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@fgrieu's answer uses a stateful oracle, which I think is cheating a bit. The problem is impossible with stateless oracles (and perfect correctness). Suppose the encryption algorithm is written as $E^{\mathcal O}(pk,m;r)$ where $\mathcal O$ is any stateless oracle; $pk$ is the public key; $m$ is the plaintext; $r$ is the randomness; $E$ is a deterministic ...


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Yes, it is possible to have perfectly secure public-key cryptography with oracles (though the oracles I'll exhibit do not seem quite reducible to those of the question). As pointed in the question, there can't be a completely public encryption procedure that works (in the sense that decryption is possible with the appropriate secret) and is perfectly secure ...


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What you're saying is unclear... If you have uncountably many possible keys, if the scheme is computationally secure in the normal case (you're using an already-secure algorithm), your algorithm would fit your definition of being perfectly secure - the computation required to break it goes up with the key size, effectively creating an infinite search time ...


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