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We study efficiency tradeoffs for secure two-party computation in presence of malicious behavior. We investigate two main approaches for defending against malicious behavior in \emph{Yao's garbled circuit} method: (1) \emph{Committed-input} scheme, (2) \emph{Equality-checker} scheme. We provide asymptotic and concrete analysis of communication and computation costs of the designed protocols. We also develop a weaker definition of security (\emph{k-leaked model}) for malicious two-party computation that allows for disclosure of some information to a malicious party. We design more efficient variations of \emph{Yao's} protocol that are secure in the proposed model.
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