20051121, 10:18  #1 
2^{3}·1,097 Posts 
Same team factored RSA challenge numbers in recent time
J. Franke & his team factord all recent challenge(Rsa576, Rsa200 & Rsa640) numbers.
1)All three numbers are factored using GNFS.This is widely known algorithm.Why others can't factor challenge numbers?. 2)Is they follow any unpublished tricks in either Polynominal selection,sieving & matrix step?. 3)What is the cost of factoring?.& how much money spend for factoring & anticipated return ?. 4) Why NFSNET project not aims to solve RSA challenge numbers? 5)The main objective of prime factorization research is to predict secure key size for crpto systems which security is based on the hardness of factoring.In real time networks people are still using 128 bit RSA keys .Because they are having multilayer security using more than one cryptographic algorithm.So the prime factorization research are not impotant to industry.Whether this statement is true or not?. Last fiddled with by koders333 on 20051121 at 10:23 
20051121, 10:39  #2  
Bamboozled!
"πΊππ·π·π"
May 2003
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2) Not as far as I know. Note that is a statement of ignorance. It is not a statement that they do not use unpublished methods. 3) Cost is very hard to estimate. The cost is almost certainly much more than the prize money gained from the factorizations. The power and environmental expenses to run almost a hundred machines for almost six months is noticeable. Six months is a noticeable fraction of the lifetime of the machines, so you need to pay that fraction of the purchase cost. A significant amount of time is used by highly skilled people (though not always highly paid!) is required to complete a bleedingedge factorization. Those people expect to be paid, to have office space and facilities and so on. 4) Two reasons. The first is that they are too hard for our resources. The other is that prize money is given for a successful result. The administrative hassles in dealing with the prize money is a very real disincentive. 5) To the best of my knowledge, noone is using 128bit RSA keys for anything other than educational purposes. 128bit symmetric encryption keys (e.g, for AES) are very widely used but that is an entirely different matter from RSA. My personal view is that integer factorization is not particularly important to industry in general (compared with the price of oil, for instance) but that it has some interest to the providers of cryptographic software. Paul 

20051121, 13:50  #3  
Tribal Bullet
Oct 2004
110111001100_{2} Posts 
Quote:
Everybody else who goes after RSA challenge numbers seems to think they can get by with more computers but less math. Is it any wonder that only Franke et. al. succeed? Quote:
jasonp 

20051121, 19:35  #4  
Aug 2004
New Zealand
2^{2}×5×11 Posts 
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20051121, 21:04  #5  
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May 2003
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If you use a value of 18 months for the exponent in Moore's law and assume no algorithmic improvements (a false assumption), factoring should be 16 (i.e., 2^{6/1.5}) times easier today. You should be able to conclude that factoring a 512bit number ought to take around 75 machines running for 2 months. The discrepancy between this estimate of 75 machines and Sean's of 10 is, in my opinion, largely due to algorithmic improvements. In particular, modern polynomial finding algorithms produce markedly better polynomials than were available in 1999. Roughly 1/3 of the difference is due to the fact that all 350 machines were not running continuously for the 7 months elapsed time. Paul 

20051121, 21:12  #6  
Nov 2003
2^{2}×5×373 Posts 
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20051121, 21:16  #7  
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May 2003
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I forget now exactly how much effort came from the CWI line siever and from Arjen Lenstra's lattice siever. Paul 

20051121, 21:21  #8  
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May 2003
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Paul 

20051122, 10:11  #9  
1C4C_{16} Posts 
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My tutor says all prime factorization algorithms are intelligent brute force methods. is it true? 

20051122, 10:25  #10  
Bamboozled!
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May 2003
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The statement made by your tutor is at best immensely misleading. The term "brute force" is not adequately defined. If it is used as shorthand for "division by all primes", then the statement is just plain wrong. Paul 

20051123, 20:58  #11  
Jun 2003
Ottawa, Canada
2221_{8} Posts 
Quote:
Jeff. 

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