Confidentiality in a very strong sense. Ciphers reaching perfect-secrecy can't be broken to disclose informations over the plaintext from the ciphertext, even with unlimited computing power. The most known example cipher reaching perfect screcy is the one-time-pad.
I suspect the answer is no, but I am not able to either prove it, or provide an example. In Katz and Lindell's book, it is only said that with a perfectly secret encryption scheme, the plain and ...