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Claim Fact - 512 Bit number factored by '97

Category: Science & Technology:Encryption, Factoring JUDGED at 0
Owner:0, Bank
Judge:483, patrik
due date:1998/01/01

The Claim

Before 1997 GMT a number of the following form will have been factored. The number must be at least 512 bits long, and be the product of two primes, each at least 200 bits long. The factoring method must not rely on any special properties of the number (except the fact that there are only two factors). In particular, if the factors were chosen by the group doing the factoring, then the technique must not have used any information about the particular factors chosen. The result must be published in a reputable journal. The paper must include a description of how the factoring was accomplished. The result must be reproducible, at least in theory (it need not have been reproduced). To be judged one year later to allow time for publication. Note: 512 bit number means number >= 2^511 A project to factor 512 bit number might not qualify because the factors are too small or there are 3 factors. They will know before you.

Judge's Statement

Ambiguity clause: I will judge this claim based on its precise wording, unless this wording conflicts with my perception of the intent of the claim. If both intent and wording are ambiguous, I will look for a solution that causes the least damage to FX as a market and game. If you have any questions, or think you may have found a loophole, please contact me!!

You may want to check out the RSA Factoring Challenge at http://www.rsa.com/rsalabs/newfaq/q50.html. Send email to challenge-info@rsa.com for more information. You can check on the progress of the Challenge by sending email to challenge-rsa-honor-roll@rsa.com.

The current most efficient algorithm to factor large numbers is the General Number Field Sieve (GNFS), used by several groups participating in the RSA Challenge. Note that there is also a Special Number Field Sieve (SNFS) to factor numbers of the form a^n +/- 1. Results achieved with SNFS do not count for this claim, because the method takes advantage of the properties of the number. In particular, http://www.purdue.edu/UNS/html4ever/9705.Wagstaff.number.html reports factoring of a 167-digit number in 1997, presumably using the SNFS method. This result is disqualified because it was achieved after the deadline, and because it uses a specialized method. Similarly, the previous result mentioned in the same article (162 digits in 1994) is disqualified because it uses the specialized method, and because one of its factors is too small (see http://krum.rz.uni-mannheim.de/sieve-record.html).

Crypto '97, at http://www.iacr.org/conferences/c97/index.html has been mentioned as a possible forum for late-breaking factoring results. I may decide to judge this claim early after this conference (end of August), if it seems clear that no other positive results from 96 will be released before the end of the year.

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