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.

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:

5699415246993185704183030512549594371372159029236099 =
21206469746700620316443478873837606252372049619334517 * 2446242088383181505678131390240028966538020925789314014520412213365584770951781552582188977350305

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

This article was first published on www.prace-ri.eu on Wednesday 18 December 2019.


The mission of PRACE (Partnership for Advanced Computing in Europe) is to enable high-impact scientific discovery and engineering research and development across all disciplines to enhance European competitiveness for the benefit of society. 

PRACE seeks to realise this mission by offering world class computing and data management resources and services through a peer review process. 

PRACE aisbl is funded by the PRACE Members The Implementation Phase of PRACE receives funding from the EU’s Horizon 2020 Research and Innovation Programme (2014-2020).

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