307 digit number factored

[James A. Donald]

> | > AFAIK, the only advantage of ECC is that the keys are
> | > shorter. The disadvantage is that it isn't as well
> | > studied.
> | 

James A. Donald:
> | On past performance, elliptic curves are safer than
> | integers.  From time to time, integer based asymmetric
> | encryption is abruptly and surprisingly weakened by
> | advances in discrete log algorithms.  This is just not
> | happening with elliptic curves.

Leichter, Jerry wrote:
> "Past performance does not predict future results."
> 
> I don't think this is a particularly strong argument.  A
> reasonable counter-argument is that we've been doing
> number theory over the integers for hundreds of years,
> while intensive work on computations over elliptic curves
> goes back, what, 20 years at most?

And in those twenty years we have made little progress on the division 
problem with elliptic curves, and considerable progress on the discrete 
log problem on integers.  Surely, with a thousand year start, progress 
on integers should be slowing down, not speeding up.

Further, this is what one would expect from the irregular character of 
elliptic curves.

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