We compare the relative strengths of popular notions of security for public key encryption schemes. We consider the goals of privacy and non-malleability, each under chosen-plaintext attack and two kinds of chosen-ciphertext attack. For each of the resulting pairs of definitions we prove either an implication (every scheme meeting one notion must meet the other) or a separation (there is a scheme meeting one notion but not the other, assuming the first notion can be met at all). We similarly treat plaintext awareness, a notion of security in the random oracle model. An additional contribution of this paper is a new definition of non-malleability which we believe is simpler than the previous one.
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