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That at least does not contradict "the definition of PAKE that supports" sets $PW$ which are known, since the adversary can just try an element of $PW\hspace{-0.03 in}$. ​ However, that does not give meaningful assurance against, for example adversaries who have information which uniquely determines the password without letting the adversary find the ...


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A cryptosystem is not "based on an assumption" ; it is based on some mathematical structure (e.g. prime order elliptic curves, or prime order fields). Informally, a cryptosystem is said IND-CCA secure (which means: it satisfies the indistinguishability security notion, against adversaries which are given access to a decryption oracle) under some assumption A ...


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In short, the operations may be different, but they do not must be. For instance, in the scheme presented on the pages 6 and 7 of this paper the homomorphic addition is simply a addition, but the homomorphic multiplication is a complex operation involving auxiliary functions and operations... About your question: Can somebody clear up which one is ...


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The operation does not have to be the same. For example, with Paillier, we multiply ciphertexts to get the addition of the plaintexts. That said, I think what the 2nd quotation is saying is that the operation that is passed to the oracle is the desired operation in the plaintext domain. The oracle knows how to translate that operation into something that, ...


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Sure. Parties: ​ more than 1 Input: ​ each party has a secret input Output: ​ empty string "Protocol": ​ Each party broadcasts their secret input then outputs the empty string. That is robust for arbitrary thresholds, but is not private against even a single semi-honest adversary.



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