What methods are provably secure?
The one-time pad (where the plaintext is XORed into random key stream) is provably secure in a certain academic sense. But it is not really very practical (because it needs long keys that can never be repeated) and not really very secure (because someone can intercept the message and alter it without the recipient noticing). Furthermore, the random key stream is usually simulated with a pseudo-random number generator, and all security properties are lost if that PRNG is weak. Computational complexity theory is just not good enough to prove that DES or RSA encryption is secure. The academic literature has lots of theorems that prove that certain constructions have certain properties provided that factoring is hard, or under some similar assumption. Another class of arguments involves some idealized model like the random oracle model. These arguments are valuable for the insights that they offer to experts, but have virtually no significance to the casual crypto consumer.
