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I'll further explain the comment of @CodesInChaos and then give a simple example: Explanation When the correctness requirement is weakened the encryption scheme can omit part of the message $m$ (of length $|m|$) to be encrypted and just "loose" it in a way that the cipher (the output of the Encrypt method) is totally independent of that part. Thus the ...


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I think they are similar but not equivalent. The first condition says that for any ciphertext $c$ all messages $m$ have equal probability to encrypt to $c$. The second says that for any message $m$ all ciphertexts $c$ have equally probability of encrypting $m$. So I think you can demonstrate non-equivalence as follows: Imagine a (somewhat contrived) ...



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