20050610, 04:04  #23  
Sep 2002
2·331 Posts 
Quote:
None, It was an actual run of GNFS that solved it. It required people, software, hardware, mathematical understanding, programming skill, time to solve it. It is the continued effort of skilled mathematicians and programmers over many years that have resulted in the current factoring methods. A reason to care about the challenges is the security of RSA numbers used for encrypting real information. The various math projects have value in multiple ways. They promote testing the assumptions and limits of current algorithms and the developing of new ones, the study of more advanced mathematical methods to create better/more effective systems of factoring with improved math libraries and tools. They expose many people to the richness of mathematical fields with the possibility of getting a general idea behind the process of solving the particular problem. Without the various projects, I would not have known of the existance of the various factoring methods that are/have been employed. They have lead me to this forum and to search various math sites for more information about the math these programs employ. I have tried to implement some of the algorithms, with varying amounts of success, and I keep trying, but I continue to learn by reading what people with much more mathematical knowledge and skill than I are posting and then lookup further information at math reference sites. 

20050610, 04:41  #24  
"Nancy"
Aug 2002
Alexandria
2,467 Posts 
Quote:
Is there any chance that lattice sieving would speed up MPQS? Alex 

20050610, 07:24  #25  
Bamboozled!
"πΊππ·π·π"
May 2003
Down not across
73×151 Posts 
Quote:
See, I knew you could post something of value to most readers here if you answered the questions as asked, even though the questions indicated a certain hopeless naivety. Paul 

20050610, 12:05  #26  
Tribal Bullet
Oct 2004
3·1,181 Posts 
Quote:
The ideas I was referring to was Bernstein's paper "How to Find Small Factors of Integers", available at http://cr.yp.to/papers.html#sf jasonp 

20050610, 16:28  #27  
Oct 2004
tropical Massachusetts
3×23 Posts 
ECM sigma
Quote:
Sam 

20050610, 17:06  #28  
Nov 2003
2^{2}×5×373 Posts 
Quote:
However, it is a theoretical concern only because noone has come close to running 65K curves on a single number. And a small number of collisions is only a very slight loss in efficiency. As machines get fast enough to let us run 65K curves, then we will indeed need to use 64 bit seeds 

20050610, 20:40  #29  
"Nancy"
Aug 2002
Alexandria
2,467 Posts 
Torbjorn Granlund suggested allowing larger sigma values in late 2003. This was my reply:
Quote:
Last fiddled with by akruppa on 20050612 at 12:20 Reason: B1<>B2 

20050610, 21:11  #30 
"Mark"
Apr 2003
Between here and the
2^{2}·5·17·19 Posts 
I assume that 64bit CPUs generate 64bit random numbers. If so, then it is even probably less of an issue. Bruce Dodson runs many of his curves on a 64bit AMD. I would not be surprised if many others use 64bit machines for large B1s.

20050610, 21:31  #31 
"Nancy"
Aug 2002
Alexandria
4643_{8} Posts 
The register size of the cpu has nothing to do with it. The question is:
(1) how large must the range for the sigma values be that in practical application the efficiency loss due to sigma collisions is negligible (2) where do we find enough entropy to seed the RNG for generating such sigma values For the time being and the forseeable future, 32 bit sigmas are quite sufficient and easy to seed even on systems that don't feature a /dev/urandom device. Incidentally, does someone know of a simliar source of entropy under Windows? Is there a system call or something? Alex 
20050610, 22:23  #32  
P90 years forever!
Aug 2002
Yeehaw, FL
2^{3}·7·137 Posts 
Quote:


20050611, 06:12  #33 
Jun 2005
1111_{2} Posts 
Probably the best source of randomness for windows is from the CryptGenRandom function. It is supposed to be used for random seeds, IVs, chanlenges, etc in cryptographic circumstances.

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