Unless you're dealing with OTPs, hashing, or lattice-based schemes, there are almost no information theoretical guarantees in encryption. For a field that uses math so heavily, it's surprising how rare traditional proofs are in the cryptology literature. Most encryption schemes are specifically designed to be hard to analyze.
This isn't for lack of trying on the part of cryptographers - unconditional proofs of security for most modern cryptosystems would imply that P and NP are separate. For example, a direct proof that SHA-256 is collision-resistant would imply that one-way functions exist unconditionally.
