From: "Peter L. Montgomery" Subject: Re: State-of-the-art in integer factorization Date: Fri, 29 Sep 2000 06:23:34 GMT Newsgroups: sci.math,sci.crypt Summary: [missing] In article <39CB719C.26FEFD5@hp.com> JCA writes: > I thought this was common knowledge but in fact I have received several >email requests along these lines. > I got the paper from ftp://ftp.cwi.nl/pub/pmontgom. Peter Montgomery >himself appears in this forum every now and then, and I was hoping he >would have something new to contribute to this issue. As Silverman observes, little has changed recently. ECM has found prime factors as large as 54 digits. SNFS has been used to factor special-form numbers as large as (10^211 - 1)/9 (211 digits). GNFS has been used to factor arbitrary integers up to 155 digits. The only significant improvement has been improved polynomial selection for GNFS. Peter >Jeffrey Williams wrote: >> Would the Montgomery paper happen to be available on-line? And if so, could >> someone please post a pointer to it? >> LL&P >> Jeff Williams >> Bob Silverman wrote: >> > In article <39CA3935.F6F829CF@hp.com>, >> > JCA wrote: >> > > I've got Peter Montgomery's excellent survey on integer >> > > factorization >> > > algorithms. However, being as it is five years old now I was wondering >> > > if there is something more up to date out there. Or, at the very >> > least, >> > > and >> > > addendum to this paper. >> > Nothing has been written. Improvements have been only incremental. >> > (i.e. slightly faster machines, a few more percent squeezed from >> > code, etc.). There hasn't been a new algorithm in 11 years. >> > -- >> > Bob Silverman >> > "You can lead a horse's ass to knowledge, but you can't make him think" >> > Sent via Deja.com http://www.deja.com/ >> > Before you buy. -- E = m c^2. Einstein = Man of the Century. Why the squaring? Peter-Lawrence.Montgomery@cwi.nl Home: San Rafael, California Microsoft Research and CWI