Cryptography elements needed for a story Note: following Maarten Bodewes's answer, I edited this post to make it clearer.
I'm writing something partly driven by the need to crack a few encrypted files.
This is what needs to happen in the story:
There are two parties involved that are trying to crack them, party A and party B. Party A has had them for four years, and despite all attempts, they failed. Party B got the files later on and managed to crack them in less than two months of non-stop trying.
Party A has available state-of the-art tech, but party B are the good guys and this is a sci-fi story, so they have far, far better tech that nobody else has. The details of the technology aren't relevant to the story so I don't need to establish them.
Party B will eventually succeed; still, to keep a modicum of suspense up, it must still be possible for them to fail. By this I don't mean that something throws a spanner in their works; I mean that their decryption attempt, however more advanced than party B's, isn't guaranteed to work. In other words, party B can't just sit and wait until whatever they're doing is done knowing that at that point they will have the decrypted file.
This is what I need:

An algorithm such that, if you encrypt a file with it using a high-entropy password, is beyond any brute-force attempts using known methods and tech. (This is why party A fails.) I understand that AES-256 might be what I'm looking for.
An approach that will allow party B to succeed nonetheless. The fact that party B has much faster computers available than anyone on Earth is central to the story so you can assume that. However, if brute-forcing these files required ridiculous amounts of energy or other very unrealistic things, I'm not prepared to claim party B has any of that. Other approaches or situations that would give party B an edge—such knowing what algorithm was used, being able to guess details about the password, or knowing about possible key files—are certainly options I would consider. If quantum computers could plausibly break AES, that's another option I would consider because it's not too far-fetched for party B to have them. I just don't know if QC could actually do that.
Though quantum computers fit the requirements, I'm not sure they are the best option. A general purpose quantum computer capable of attacking modern encryption (RSA, AES) would have serious ramifications on society. It's not only applicable to this one cipher you are breaking.
Does it have to be the superior computing resources which gives the good guys the edge? Because I can think of several plausible storylines where the edge comes from a bright idea.
Option 1: Information about the passphrase.
If the good guys learn something about how the passphrase used to derive the encryption key was chosen they could easily reduce the search space time from millennia to months. For example the passwords are always lines from a book where some of the words are replaced with the first letter. Or something else. One way to learn such a pattern is they crack some other password picked by the same person which was encrypted with weaker encryption. The hero recognizes the pattern in this other password hypothesizes it may be a common method of selecting passwords and starts a brute force dictionary attack on the reduced space.
Option 2: General Cryptanalytic improvement.
Our hero is a master cryptographer. And uses an unknown but plausible cryptanalytic attack on AES to greatly improve speed. This attack could have greatly reduced runtime and it could work on only a fraction of the keys. It could be discovered that a sizeable fraction of keys have some undesired property which makes a superior attack possible (which still requires great computational resources) and they are unsure if the key happens to be such a weak key, they are likely to be able to quantify their success probability in advance.
Option 3: Identifying a flaw in how the data was encrypted
Whoever encrypted the data may have messed up. And accidentally left an easier route to attack it. It could be something like applying error correction after compression before encryption (the flaw in GSM). Or something which more directly leads to an attack like keeping a simple hash of the password. The heroes find this flaw and launch a more efficient brute force based on it.
Option 4: Attack the message not the key
Out heroes don't try to crack the encryption at all. They utilize knowledge of message and compression system used. and find what possible messages would result in desired size. Though if it's only size it's only viable if we had a small collection of possible messages and the attack will be quick. There are attacks on voice for example where we use size and timing to decipher words and phrases without breaking the encryption.