In this case, the adversary can build a large "dictionary" of useful plaintext/ciphertext pairs, then observe the encrypted channel for matching ciphertexts.
Assuming that a deterministic encryption scheme is going to be used, it is important to understand what is the maximum level of security that can be guaranteed.
Two follow-up works appeared the next year in CRYPTO 2008, giving definitional equivalences and constructions without random oracles.
[5][6] To counter this problem, cryptographers proposed the notion of "randomized" or probabilistic encryption.
Under sufficiently strong security guarantees the attacks proposed above become infeasible, as the adversary will be unable to correlate any two encryptions of the same message, or correlate a message to its ciphertext, even given access to the public encryption key.