Are there public key schemes that have perfect secrecy? The perfect secrecy notion is defined for symmetric key encryption. If P is a message and C the corresponding ciphertext then the cipher has perfect secrecy if pr(P|C)=pr(P). This equivalently means in terms of entropy that the conditional entropy H(P|C)=H(P). Originally as defined in Shannon's paper the encryption system is not classified as block or stream cipher. In practice it has to be one of the two and the message length is a priori fixed to a maximum. Hence for a public key scheme with the message length fixed perfect secrecy is still meaningful when probability distribution of the maximum length message is considered. In general H(P|C)< H(P). Since all public key schemes are secured in computational sense H(P|C)=0 which means an infinitely powerful adversary can always break the encryption. Can a perfectly secure public key scheme be defined? If there is one which scheme is it?
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