Using AES in CBC with the same IV for messages

Will encrypting two identical plaintext messages with AES in CBC with the same IV yield the same ciphertext?

From my understanding the first block is XOR'd with the IV, and then each subsequent block with the previous. Does this mean that with the same IV and identical messages that every block will be encrypted to the same thing? I understand using a predictable or non-changing IV for encryption is a very bad thing to do, and I am wondering why - is it because attackers can build up a "book" of known messages, or because we leave the first block vulnerable to frequency c开发者_开发百科hecks?

Thanks

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If you use the same key both times, then yes, you'd get identical output. If you use a different key, then you'd get different output (you XOR the previous block with the current block, but then you encrypt the result to produce a block of ciphertext).

That, however, is generally of little help. One of the basic reasons for using something like CBC is to avoid repetition among messages even if they contain the same data and you continue to use the same key (though of course, it's also useful that it avoids patterns within a single message as well). Changing the IV keeps each message unique (even if some of the plaintext content is predictable) without going to all the work of distributing a new key for every message (which would generally be relatively painful).