RSA-230 has been factored

    #!/usr/bin/python

    from math import *

    ln = log

    def complexity( n ):

        return exp( \
            (64./9)**(1./3) * \
            (ln(n)**(1./3)) * \
            (ln(ln(n))**(2./3)) \
            )

    print complexity(762)
    print complexity(1024)
    print complexity(1024)/complexity(762)

ggm3• 8 years ago

Oh dear. That's very close. RSA2048 and RSA4096 make for very long outcomes in certs and dnssec and the like and I suspect HSM upgrades are coming too if we don't walk to the ECC stuff for shorter representations of the signings at equivalent complexity in solving (so I am told)

[Edit] thanks for simple python too!

malft• 8 years ago

It's very rare for something to scale sublinearly in the number of bits :-)

complexity(2∗∗1024)/complexity(2∗∗762) comes out to about 1500x more work.

ColinWright4• 8 years ago

That's a substantial achievement, I look forward to reading the details. A little searching around suggests that it was a run of CADO-NFS[0] and it's likely that they simply ran it for long enough on a large enough cluster, but we'll wait for the details.

Congratulations to the team.

[0] http://cado-nfs.gforge.inria.fr/

RSA-230 has been factored

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