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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