I have some base-64 encoded encrypted data and noticed a fair amount of repetition. In a (approx) 200-character-long string, a certain base-64 character is repeated up to 7 times in several separate repeated runs.
Is this a red flag that there is a problem in the encryption? According to my understanding, encrypted data should never show significant repetition, even if the plaintext is entirely uniform (i.e. even if I encrypt 2 GB of nothing but the letter A, there should be no significant repetition in the encrypted version).
According to the binomial distribution, there is about a 2.5% chance that you'd see one character from a set of 64 appear seven times in a series of 200 random characters. That's a small chance, but not negligible. With more information, you might raise your confidence from 97.5% to something very close to 100% … or find that the cipher text really is uniformly distributed.
You say that the "character is repeated up to 7 times" in several separate repeated runs. That's not enough information to say whether the cipher text has a bias. Instead, tell us the total number of times the character appeared, and the total number of cipher text characters. For example, "it appeared a total of 3125 times in 1000 runs of 200 characters each."
Also, you need to be sure that you are talking about the raw output of a cipher. Cipher text is often encapsulated in an "envelope" like that defined by the Cryptographic Message Syntax. Of course, this enclosing structure will have predictable patterns.