See the links here:

http://the-point-of-view-of-frank.blogspot.com/2012/08/p-versus-up.html

]]>I’m sure it would help me to be a better programmer as well. Since most of the modern programmer’s time is spent understanding and manipulating provided APIs rather than developing new algorithms, the mathematical side of my programming is rather weak.

]]>I largely agree with your comment (see my comment above) but there *are* certain properties of public key crypto today which we would probably lose, like good forward secrecy for one-sided messages (i.e., messages generated without a key exchange dialog). This is because computing power is still increasing exponentially with time, so limiting the difficulty of decryption to poly-time is a problem.

All it requires that decryption without a private key took so much longer so as to make it impractical while encryption is still fast.

]]>Ah, thanks, I had forgotten that checking whether a factorization was correct was poly-time. It still strikes me as a strange assumption that public key encryption *requires* a hard problem which is not in P. I vaguely remember a paper which proposed a (not very practical) poly-time public-key cryptosystem where there was a provable gap in the order of the decryption complexity between an attacker without the private key (having O(n^2) complexity?) and with the private key (having O(n) complexity?). Unfortunately, I don’t manage to find this paper anywhere.

It seems to me possible to have a relatively workable public-key cryptosystem based on the difficulty of a problem with complexity O(n^20) vs. O(n^2), for example, which could provide *a lot* of the functionality which we have today. There would be a lot more headache to constantly roll-over keys, update the security parameters, and have to deal with very large keys and messages, but it would still be possible.

If you elect me… I will prove, that P=NP. The world will be better and brighter. Now is the time for change. The other canidates say we can’t do it… to that I say “Yes we can.”

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