That would be *very* few. Only those who have access to water-cooled mainframes they can use for personal purposes. Numbers which are factorised now are immensely huge, far beyond the capability of Windows Calculator. I think posting a factorisation of such a number without sources would have to be deleted as not being reasonably verifiable.
molu
Message: 11 Date: Wed, 10 May 2006 21:28:22 +0000 (GMT) From: Matt R Subject: Re: [WikiEN-l] Wikipedia-X-Files To: English Wikipedia Message-ID: 20060510212822.34571.qmail@web25015.mail.ukl.yahoo.com Content-Type: text/plain; charset=us-ascii
Steve Bennett wrote:
On 5/10/06, Matt R wrote:
I've got a feeling that the factorisation of an RSA number (either [[RSA-200]] or [[RSA-640]], I forget which) was scooped by Wikipedia last year; or at least, I couldn't find any public announcement that predated it at the time.
Incidentally, factorisations of challenge numbers are one of those exceedingly rare occasions where researchers can publish original research on Wikipedia without it being a problem for us.
Because readers can verify the fact by multiplying the numbers together?
Yes, or at least some can ;-)
-- Matt
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Molu wrote:
That would be *very* few. Only those who have access to water-cooled mainframes they can use for personal purposes. Numbers which are factorised now are immensely huge, far beyond the capability of Windows Calculator. I think posting a factorisation of such a number without sources would have to be deleted as not being reasonably verifiable.
molu
No, multiplication of large numbers is actually very fast, particularly if you use FFT-based algorithms.
In most cases of practically factorizable numbers, even this is not necessary. For example, I can multiply
16347336458092538484431338838650908598417836700330 92312181110852389333100104508151212118167511579
by
1900871281664822113126851573935413975471896789968 515493666638539088027103802104498957191261465571
to get
RSA-640 = 3107418240490043721350750035888567930037346022842727545720161948823206440518081504556346829671723286782437916272838033415471073108501919548529007337724822783525742386454014691736602477652346609
in a tiny fraction of a second, using Python as a bignum calculator on a bog-standard uniprocessor CPU.
Now, _factoring_ it is a different matter: that took 5 CPU-years using 30 2.2 GHz Opteron CPUs in late 2005. See http://www.loria.fr/~zimmerma/records/factor.html and http://www.rsasecurity.com/rsalabs/node.asp?id=2093 for more background.
-- Neil