How would one crack a weak but unknown encryption protocol? I asked a question on security.stackexchange, but was told it would be a better fit here:

https://security.stackexchange.com/questions/32779/how-would-one-crack-a-weak-but-unknown-encryption-protocol

My question is: Assume I'm an attacker trying to break a weak-but-unknown encryption algorithm. i.e., someone not too bright made a home-brew encryption algorithm, and I'm trying to break it.

BIG FAT DISCLAIMER: Using home-brew security algorithms is very bad for many reasons. Everybody in the security community agrees about it. It's very hard to keep algorithms secret. Please don't answer this question explaining why it's a bad idea to use a home-brew algorithm. I know it's bad. Assume the algorithm is completely unknown.

Okay, now back to my question.

How would you approach a completely mysterious ciphertext when you have no idea what algorithm was used to make it? For me it would look like a meaningless stream of hex, but I'm very curious to know if there's a method to analyze such data and try to break the code.

Here's an example of such a ciphertext.

Is there a way to break it using a single ciphertext? If that's very difficult, I'll be happy to learn how to do it from multiple ciphertexts. I can create more ciphertexts using the same home-brew algorithm, if someone here thinks he can use that to figure out the algorithm.
It depends on what information you have. If all you have is that one ciphertext and no way of acquiring more, there's not much you can do.

If you have multiple ciphertexts, you can try to observe any patterns in them. If you have the corresponding plaintexts, you can really start to make some useful observations. If you have some plaintext, ciphertext pairs, you can try to find patterns in the data.

An even stronger attack would having access to the encryption oracle. That is, being able to encrypt plaintexts of your choosing. Here you could try special encryption strings to see if they leak any information about the algorithm. You can try things like "a", "aaaaaaa", or string of null bytes and see what information you can extract about the algorithm.

If the encryption algorithm is insecure, your goal should be to figure out what the algorithm does. Once you know how the algorithm works, you can presumably figure out a way to break ciphertexts or get the key.