It was created by RSA Laboratories in March 1991 to encourage research into computational number theory and the practical difficulty of factoring large integers.
[1] RSA Laboratories (which is an initialism of the creators of the technique; Rivest, Shamir and Adleman) published a number of semiprimes with 100 to 617 decimal digits.
According to RSA Laboratories, "Now that the industry has a considerably more advanced understanding of the cryptanalytic strength of common symmetric-key and public-key algorithms, these challenges are no longer active.
Note: until work on this article is finished, please check both the table and the list, since they include different values and different information.
matrix (67.5 hours on the Cray-C90 at SARA, Amsterdam) and square root (48 hours per dependency on an SGI Challenge processor) run by Peter L. Montgomery and Marije Elkenbracht-Huizing sieving: 8.9 CPU-years on about 125 SGI and Sun workstations running at 175 MHZ on average, and on about 60 PCs running at 300 MHZ on average; approximately equivalent to 1500 mips years; run by Peter L. Montgomery, Stefania Cavallar, Herman J.J. te Riele, and Walter M. Lioen (36.8%), Paul Leyland (28.8%), Bruce Dodson (26.6%), Paul Zimmermann (5.4%), and Arjen K. Lenstra (2.5%).
[3][4] Reportedly, the factorization took a few days using the multiple-polynomial quadratic sieve algorithm on a MasPar parallel computer.
The number can be factorized in 72 minutes on overclocked to 3.5 GHz Intel Core2 Quad q9300, using GGNFS and Msieve binaries running by distributed version of the factmsieve Perl script.
[6] RSA-110 has 110 decimal digits (364 bits), and was factored in April 1992 by Arjen K. Lenstra and Mark S. Manasse in approximately one month.
[4][5] The number can be factorized in less than four hours on overclocked to 3.5 GHz Intel Core2 Quad q9300, using GGNFS and Msieve binaries running by distributed version of the factmsieve Perl script.
[3] RSA-129 was factored in April 1994 by a team led by Derek Atkins, Michael Graff, Arjen K. Lenstra and Paul Leyland, using approximately 1600 computers[8] from around 600 volunteers connected over the Internet.
[9] A US$100 token prize was awarded by RSA Security for the factorization, which was donated to the Free Software Foundation.
In 2015, RSA-129 was factored in about one day, with the CADO-NFS open source implementation of number field sieve, using a commercial cloud computing service for about $30.
[10] RSA-130 has 130 decimal digits (430 bits), and was factored on April 10, 1996, by a team led by Arjen K. Lenstra and composed of Jim Cowie, Marije Elkenbracht-Huizing, Wojtek Furmanski, Peter L. Montgomery, Damian Weber and Joerg Zayer.
RSA-140 has 140 decimal digits (463 bits), and was factored on February 2, 1999, by a team led by Herman te Riele and composed of Stefania Cavallar, Bruce Dodson, Arjen K. Lenstra, Paul Leyland, Walter Lioen, Peter L. Montgomery, Brian Murphy and Paul Zimmermann.
The value and factorization are as follows: RSA-155 has 155 decimal digits (512 bits), and was factored on August 22, 1999, in a span of six months, by a team led by Herman te Riele and composed of Stefania Cavallar, Bruce Dodson, Arjen K. Lenstra, Walter Lioen, Peter L. Montgomery, Brian Murphy, Karen Aardal, Jeff Gilchrist, Gerard Guillerm, Paul Leyland, Joel Marchand, François Morain, Alec Muffett, Craig Putnam, Chris Putnam and Paul Zimmermann.
[3] RSA-160 has 160 decimal digits (530 bits), and was factored on April 1, 2003, by a team from the University of Bonn and the German Federal Office for Information Security (BSI).
[23] The factorization was found using the general number field sieve algorithm implementation running on three Intel Core i7 PCs.
On November 2, 2005, F. Bahr, M. Boehm, J. Franke and T. Kleinjung of the German Federal Office for Information Security announced that they had factorized the number using GNFS as follows:[25][26][27] The computation took five months on 80 2.2 GHz AMD Opteron CPUs.
On May 9, 2005, F. Bahr, M. Boehm, J. Franke, and T. Kleinjung announced[28][29] that they had factorized the number using GNFS as follows: The CPU time spent on finding these factors by a collection of parallel computers amounted – very approximately – to the equivalent of 75 years work for a single 2.2 GHz Opteron-based computer.
[28] Note that while this approximation serves to suggest the scale of the effort, it leaves out many complicating factors; the announcement states it more precisely.
[35][36][37] RSA-768 has 232 decimal digits (768 bits), and was factored on December 12, 2009, over the span of two years, by Thorsten Kleinjung, Kazumaro Aoki, Jens Franke, Arjen K. Lenstra, Emmanuel Thomé, Pierrick Gaudry, Alexander Kruppa, Peter Montgomery, Joppe W. Bos, Dag Arne Osvik, Herman te Riele, Andrey Timofeev, and Paul Zimmermann.
[38] RSA-240 has 240 decimal digits (795 bits), and was factored in November 2019 by Fabrice Boudot, Pierrick Gaudry, Aurore Guillevic, Nadia Heninger, Emmanuel Thomé and Paul Zimmermann.
RSA-250 has 250 decimal digits (829 bits), and was factored in February 2020 by Fabrice Boudot, Pierrick Gaudry, Aurore Guillevic, Nadia Heninger, Emmanuel Thomé, and Paul Zimmermann.
The computation was performed with the Number Field Sieve algorithm, using the open source CADO-NFS software.