RSA-240 Factored
stormwyrm writes:
The RSA numbers are a set of numbers that are each the product of two large primes generated by RSA in 1991 as part of the RSA Factoring Challenge, to foster research in computational number theory and the practical challenges in factoring large numbers. While the Challenge was declared inactive in 2007 and RSA will no longer award prize money for it, researchers continue to try their hardware and software against the numbers. It has just been announced that a team including Fabrice Boudot, Pierrick Gaudry, Aurore Guillevic, Nadia Heninger, Emmanuel Thomi(C) and Paul Zimmermann has just factored RSA-240, a 795-bit number, taking 900 core-years on a 2.1 GHz Intel Xeon Gold 6130 CPU. They also demonstrated the calculation of a 795-bit discrete logarithm on the same hardware. The previous records were for RSA-768 in 2009 and a 768-bit discrete logarithm in 2016. The speed improvements that led to this work were attributable more to algorithmic improvements than better hardware.
Dear number theorists,
We are pleased to announce the factorization of RSA-240, from RSA's challengelist, and the computation of a discrete logarithm of the same size (795 bits):
RSA-240 = 124620366781718784065835044608106590434820374651678805754818788883289666801188210855036039570272508747509864768438458621054865537970253930571891217684318286362846948405301614416430468066875699415246993185704183030512549594371372159029236099 = 509435952285839914555051023580843714132648382024111473186660296521821206469746700620316443478873837606252372049619334517 * 244624208838318150567813139024002896653802092578931401452041221336558477095178155258218897735030590669041302045908071447
[...] The previous records were RSA-768 (768 bits) in December 2009 [2], and a 768-bit prime discrete logarithm in June 2016 [3].
It is the first time that two records for integer factorization and discrete logarithm are broken together, moreover with the same hardware and software.
Both computations were performed with the Number Field Sieve algorithm, using the open-source CADO-NFS software [4].
The sum of the computation time for both records is roughly 4000 core-years, using Intel Xeon Gold 6130 CPUs as a reference (2.1GHz).
[...] The acceleration can be attributed to various algorithmic improvements that were implemented for these computations. The CADO-NFS implementation was also vastly improved.
We used computer resources of the Grid'5000 experimental testbed in France (INRIA, CNRS, and partner institutions) [5], of the EXPLOR computing center at Universiti(C) de Lorraine, Nancy, France [6], an allocation of computing hours on the PRACE research infrastructure using resources at the Juelich supercomputing center in Germany [7], as well as computer equipment gifted by Cisco Systems, Inc. to the University of Pennsylvania.
More details will be given in a forthcoming scientific publication.
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