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> In fact, we know that the intermediate results are not necessary to compute the final result, because that is how the message gets enciphered in the first place. It can be done by factoring the modulus, and obviously there is no proof that that is difficult to do.

Well, there's no mathematical proof. But physicists and judges would accept that there's lots of money and fame to be made breaking eg RSA, so countless people have tried and keep trying, but haven't come up with much good so far.

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