mersenneforum.org  

Go Back   mersenneforum.org > Factoring Projects > Factoring

Reply
 
Thread Tools
Old 2010-01-07, 19:45   #23
TimSorbet
Account Deleted
 
TimSorbet's Avatar
 
"Tim Sorbera"
Aug 2006
San Antonio, TX USA

10000101101112 Posts
Default

Quote:
Originally Posted by FactorEyes View Post
Then I'm lost.

Why even run 1 ECM curve on such a number?
Well, there's always a very, very slight chance that an ECM curve might find one of the factors. You're probably more likely to be struck by lightning while winning 5 lotteries, but it's possible.

Edit: Out of curiosity, how long, and how much memory, would it take to find one of these factors by P-1 or P+1, knowing what their factorizations are? P-1 bounds could be B1=1e30 and B2=1e47 or B1=360 and B2=1e113, P+1 bounds could be B1=1e44 and B2=1e71 or B1=1e21 and B2=1e90.
BTW here are FactorDB links for a few of the related numbers here:
N: http://factordb.com/search.php?id=9946820
p: http://factordb.com/search.php?id=91768521
p-1: http://factordb.com/search.php?id=91919514
p+1: http://factordb.com/search.php?id=91919521
q: http://factordb.com/search.php?id=91768522
q-1: http://factordb.com/search.php?id=91919525
q+1: http://factordb.com/search.php?id=91919527

Last fiddled with by TimSorbet on 2010-01-07 at 20:00
TimSorbet is offline   Reply With Quote
Old 2010-01-07, 19:49   #24
xilman
Bamboozled!
 
xilman's Avatar
 
"๐’‰บ๐’ŒŒ๐’‡ท๐’†ท๐’€ญ"
May 2003
Down not across

2·73·17 Posts
Default

Quote:
Originally Posted by FactorEyes View Post
Then I'm lost.

Why even run 1 ECM curve on such a number?
Remember the Golden Rule: Never ascribe to malice that which is adequately explained by incompetence.

If I were a betting man, I would put much more money on incompetence by the ECM people than on malice(*) by Bob (or incompetence, for that matter!). My instincts were proven correct in this case.

The best response to those who propose to run ECM on RSA moduli is: do you feel lucky, punk?

Paul

(*)I freely admit to malice when creating the RSA modulus in The Code Book challenge. It was a source of some amusement, and re-assurance, that noone tried P-1 with sufficiently large limits on the modulus.
xilman is offline   Reply With Quote
Old 2010-01-07, 20:00   #25
Batalov
 
Batalov's Avatar
 
"Serge"
Mar 2008
Phi(4,2^7658614+1)/2

3×7×479 Posts
Default

Congratulations on the fantastic job!
Batalov is offline   Reply With Quote
Old 2010-01-07, 20:03   #26
jasonp
Tribal Bullet
 
jasonp's Avatar
 
Oct 2004

DE316 Posts
Default

Congratulations to everyone involved; we were long overdue for a GNFS record, and this moves the state of the art far in front of what's reasonably possible with individual contributors.

Msieve can now handle arbitrary numbers of large primes per relation, up to 48 bits each (this size keeps down the expansion in the size of the hashtable used in the singleton removal phase). It's also limited to 4 billion relations, but this is 10x larger than what anyone has tried.

Edit: Andi, I think GNFS-232 is well within the range where a degree 6 polynomial is a better idea than degree 5

Last fiddled with by jasonp on 2010-01-07 at 20:06
jasonp is offline   Reply With Quote
Old 2010-01-07, 20:09   #27
10metreh
 
10metreh's Avatar
 
Nov 2008

2·33·43 Posts
Default

An amazing achievement!

This shows that HP49:100 is a possibility if we have a degree 6 poyfinder and a block Wiedemann implementation; is there a chance that any of the software used could become available to the public?

Last fiddled with by 10metreh on 2010-01-07 at 20:10 Reason: i before e except after c (grrr...)
10metreh is offline   Reply With Quote
Old 2010-01-07, 20:12   #28
mdettweiler
A Sunny Moo
 
mdettweiler's Avatar
 
Aug 2007
USA (GMT-5)

186916 Posts
Default

Quote:
Originally Posted by akruppa View Post
Yield:
64 334 489 730 relations
(38% INRIA, 30% EPFL, 15% NTT, 8% Bonn, 3.5% CWI, 5.5% others)
Quote:
Originally Posted by jasonp View Post
It's also limited to 4 billion relations, but this is 10x larger than what anyone has tried.
Eh? Does not compute. If 4 billion relations is 10x larger than what anyone has tried, how come this job produced 64 billion? (Or am I missing something here?)
mdettweiler is offline   Reply With Quote
Old 2010-01-07, 20:16   #29
henryzz
Just call me Henry
 
henryzz's Avatar
 
"David"
Sep 2007
Liverpool (GMT/BST)

10111100100002 Posts
Default

Quote:
Originally Posted by mdettweiler View Post
Eh? Does not compute. If 4 billion relations is 10x larger than what anyone has tried, how come this job produced 64 billion? (Or am I missing something here?)
tried using msieve
henryzz is offline   Reply With Quote
Old 2010-01-07, 20:18   #30
mdettweiler
A Sunny Moo
 
mdettweiler's Avatar
 
Aug 2007
USA (GMT-5)

3·2,083 Posts
Default

Quote:
Originally Posted by henryzz View Post
tried using msieve
Ah, that makes sense, since this job wasn't done using msieve. Speaking of which, as 10metreh said, is it planned to make the software used available to the public?
mdettweiler is offline   Reply With Quote
Old 2010-01-07, 21:06   #31
Andi47
 
Andi47's Avatar
 
Oct 2004
Austria

2·17·73 Posts
Default

Quote:
Originally Posted by jasonp View Post
Edit: Andi, I think GNFS-232 is well within the range where a degree 6 polynomial is a better idea than degree 5
I think so too, but how to FIND a sextic polynomial?
Andi47 is offline   Reply With Quote
Old 2010-01-07, 22:16   #32
bsquared
 
bsquared's Avatar
 
"Ben"
Feb 2007

373310 Posts
Default

Fantastic! Cheers to all involved!

