Repeatedly encrypting the same message to the same ciphertext is
full of practical attacks. Encryption is supposed to leak no
information about the content of the message other than its
length, and there are very real ways to exploit the information
leakage you mention. Some of them have to do with the fact that
plaintext domains are not always very large. Others have to do
with the fact that an attacker who can perform a chosen
plaintext attack (CPA) gets to learn a lot about the ciphertext.
Here are some attacks, assuming that we use a CBC-like
encryption scheme that is deterministic (and thus not
semantically secure): If the attacker sees the encryption of
message A, then later learns message A, he can then know the
contents of message A whenever it was sent in the past or the
future. That's a very real threat if the total messages that
could be sent are reasonably small. - Example: Consider an army
that coordinates movement by sending instructions to each other
on who is to move where. The attacker might