112-bit prime ECDLP solved

[James A. Donald]

> Hi all,
> 
> We are pleased to announce that we have set a new record for the elliptic
> curve discrete logarithm problem (ECDLP) by solving it over a 112-bit
> finite field. The previous record was for a 109-bit prime field and
> dates back from October 2002.

 > See for more details our announcement at 
<http://lacal.epfl.ch/page81774.html.>

Computing power doubles every 18 months to two years, so the required EC 
length should gain a bit every year or every nine months.

Which suggests that existing deployments should default to 128 bits. 
with 160 bits being overkill.  Of course overkill does not cost much. 
If one shoots someone the head, it is wise to follow up with a second 
shot through the head at very short range just to be on the safe side.

Year    Breakable keys.
2009	112
2010	113
2015	117
2020	121
2025	124

I am assuming a rapid rate of progress, in which case line widths halve 
every four years.

In which case Moore's law breaks in 2033 when we get nanometer line 
widths, for lines will then be molecules - probably carbon nanotubes.

2033	130

Subsequent expansions in computing power will involve breaking up 
Jupiter to build really big computers, and so forth, which will slow 
things down a bit.

So 144 bit EC keys should be good all the way to the singularity and a 
fair way past it.

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