It's not impossible to prove cryptographic algorithms are secure. It's just really, really, really difficult. So difficult it's not even proven that one way fun

It's not impossible to prove cryptographic algorithms are secure. It's just really, really, really difficult. So difficult it's not even proven that one way functions exist in the first place! (For context: if one way functions exist, then P!=NP). Proving cryptographic algorithms are secure involves proving statements over all turing machines. For example, one definition of a 'secure' pseudo random number generator is one such that no turing machine can distinguish its output from 'true' random (with 2/3 certainty) in polynomial time. However, we do know a really-really-probably secure one way function. If there are any one way functions, then it is secure. It just isn't really practical. http://en.wikipedia.org/wiki/One-way_function#Universal_one-way_function http://en.wikipedia.org/wiki/One-way_function#Universal_one-...