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For semi honest MPC protocols, adding some errors can easily make the output wrong. I wonder beyond that, can malicious adversaries make some attacks against semi-honest protocols to obtain private inputs or some other private data? And if they can, how to do that?

I wish to get some answers or literature about this question.

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Suppose you give me a protocol $\Pi$, then I will use it to construct a new protocol $\Pi'$:

$\Pi'$:

  • Initially every party $P_i$ chooses a random string $r_i \gets \{0,1\}^\lambda$ and broadcasts it to all other parties.
  • Then, the parties run the $\Pi$ protocol normally, with one exception:

    If party $P_i$ ever receives a message of the form $(r_i,z)$ from party $P_j$, then $P_i$ will send all of its private inputs to $P_j$, and also immediately output $z$.

I will leave the following two observations as exercises for the curious reader:

  1. If $\Pi$ is secure against semi-honest adversaries, then so is $\Pi'$. Hint: there is negligible probability that a semi-honest execution of $\Pi$ would include a protocol message of the form $(r_i,z)$.

  2. In the presence of a malicious adversary, $\Pi'$ is maximally insecure (if there is such a thing). The adversary can learn every honest party's private input, and can force any honest party to output anything of the adversary's choice.

So, a protocol can be secure against semi-honest adversaries and totally insecure against malicious adversaries. This doesn't mean that every semi-honest protocol is insecure against malicious adversaries. But it shows that the definition of semi-honest security itself is not enough to give you any guarantees about what can happen in the presence of malicious adversaries.

I refer to protocols like $\Pi'$ as protocols with a "wings-fall-off button", after Gary Larson's Far Side cartoon:

Far Side cartoon with an airplane that has a switch labeled "Wings stay on / wings fall off"

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    $\begingroup$ It can be interesting to note that some natural protocols also have a similar extreme failure mode in the malicious setting. For example, this is the case for the seminal construction of semi-honest OT from trapdoor permutations: a cheating receiver can trivially get both sender outputs by picking two values with known preimages instead of one (and this is undetectable). $\endgroup$ Feb 7, 2023 at 9:32

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