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One could split both secrets into smaller parts, commit to parts and "gradually" open that commitments to each other, so that no party is better than (ahead of the other) one such part. For example, let secret be a big number split into bits. With an additively homomorphic bit commitment scheme, the other party could verify that bit commitments correspond ...


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That can be done if and only if oblivious transfer can be done. (In that case, one could do it with a protocol that securely solves the Socialist Millionaire Problem, rather than the protocol given on wikipedia.) It would be difficult to remove the "this can be detected by the other party" allowance, since the restriction of the desired functionality to ...



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