Generating and standardizing elliptic curves to use
them in a cryptographic context is a hard task.
In this note, we don't make an explicit proposal
for an elliptic curve, but we deal with the following
issues.
Security: We give a list of criteria that should be
satisfied by a secure elliptic curve. Although a few
of these criteria are incompatible, we detail what we
think are the best choices for optimal security.
Transparency: We sketch a way to generate a
curve in a fully transparent way so that it can be
trusted and not suspected to belong to a (not publicly
known to be) vulnerable class. In particular, since the
computational cost of verifying the output of such a
process may be quite high, we sketch out the format
of a certificate that eases the computations. We think
that this format might deserve being standardized.
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