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A recent proof of the ABC Conjecture has been released by one Shinichi Mochizuki. Now, I'm not well versed in mathematics but it would appear that this proof implies that finding prime factors could be greatly reduced in computation time. Is that right? Does this show that encryption that relies on prime factors can be cracked quicker? And if so is it possible that such an algorithm could be produced from these findings to do so either now or in the future?

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migrated from Sep 12 '12 at 13:51

This question came from our site for information security professionals.

I think this is a better fit for our sister site Cryptography. I've asked a moderator to look at the possibility of moving it. – Scott Pack Sep 12 '12 at 12:41
Welcome to cryptography Stack Exchange. Your question was migrated here, because it is mainly about the theoretical parts of cryptography, not the application thereof (which would be on topic on Security Stack Exchange). Please register your account on both sites (using the same mail address) to take ownership of your question again, be able to edit, comment and accept an answer. – Paŭlo Ebermann Sep 12 '12 at 16:46

There are no known implications of the ABC Conjecture to RSA. The ABC problem doesn't have even a superficial resemblance to the security of RSA.

(The only point of connection is the fact that they both relate to prime numbers, but that is extremely thin. Much of number theory can say it is somehow related to prime numbers. It'd be like assuming that recent improvements in building fast sailboats for the America's Cup has implications for the possible future availability of a flying car, since they both involve fluids.)

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Actually, sailboats and flying cars have a few more links than that. Aerodynamics and hydrodynamics are very similar and both are important on a sailboat. – ewanm89 Sep 12 '12 at 10:56

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