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Consider we have three parties,namely client $A$, client $B$ and a server. Client $B$ and the server can be malicious, but we do not allow the adversary to simultaneously corrupt the server and client $B$ (similar to [1]). The scenario is that both clients outsource their private data to the server. Then they ask the server to do computation and send back the result and a proof of computation correctness to client B. I have designed a protocol that satisfy the above properties but the malicious server may send an incomplete result. This can be detected by client B but after that if client $B$ proceeds it can learn client $A$'s data (and this is not desirable).

Question: Based on the above security model, is client $B$ allowed to take further action to figure out the other client's data, after it detects the server's malicious behavior?

Edit: TBN: The outsourced data is not leaked to the malicious server.

[1]. http://research.microsoft.com/pubs/194141/sapsi2.pdf

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    $\begingroup$ I would say that under that security model, if you are assuming the server is being malicious, then client B cannot proceed with any malicious action. In other words, that would be equivalent, in the security proof, to an adversary who is corrupting both the server and client B at the same time, which contradicts your initial assumptions. $\endgroup$
    – cygnusv
    Commented May 7, 2015 at 10:45

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$A$ has outsourced it's private data to the server, right? In that case $A$'s private data has already been leaked to the adversary when the server was corrupted. So there is no added leakage in $B$ also learning this data. In fact since only one of $B$ and the server can be corrupted (assuming static corruptions) we can conclude that $B$ is honest, and there is really no problem.

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  • $\begingroup$ "A's private data has already been leaked to the adversary when the server was corrupted" : I would say no, it's protected from the server, thus there's no data leakage to the server. However, I should have mentioned that in the question. $\endgroup$
    – user13676
    Commented May 7, 2015 at 10:55
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    $\begingroup$ Even then there is probably no problem. The argument that $B$ must be honest still holds. So $B$ learning $A$'s data should not be a problem, since what we are trying to do is to protect ourselves from the adversary, not the honest parties. $\endgroup$
    – Guut Boy
    Commented May 7, 2015 at 12:12

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