[ncolug] RSA640 factored; large primes not secure
- From: nor thern <zboson2003@xxxxxxxxx>
- To: ncolug@xxxxxxxxxxxxx
- Date: Wed, 9 Nov 2005 14:25:29 -0800 (PST)
another algorithm is on the way to obsolete.
did not use intel chips for factoring.
http://www.crypto-world.com/announcements/rsa640.txt
"From: "Jens Franke"
Date: Fri, 04 Nov 2005 16:53:08 +0100
We have factored RSA640 by GNFS. The factors are
16347336458092538484431338838650908598417836700330\
92312181110852389333100104508151212118167511579
and
19008712816648221131268515739354139754718967899685\
15493666638539088027103802104498957191261465571
We did lattice sieving for most special q between 28e7
and 77e7
using factor base bounds of 28e7 on the algebraic side
and 15e7 on
the rational side. The bounds for large primes were
2^34. This produced
166e7 relations. After removing duplicates 143e7
relations
remained. A filter job produced a matrix with 36e6
rows and columns,
having 74e8 non-zero entries. This was solved by
Block-Lanczos.
Sieving has been done on 80 2.2 GHz Opteron CPUs and
took 3 months.
The matrix step was performed on a cluster of 80 2.2
GHz Opterons
connected via a Gigabit network and took about 1.5
months.
Calendar time for the factorization (without
polynomial selection)
was 5 months.
More details will be given later.
F. Bahr, M. Boehm, J. Franke, T. Kleinjung"
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