest prime 
factor q, and then find a generator by brute-force search for a point P such 
that qP=-P.  Is that anywhere close to being the right answer?  Is there a 
reference I can cite?

Thanks,
rg

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