112-bit prime ECDLP solved

[Tanja Lange]

> >So with about 1 000 000 USD and a full year you would get 122 bits 
> >already now and agencies have a bit more budget than this! Furthermore,
> >the algorithm parallelizes extremely well and can handle a batch of 100
> >targets at only 10 times the cost. 
> 
> No it cannot handle a bunch of a hundred targets at only ten times the 
> cost.  It is already parallelized.  A hundred targets is a hundred times 
> the cost.
> 
NO. Read
Fabian Kuhn, René Struik: Random Walks Revisited: Extensions of
Pollard's Rho Algorithm for Computing Multiple Discrete Logarithms.
Selected Areas in Cryptography 2001: 212-229
Section 4.

Besides, the estimates assume only playstations and the EPFL code instead 
of special purpose hardware which would give an extra speed up.

And, no, I'm not suggesting to use the entire US gross national product
for a year to break your key but given that that breaks 172 bits (SHARCS
2006 estimates for ECC-163 and 9 bits to scale from USD 5.8*10^11 to the
GDP 1.4*10^13) I'm not comfortable with 160 bits, let alone 144.

All the best	
	Tanja

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