Batalov



"Serge" Mar 2008 Phi(4,2^7658614+1)/2

53·73 Posts

RSA-250



Quote: Date: February 28, 2020



For the past three months, ever since the DLP-240 record announced in December 2019 [1], we have been in a historically unique state of affairs: the discrete logarithm record (in a prime field) has been larger than the integer factorization record. We are pleased to rectify this situation with the factorization of RSA-250 from the RSA challenge list:



Code: RSA-250 = 2140324650240744961264423072839333563008614715144755017797754920881418023447140136643345519095804679610992851872470914587687396261921557363047454770520805119056493106687691590019759405693457452230589325976697471681738069364894699871578494975937497937 = 64135289477071580278790190170577389084825014742943447208116859632024532344630238623598752668347708737661925585694639798853367 * 33372027594978156556226010605355114227940760344767554666784520987023841729210037080257448673296881877565718986258036932062711

using the open-source CADO-NFS software [2].



The total computation time was roughly 2700 core-years, using Intel Xeon Gold 6130 CPUs as a reference (2.1GHz):



RSA-250 sieving: 2450 physical core-years

RSA-250 matrix: 250 physical core-years



Here are the factors of p+/-1 and q+/-1:



p-1 = 2 * 6213239 * 101910617047160921359 * 4597395223158209096147 * p77

p+1 = 2^3 * 3 * 7 * 223 * 587131 * 6071858568668069951281 * p93

q-1 = 2 * 5 * 13 * 440117350342384303 * 8015381692860102796237 * p83

q+1 = 2^3 * 3^3 * 23 * 2531 * 11171 * 2100953 * p108



We used computer resources of the Grid'5000 experimental testbed in

France (INRIA, CNRS, and partner institutions) [3], of the EXPLOR

computing center at Universite de Lorraine, Nancy, France [4], an

allocation of computing hours on the PRACE research infrastructure using

resources at the Juelich supercomputing center in Germany [5], as well as

computer equipment gifted by Cisco Systems, Inc. at UCSD.



We would like to dedicate this computation to Peter L. Montgomery, who

passed away on February 18, 2020.



Fabrice Boudot, Education Nationale and Universite de Limoges, France

Pierrick Gaudry, CNRS, Nancy, France

Aurore Guillevic, INRIA, Nancy, France

Nadia Heninger, University of California, San Diego, United States

Emmanuel Thome, INRIA, Nancy, France

Paul Zimmermann, INRIA, Nancy, France



[1] https://caramba.loria.fr/dlp240-rsa240.txt

[2] http://cado-nfs.gforge.inria.fr/

[3] https://www.grid5000.fr

[4] http://explor.univ-lorraine.fr/

[5] http://www.prace-ri.eu/prace-in-a-few-words/ via NMBRTHRY list