## RSA-240 Factored

This just in:

We are pleased to announce the factorization of RSA-240, from RSA's challenge list, and the computation of a discrete logarithm of the same size (795 bits):

RSA-240 = 12462036678171878406583504460810659043482037465167880575481878888328 966680118821085503603957027250874750986476843845862105486553797025393057189121 768431828636284694840530161441643046806687569941524699318570418303051254959437 1372159029236099 = 509435952285839914555051023580843714132648382024111473186660296521821206469746 700620316443478873837606252372049619334517 * 244624208838318150567813139024002896653802092578931401452041221336558477095178 155258218897735030590669041302045908071447

[...]

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). A rough breakdown of the time spent in the main computation steps is as follows.

RSA-240 sieving: 800 physical core-years

RSA-240 matrix: 100 physical core-years

DLP-240 sieving: 2400 physical core-years

DLP-240 matrix: 700 physical core-yearsThe computation times above are well below the time that was spent with the previous 768-bit records. To measure how much of this can be attributed to Moore's law, we ran our software on machines that are identical to those cited in the 768-bit DLP computation [3], and reach the conclusion that sieving for our new record size on these old machines would have taken 25% less time than the reported sieving time of the 768-bit DLP computation.

EDITED TO ADD (12/4): News article. Dan Goodin points out that the speed improvements were more due to improvements in the algorithms than from Moore's Law.

Posted on December 3, 2019 at 2:12 PM • 46 Comments

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