HPC pushes cryptography beyond Moore

Two records in RSA factorisation were achieved through HPC and with the support of PRACE, going above and beyond Moore’s law.

On 2 December 2019 at ECC 2019 in Bochum, a team of European scientists led by Paul Zimmermann of INRIA, France, announced that they computed the largest-ever RSA key size (RSA-240), alongside the largest-ever integer discrete logarithm (795 bits). The achievement is extra remarkable, because the feat goes beyond Moore’s law: based on the current improvements in hardware, we would have had to wait a few more years for this result. Improvements in the software that carries out the Number Field Sieving, and algorithms allowed for the two records to be broken at the same time, and for Moore’s law to be bypassed.

The project in which these achievements were recorded, named “New Records for Integer Factorization and Discrete Logarithm” received 32 million core hours on the German JUWELS supercomputer, hosted by GCS at FZJ, via an allocation under the 18th Call for Proposals for PRACE Project Access

These achievements prove that in the race for the largest and fastest supercomputer, we should continue to focus on scaling up and improving the applications that run on these machines. With phones, cars, homes, and even cities becoming “smart” the need for digital security is ever increasing, and Europe can play a leading role here.” says Núria López, Chair of the PRACE Scientific Steering Committee.

RSA-240 is an extremely large number that is the product of two prime numbers. It looks like this:

1246203667817187840658350446081065904348203746516788057548187888832896668011882108550360395702725
0874750986476843845862105486553797025393057189121768431828636284694840530161441643046806687
5699415246993185704183030512549594371372159029236099 =
5094359522858399145550510235808437141326483820241114731866602965218
21206469746700620316443478873837606252372049619334517 * 2446242088383181505678131390240028966538020925789314014520412213365584770951781552582188977350305
90669041302045908071447

Such numbers are used in cryptography which secures communication, protecting for instance your WhatsApp messages from being read by others, and your online banking from being hacked by criminals. It is expected that quantum computers will be able to easily crack these RSA numbers, and researchers are already developing more complex protection measures. Until then, 2048-bit RSA, Diffie-Hellman, and DSA keys are recommended, as these can still lock adversaries out.

Further reading

ECC 2019: 23rd Workshop on Elliptic Curve Cryptography eccworkshop.org/2019/index.html

About PRACE

Contact