> Does that mean long-term confidence in elliptic curves would be better
> placed?

I don't know.  Sorry.  :(

What I do know is that, judging from past experience, our projections on
key lengths need to take into account the possibility of radical
improvements in mathematics that make our original projections optimistic.

ECC-256 is probably good enough for any imaginable purpose for the
foreseeable future, at least up until quantum computers come along.
That's why I favor using ECC-512 instead.  :)

> Does ECC rely on a stronger mathematical basis

Different, but I'm not sure I'd say stronger.  And yes, it's still
susceptible to mathematical breakthroughs.

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