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Message: [QUOTE="JSH, post: 3617160"] My research approach to factoring has been towards finding something that would be faster than public key use, which I'm worried now can be achieved--if the research is correct. So, regardless of the size of the public key, it could be factored faster than it could be used. But if P=NP then there are polynomial time solutions out there for ANY of them. That's why I think the research community has resisted any claims of proof of P=NP, for political and economic reasons, so that people would use these systems without fear that down the line--out of the blue--they could be completely cracked. Possibly they have believed like the poster Alan Morgan that even if factoring can fall to a polynomial time solution, it'd be a very slow one, so they can rationalize their behavior as not being threatening to security. In considering my own latest research with the optimal path engine, however, if it is correct then they are very, very, very wrong, and if P=NP then super fast algorithms are possible that would make one way systems non-viable. That could have military implications as well if I'm reading some info correctly that <gasp> the military has also thought to use one way systems as well, though I'm not sure on that one, as I don't know really what military agencies do for encryption. James Harris [/QUOTE]