Proof that a hash matches an encrypted file
If you use a one-time pad as your encryption function then this simplifies to a proof that Alice knows some $F$ that hashes to $H$. $K$ can be trivially derived from $F$ and $E(K, F)$ by xor-ing.

An interactive zero-knowledge proof of this simpler problem - Alice proving she knows a pre-image of $H(F)$ - would go something like this:

You need to use a partially homomorphic hash such that $H(A+B) = H(A) \oplus H(B)$ for some composition operation on each domain. An example might be to add/xor the pre-images and use scalar multiplication of an elliptic curve base point as your hashing function - though note for an arbitrary length message this is going to be magnitudes slower than a traditional cryptographic hash function.

In a single trial in the proof Alice generates a one-time pad - $P$ - and commits to $H(P)$. Bob calculates $H(F+P) = H(F) \oplus H(P)$. He can challenge Alice to reveal either $P$ or $F+P$. Each trial halves the probability that Alice is cheating.

You can turn this into a non-interactive proof by Fiat-Shamir. It's not very succinct however, the proof ends up being many times longer than $F$.

I guess with a homomorphic DRBG you could extend the proof to show that Alice knows a stream cipher key $K$ that defines the tranformation $F \rightarrow E(K, F)$. This would improve the succinctness of the proof as well as being a closer match for what you asked for.