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A distinguisher describes an adversary's advantage. In cryptography, an adversary's advantage is a measure of how successfully it can attack a cryptographic algorithm, by distinguishing it from an idealized version of that type of algorithm.
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Ciphertext indistinguishability (IND-CPA) for symmetric cryptography
First off, your definition is not IND-CPA: In the IND-CPA setting, the adversary has access to an encryption oracle. As you have already determined, no deterministic encryption scheme can be IND-CPA s …