Re: Fate of Ecash if RSA is cracked?

[ichudov@algebra.com (Igor Chudov @ home)]

Jeremey Barrett wrote:
> > The "Idea Futures" forum has established odds on this. The current odds are
> > currently 60% that a 1024 bit number will be factored by 2010 and 30% that
> > a 512 bit number will be factored by 1997.
> > 
> 
> True, but by that time I'll be able to use 2048 or bigger keys with the same
> or better performance as 1024 bit keys now.  As long as factoring is
> exponential, you can always make it impossible to factor your keys. 
> And I think it will always be exponential.

Actually factoring is not exponential even now. For Number Fiels Sieve 
method the number of operations is estimated as

N ~= exp(((1.923+O(1)) * (ln n)^(1/3) * ln ln n)^(2/3))

(taken from Schneier, A.C., page 256)

	- Igor.