Cryptography Reference
In-Depth Information
RSA-130
= 39685999459597454290161126162883786067576449112810064
832555157243
×
4553449864673597218840368689727440886435630126320506
9600999044599
.
Then in February 1999, RSA-140 was factored into its two 70-digit factors. This
success was accomplished under the direction of Herman J. J. te Riele of CWI
in the Netherlands with teams from the Netherlands, Australia, France, Great
Britain, and the USA.
4
RSA-130 and RSA-140 came from a list of 42 RSA moduli
published in 1991 by the firm RSA Data Security, Inc. as encouragement to the
cryptographic research community.
5
The calculations that led to the factorization
of RSA-130 and RSA-140 were divided among a large number of workstations and
the results collated. The calculational effort to factor RSA-140 was estimated to be
2000 MIPS years
6
(for RSA-130 it was about 1000 MIPS years).
Only a short time later, namely at the end of August 1999, news of the
factorization of RSA-155 flashed across the globe. At a cost of about 8000 MIPS
years the next number in the list of RSA challenges had been laid to rest, again
under the direction of Herman te Riele with international participation. With the
factorization of
RSA-155
= 1094173864157052742180970732204035761200373294544920599
0913842131476349984288934784717997257891267332497
625752899781833797076537244027146743531593354333897
into the two 78-digit factors
RSA-155
= 10263959282974110577205419657399167590071656780803
8066803341933521790711307779
×
1066034883801684548209272203600128786792079585759
89291522270608237193062808643
the magical threshold of 512 was crossed, a length that for many years had been
considered safe for key lengths.
4
5
6
MIPS = mega instructions per second measures the speed of a computer. A computer works at
1 MIPS if is can execute 700,000 additions and 300,000 multiplications per second.
