Arsen Ray A. writes:
To quote you: <<Not to attack Doug's point, which has validity here (that we don't know what factoring advances NSA may have made), but I personally think the combined capabilities of "public domain mathematicians" are now far greater than what NSA has. Shamir, Odzylko, Blum, Micali, Rackoff, Goldwasser, Solovay, Berlenkamp, etc., are top-flight researchers, publishing many papers a year on these topics. It is unlikely that some GS-14 mathematicians at the Fort, not able to publish openly, have made much more progress. I think the resurgence of crypto in the 70s, triggered by public key methods and fueled by complexity theory breakthrough, caused a "sea change" in inside NSA-outside NSA algorithm expertise.
You mention Shamir, etc. However I would point out that even if any of the original RSA mathematicians found a better factoring algorithm, they'd be more than likely to keep it under lock and key. The obvious reason is that their money supply depends on such an algorithm being suppressed.
Now, someone outside of their circle with a little less to worry about the impact of such a factoring algirthm would be likely to publish it, but I doubt that PKP's founders would.
Several points: 1. Adi Shamir sold out what little share he had some years back. He has no financial links to PKP or RSADSI. 2. Shamir is Israeli. (This has led to more than one humorous situation in which Shamir has received notification from the U.S. government that he cannot "export" something he's working on--as an Israeli, living in Israel.) 3. Shamir was the coinventor (with Biham), or at least the recent rediscoverer, of differential cryptanalysis. He apparently felt no constraint to not publish. 4. Some of the others I listed, such as Odzylko, are in fact the known leaders of making improvements in factoring. (Not that various linear factors matter much, in the long run, of course.) It's only speculation as to the relative competence of mathematicians inside vs. outside the NSA; my main point remains that the outside community is very dynamic and robust and shows no signs that I can see of holding back on reporting breakthroughs. Nor could a major breakthrough be contained, I think. --Tim May -- .......................................................................... Timothy C. May | Crypto Anarchy: encryption, digital money, tcmay@netcom.com | anonymous networks, digital pseudonyms, zero 408-688-5409 | knowledge, reputations, information markets, W.A.S.T.E.: Aptos, CA | black markets, collapse of governments. Higher Power: 2^859433 | Public Key: PGP and MailSafe available. "National borders are just speed bumps on the information superhighway."