Let $C$ be a symmetric cipher $H$ a hash function.
Alice uses $C$ with a key $k$ to encrypt plaintext message $m$ yielding ciphertext $c$. She then calculates the hash of the message $h_m = H(m)$ and the hash of the ciphertext $h_c = H(c)$.
Alice then sends $k$, $h_m$, and $h_c$ to Bob.
Is there any combination of $C$ and $H$ for which Bob can prove -- just from the hashes and the key alone -- that there is indeed some message $m$ for which $h_m = H(m)$ and $h_c = H(C(m,k)$.
Note that Bob does not actually have to discover $m$ and that there can be multiple $m$ that have the same hashes.
In short: find the function $magic$ in this diagram
m --------- H --------> h_m | | C(_, k) magic(_, k) | | V V c ---------- H --------> h_c
where $magic(h_m, k)$ calculates the hash of the ciphertext from the hash of the plaintext (but the other way around would also work).