[curves] How do you find a generator of an EC group?
Ben Smith
hyperelliptic at gmail.com
Mon Dec 12 01:45:54 PST 2016
2016-12-12 0:58 GMT+01:00 Mike Hamburg <mike at shiftleft.org>:
> This is definitely the most straightforward way find the generator of a subgroup, except that you want qP = 0. If you want a NUMS property, you could take the first generator with x-coordinate greater than or equal to some hash value, or similar.
>
> An alternative method is to obtain a point on the curve (either by brute force or with SWU or Elligator), and then multiply it by the cofactor h = #E/q, and then check that itâ€™s not 0.
It's worth noting that multiplying-by-the-cofactor is something that
you'll definitely need to do if you have larger cofactors, like if
you're in a pairing-based situation, because otherwise the probability
that your randomly generated point is even in the subgroup is
somewhere between "annoyingly small" and "negligible".
ben
--
You know we all became mathematicians for the same reason: we were lazy.
--Max Rosenlicht
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