{"id":289,"date":"2017-09-09T15:25:38","date_gmt":"2017-09-09T13:25:38","guid":{"rendered":"http:\/\/members.loria.fr\/PGaudry\/?page_id=289"},"modified":"2021-06-01T07:50:55","modified_gmt":"2021-06-01T05:50:55","slug":"computations","status":"publish","type":"page","link":"https:\/\/members.loria.fr\/PGaudry\/computations\/","title":{"rendered":"Computations"},"content":{"rendered":"<p>Useful links related to record computations: the <a href=\"https:\/\/en.wikipedia.org\/wiki\/Discrete_logarithm_records\">Discrete logarithm records<\/a> Wikipedia page; the <a href=\"https:\/\/dldb.loria.fr\/\">DLDB database<\/a> of discrete logarithm records; the <a href=\"https:\/\/en.wikipedia.org\/wiki\/RSA_numbers\">RSA numbers<\/a> Wikipedia page.<\/p>\n<p>Here is a list of some large-scale computations I have done in the last decade. Many of them have been done with the <a href=\"http:\/\/cado-nfs.gforge.inria.fr\/\">CADO-NFS<\/a> software.<\/p>\n<ul>\n<li>2021. Discrete logarithm computation in a 521-bit field of the form GF(p^6) with TNFS. See the corresponding <a href=\"https:\/\/eprint.iacr.org\/2021\/707\">article<\/a>.<\/li>\n<li>2020. Factorization of the RSA-250 challenge. See Appendix B of the <a href=\"https:\/\/eprint.iacr.org\/2020\/697\">240-digit article<\/a>.<\/li>\n<li>2019. Discrete logarithm computation and integer factorization of 240-digit inputs. These records were set with the same hardware and the same software, in order to compare the relative difficulties of these two hard problems. More details in the <a href=\"https:\/\/eprint.iacr.org\/2020\/697\">article<\/a>.<\/li>\n<li>2016. Discrete logarithm computation in a prime field with a trapped 1024-bit prime. SNFS algorithm. See the <a href=\"http:\/\/caramba.loria.fr\/hsnfs1024.en.html\">announcement<\/a> and the <a href=\"https:\/\/hal.inria.fr\/hal-01376934\/file\/paper.pdf\">article<\/a>.<\/li>\n<li>2016. Discrete logarithm computation in a field of the form GF(p^3) where p has 60 digits, with the NFS algorithm. See the <a href=\"https:\/\/listserv.nodak.edu\/cgi-bin\/wa.exe?A2=NMBRTHRY;ae418648.1608\">announcement<\/a>.<\/li>\n<li>2014. Discrete logarithm computation in a 180-digit prime field with the NFS algorithm. See the <a href=\"http:\/\/caramel.loria.fr\/p180.txt\">announcement<\/a>.<\/li>\n<li>2014. Discrete logarithm computation in a field of the form GF(p^2) where p has 90 digits, with the NFS algorithm. See the <a href=\"http:\/\/caramel.loria.fr\/p2dd80.txt\">announcement<\/a> of a warm-up 80-digit record, and the <a href=\"https:\/\/hal.inria.fr\/hal-01112879\/file\/BGGM-Eurocrypt15.pdf\">article<\/a>.<\/li>\n<li>2013. Discrete logarithm computation in GF(2^809) with the FFS algorithm. See the <a href=\"https:\/\/listserv.nodak.edu\/cgi-bin\/wa.exe?A2=NMBRTHRY;6ac1ef5b.1304\">announcement<\/a> and the <a href=\"https:\/\/hal.inria.fr\/hal-00818124\/file\/ffs809.pdf\">article<\/a>.<\/li>\n<li>2010. Factorization of the RSA-768 challenge with the NFS algorithm. See the <a href=\"http:\/\/caramel.loria.fr\/rsa768.txt\">announcement<\/a> and the <a href=\"https:\/\/hal.inria.fr\/inria-00444693\/file\/rsa768.pdf\">article<\/a>.<\/li>\n<li>2008. Point counting on a 254-bit Jacobian of a genus 2 curve over a prime field. This was later followed by the construction of a twist-secure genus 2 curve. See the <a href=\"https:\/\/members.loria.fr\/PGaudry\/files\/record127\/\">announcement<\/a> and the <a href=\"https:\/\/hal.inria.fr\/inria-00542650\/file\/countg2.pdf\">article<\/a>.<\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>Useful links related to record computations: the <a href=\"https:\/\/en.wikipedia.org\/wiki\/Discrete_logarithm_records\">Discrete logarithm records<\/a> Wikipedia page; the <a href=\"https:\/\/dldb.loria.fr\/\">DLDB database<\/a> of discrete logarithm records; the <a href=\"https:\/\/en.wikipedia.org\/wiki\/RSA_numbers\">RSA numbers<\/a> Wikipedia page.<\/p>\n<p>Here is a list of some large-scale computations I have done in the last decade. Many of them have been done with the <a href=\"http:\/\/cado-nfs.gforge.inria.fr\/\">CADO-NFS<\/a> software.<\/p>\n<ul>\n<li>2021. Discrete logarithm computation in a 521-bit field of the form GF(p^6) with TNFS. See the corresponding <a href=\"https:\/\/eprint.iacr.org\/2021\/707\">article<\/a>.<\/li>\n<li>2020. Factorization of the RSA-250 challenge. See Appendix B of the <a href=\"https:\/\/eprint.iacr.org\/2020\/697\">240-digit article<\/a>.<\/li>\n<\/ul>\n","protected":false},"author":86,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"footnotes":""},"class_list":["post-289","page","type-page","status-publish","hentry"],"_links":{"self":[{"href":"https:\/\/members.loria.fr\/PGaudry\/wp-json\/wp\/v2\/pages\/289","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/members.loria.fr\/PGaudry\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/members.loria.fr\/PGaudry\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/members.loria.fr\/PGaudry\/wp-json\/wp\/v2\/users\/86"}],"replies":[{"embeddable":true,"href":"https:\/\/members.loria.fr\/PGaudry\/wp-json\/wp\/v2\/comments?post=289"}],"version-history":[{"count":14,"href":"https:\/\/members.loria.fr\/PGaudry\/wp-json\/wp\/v2\/pages\/289\/revisions"}],"predecessor-version":[{"id":447,"href":"https:\/\/members.loria.fr\/PGaudry\/wp-json\/wp\/v2\/pages\/289\/revisions\/447"}],"wp:attachment":[{"href":"https:\/\/members.loria.fr\/PGaudry\/wp-json\/wp\/v2\/media?parent=289"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}