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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.
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Why does a perfect secrecy can be achieved when decryption correctness is not totally required?
By Shanon theorem, a perfect secrecy encryption scheme must use a key space of equal size as the message space.
But when the correctness requirement is weakened such that $Pr[Dec_k(Enc_k(m))=m]=1/2$ …