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Aumann and Lindell defined security against covert attacks, where the adversary is malicious, but is only caught cheating with a certain probability, where the idea is that in many real-world cases, a large probability of being caught is sufficient to prevent the adversary from trying to cheat. In this paper, the authors show how to compile a passively secure protocol for honest majority into one that is secure against covert attacks, again for honest majority and catches cheating with probability 1/4. The cost of the modified protocol is essentially twice that of the original plus an overhead that only depends on the number of inputs.
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