The paper mentions that a deliberate decision was made to not BOINCify or otherwise open up the sieving stage of the computation; mostly I gather from the desire to set a reasonably precise completion date and from a data management standpoint. I wonder how much could be gained if they opened it up, assuming the resources (administration/data management) were available? If not BOINC then at least a more widespread invitation to contribute. It seems like there would be lots of interest from the community to contribute to a record factorization, but maybe that's just the euphoria talking.

Anyway, congrats again!
bsquared is offline   Reply With Quote
Old 2010-01-07, 23:29   #33
bdodson
 
bdodson's Avatar
 
Jun 2005
lehigh.edu

210 Posts
Default

Quote:
Originally Posted by bsquared View Post
... I wonder how much could be gained if they opened it up, assuming the resources (administration/data management) were available? If not BOINC then at least a more widespread invitation to contribute. It seems like there would be lots of interest from the community to contribute to a record factorization, ...
Arjen reports having looked at this thread. I'm fairly certain that no
serious consideration was given to opening up this computation to the
public. Neither BSI nor NTT are inclined toward having their interests
reported before they're ready. -Bruce
bdodson is offline   Reply With Quote
Reply

Thread Tools


Similar Threads
Thread Thread Starter Forum Replies Last Post
Modulus function on a linear convolution lukerichards Number Theory Discussion Group 4 2018-04-06 12:57
Extracting the Modulus from publickeyblob RSA 512 26B Homework Help 2 2014-11-30 07:31
It's possible to calculate an unknown RSA modulus? D2MAC Math 8 2010-12-26 16:32
Fixed leading bits in RSA modulus, vs NFS fgrieu Factoring 7 2009-09-23 11:45
Factoring with Highly Composite Modulus mgb Math 3 2006-09-09 10:35

All times are UTC. The time now is 05:35.


Tue Feb 7 05:35:35 UTC 2023 up 173 days, 3:04, 1 user, load averages: 0.95, 1.11, 1.21

Powered by vBulletin® Version 3.8.11
Copyright ©2000 - 2023, Jelsoft Enterprises Ltd.

This forum has received and complied with 0 (zero) government requests for information.

Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or any later version published by the Free Software Foundation.
A copy of the license is included in the FAQ.

โ‰  ยฑ โˆ“ รท ร— ยท โˆ’ โˆš โ€ฐ โŠ— โŠ• โŠ– โŠ˜ โŠ™ โ‰ค โ‰ฅ โ‰ฆ โ‰ง โ‰จ โ‰ฉ โ‰บ โ‰ป โ‰ผ โ‰ฝ โŠ โŠ โŠ‘ โŠ’ ยฒ ยณ ยฐ
โˆ  โˆŸ ยฐ โ‰… ~ โ€– โŸ‚ โซ›
โ‰ก โ‰œ โ‰ˆ โˆ โˆž โ‰ช โ‰ซ โŒŠโŒ‹ โŒˆโŒ‰ โˆ˜ โˆ โˆ โˆ‘ โˆง โˆจ โˆฉ โˆช โจ€ โŠ• โŠ— ๐–• ๐–– ๐–— โŠฒ โŠณ
โˆ… โˆ– โˆ โ†ฆ โ†ฃ โˆฉ โˆช โŠ† โŠ‚ โŠ„ โŠŠ โŠ‡ โŠƒ โŠ… โŠ‹ โŠ– โˆˆ โˆ‰ โˆ‹ โˆŒ โ„• โ„ค โ„š โ„ โ„‚ โ„ต โ„ถ โ„ท โ„ธ ๐“Ÿ
ยฌ โˆจ โˆง โŠ• โ†’ โ† โ‡’ โ‡ โ‡” โˆ€ โˆƒ โˆ„ โˆด โˆต โŠค โŠฅ โŠข โŠจ โซค โŠฃ โ€ฆ โ‹ฏ โ‹ฎ โ‹ฐ โ‹ฑ
โˆซ โˆฌ โˆญ โˆฎ โˆฏ โˆฐ โˆ‡ โˆ† ฮด โˆ‚ โ„ฑ โ„’ โ„“
๐›ข๐›ผ ๐›ฃ๐›ฝ ๐›ค๐›พ ๐›ฅ๐›ฟ ๐›ฆ๐œ€๐œ– ๐›ง๐œ ๐›จ๐œ‚ ๐›ฉ๐œƒ๐œ— ๐›ช๐œ„ ๐›ซ๐œ… ๐›ฌ๐œ† ๐›ญ๐œ‡ ๐›ฎ๐œˆ ๐›ฏ๐œ‰ ๐›ฐ๐œŠ ๐›ฑ๐œ‹ ๐›ฒ๐œŒ ๐›ด๐œŽ๐œ ๐›ต๐œ ๐›ถ๐œ ๐›ท๐œ™๐œ‘ ๐›ธ๐œ’ ๐›น๐œ“ ๐›บ๐œ”