To: ssw@cerias.purdue.edu, Paul.Zimmermann@loria.fr, paul@leyland.vispa.com, scott_contini@yahoo.com, maro@isl.ntt.co.jp, Peter-Lawrence.Montgomery@cwi.nl, Herman.te.Riele@cwi.nl, A.K.Lenstra@tue.nl, BKaliski@rsasecurity.com Reply-To: franke@math.uni-bonn.de From: Jens Franke Date: Fri, 04 Nov 2005 16:53:08 +0100 X-UIDL: )oj!!_ha"!8[;!!Ie,#! We have factored RSA640 by GNFS. The factors are 16347336458092538484431338838650908598417836700330\ 92312181110852389333100104508151212118167511579 and 19008712816648221131268515739354139754718967899685\ 15493666638539088027103802104498957191261465571 We did lattice sieving for most special q between 28e7 and 77e7 using factor base bounds of 28e7 on the algebraic side and 15e7 on the rational side. The bounds for large primes were 2^34. This produced 166e7 relations. After removing duplicates 143e7 relations remained. A filter job produced a matrix with 36e6 rows and columns, having 74e8 non-zero entries. This was solved by Block-Lanczos. Sieving has been done on 80 2.2 GHz Opteron CPUs and took 3 months. The matrix step was performed on a cluster of 80 2.2 GHz Opterons connected via a Gigabit network and took about 1.5 months. Calendar time for the factorization (without polynomial selection) was 5 months. More details will be given later. F. Bahr, M. Boehm, J. Franke, T. Kleinjung [private communication from 7 Sep 2008: the polynomial used had degree 5.] [below is the polynomial used, sent by Thorsten Kleinjung, 17 Feb 2009] 3107418240490043721350750035888567930037346022842727545720161948823206440518081504556346829671723286782437916272838033415471073108501919548529007337724822783525742386454014691736602477652346609 #skewness 537038.41 norm 2.02e+26 alpha -5.85 Murphy_E 1.03e-14 X5 656968428000 X4 -5374110722304074430 X3 -1020004850302221125986301 X2 2148789685995786181805733369342 X1 348632302500316732440863567201821896 X0 -90762756948207415012030368552603530984000 Y1 2273402674003585856567 Y0 -1364492156308865169792227733901596843 M 2599644747230767668487187126639985309037781604277113291685523742475248154947323028610052084117566345315361509857716701608471787887562449278863054159612079462905666096539636051415441179103705518