[swiley]

>maths. It’s proven.

No they are not. That’s one of the things that makes designing correct crypto systems difficult. Going the wrong way through most cryptographic trap doors is conjectured to be difficult but I’m unaware of a single one that’s proven.

[mjlee]

The one-time pad has been proven to have perfect secrecy.

Given a ciphertext, the only information available is its length.

[swiley]

This makes a lot of assumptions:

You have a way to securely exchange or store the one time pad (at that point just use slices of the pad as passwords)

The pad is sufficiently random

This was how RC4 was used to encrypt things; RC4 is fundamentally a random number generator. To use it you throw away the first so many bytes (because they could be used to recover the state of the machine.) and then the rest was used as a pad. Unfortunetly patterns in the data can make it easy to recover the raw RC4 pad (uncompressed blank bitmaps for example) and this can be used (again) to recover the state of the machine generating the numbers. On top of that it turns out RC4 is a lot more predictable than people originally thought.

Essentially all a one time pad does is move the problem somewhere else, often that other place isn't great.