Are there any classical proven secure cryptographic algorithms other than OTP?

Question

Boiled down to the core as I understand it:

A cryptographic algorithm has provable security if it's unbreakable, even if an adversary has unlimited computational power / time.

If my understanding is correct then cryptographic algorithms like RSA / Diffie-Hellman are not considered to be provable secure since they would be broken to an adversary with unlimited computational power / time.

The only classical algorithm I know of that behaves in this manner is the OTP. I'm specifically asking about classical algorithms because I know that there exist quantum cryptographic algorithms that are provable secure, i.e. QKD.

My questions are:

• Is my understanding of provable security correct?

• And if so, are there any other classical algorithms that are provable secure?

Answer 1

A cryptographic algorithm has provable security if it's unbreakable, even if an adversary has unlimited computational power / time.

Is my understanding of provable security correct?

It doesn't appear to be accurate. It appears to be mixing up "provably secure" and "information-theoretically secure".

You can have a system that is provably secure as some problem X, and it could easily be the case that X is easily solved. "Provably secure as X" does not mean "it's unbreakable". It's a relation, not an absolute statement.

And if so, are there any other classical algorithms that are provable secure?

So this question should probably read:

are there any other classical algorithms that are information-theoretically secure?

The standard goals of information security are confidentiality, integrity, and availability.

One Time Pads are for the goal of confidentiality.

One Time Macs are the analogous algorithm that provide information-theoretically secure integrity.

I don't believe there is any such algorithm for availability. It's not clear what information-theoretically secure would even mean in such a context.

For the One Time Pad, I think there is a proof that any encryption algorithm that is information-theoretically secure is equivalent to a One Time Pad, but I can't think of a paper/answer to point to off hand. I think the proof I am thinking of is that any information-theoretically secure encryption algorithm requires a key that is at least as large as the plaintext.