20120723, 18:11  #12  
Basketry That Evening!
"Bunslow the Bold"
Jun 2011
40<A<43 89<O<88
3×29×83 Posts 
Quote:
How much memory would be needed for sieving? Could GGNFS handle it? 

20120723, 18:26  #13  
Bamboozled!
"๐บ๐๐ท๐ท๐ญ"
May 2003
Down not across
2×3×29×67 Posts 
Quote:
The real bottleneck, IMAO, would be twofold. The linear algebra and the project management. I can help with the latter, having had some experience in that area, but not with the former. Solving a matrix which could well be 1G square is not entirely trivial. It's approaching the level of interesting, at least, and possibly challenging on the scale of these things. A concrete start could be made by looking for sextic polynomials. A few cpumillennia should suffice  enough to be accessible right now but, again, not entirely trivial. Paul 

20120723, 18:34  #14  
Basketry That Evening!
"Bunslow the Bold"
Jun 2011
40<A<43 89<O<88
3·29·83 Posts 
Quote:
Could you/others coordinate that here? As for LinAlg, there's clusters more powerful than what frmky's got... (but getting time on them... oh boy ) Last fiddled with by Dubslow on 20120723 at 18:35 Reason: () 

20120723, 18:48  #15 
Undefined
"The unspeakable one"
Jun 2006
My evil lair
41·163 Posts 
Just invent a new algorithm. The NFS type algorithms are starting to show their age and inadequacies now so we are due for a new, fresh and updated version. Come on guys, get to it, get your finger out and starting inventing.

20120723, 18:58  #16 
Aug 2002
2×7×13×47 Posts 
Well, let's do it as a forum, and learn a lot of new things!
http://www.mersenneforum.org/forumdisplay.php?f=97 (Help us think of a snappy/witty/clever forum name.) 
20120723, 21:47  #17 
Just call me Henry
"David"
Sep 2007
Liverpool (GMT/BST)
37·163 Posts 
I am not certain that starting poly selection on RSA1024 now would really help it being finally factored. The poly selection routines in msieve have improved massively in the last couple of years. If we aren't realistically going to be able to do the sieving for a while it might be worth waiting. A better poly can make a huge difference. Considering kilobit gnfs when kilobit snfs stretched us seems silly to me.
@xilman Why is RSA dated? 1024bit obviously is but people could encode in 4096bit for example. I suppose other methods are possibly more efficient why providing the extra protection. 
20120724, 09:38  #18 
Bamboozled!
"๐บ๐๐ท๐ท๐ญ"
May 2003
Down not across
2·3·29·67 Posts 

20120724, 15:28  #19 
Aug 2010
Kansas
547 Posts 
Stupid q? Would it be possible to, instead of using a poly and a NFS (g,s, or otherwise), simply divide it into a number of ranges to TF downwards from the sqrt of RSA1024? Since the factors are roughly the same size, would this save enough time to make it feasible?

20120724, 16:01  #20  
Undefined
"The unspeakable one"
Jun 2006
My evil lair
41·163 Posts 
Quote:
Quote:
Or in other words: Forget it. 

20120724, 16:18  #21 
"Ben"
Feb 2007
2^{2}×3×311 Posts 
It's fun to put numbers to how lucky you'd have to be.
Say your computer can do one trial division in 100 nanoseconds. Then in one day you can test 864 billion 512 bit numbers for divisibility into rsa1024. If you ran 100 billion such computers for 100 billion days you'd be able to test 8.64e33 different 512 bit primes. But there are approximately 2^512 / log(2^512) = 3.78e151 different 512 bit primes. So after doing all that work you'd still only have 1 chance in never of finding the factor. Last fiddled with by bsquared on 20120724 at 16:18 
20120724, 16:29  #22 
Tribal Bullet
Oct 2004
110111100011_{2} Posts 
There is power in accepting that the only way to do something is very difficult. Do that and you're already better off than all the others who don't want to accept the truth.
The odds of guessing the right factors are enormously smaller than the odds of teleporting to Mars due to quantum effects. So did you wear your spacesuit this morning? Winning the lottery is unlikely and people win all the time. Would you buy a Powerball ticket that would only pay out if you guessed all of the next 30 Powerball outcomes correctly? Last fiddled with by jasonp on 20120724 at 16:32 
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