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            <funder>This work was possible thanks to a 32M-hour allocation on the Juwels super-computer from the PRACE research infrastructure.Experiments presented in this paper were carried out using the Grid'5000 testbed, supported by a scientific interest group hosted by Inria and including CNRS, RENATER and several Universities as well as other organizations (see https://www.grid5000.fr).This work was supported by the French ``Ministère de l'Enseignement Supérieur et de la Recherche'', by the ``Conseil Régional de Lorraine'', by theEuropean Union, through the ``Cyber-Entreprises'' project, and by the US National Science Foundation under grant no.~1651344.High Performance Computing resources were partially provided by the EXPLOR centre hosted by the University de Lorraine.Computations carried out at the University of Pennsylvania were performed on Cisco UCS servers donated by Cisco.</funder>
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              <p>We report on two new records: the factorization of RSA-240, a 795-bit number, and a discrete logarithm computation over a 795-bit prime field. Previous records were the factorization of RSA-768 in 2009 and a 768-bit discrete logarithm computation in 2016. Our two computations at the 795-bit level were done using the same hardware and software, and show that computing a discrete logarithm is not much harder than a factorization of the same size. Moreover, thanks to algorithmic variants and well-chosen parameters, our computations were significantly less expensive than anticipated based on previous records.The last page of this paper also reports on the factorization of RSA-250.</p>
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