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The authors construct protocols for secure multiparty computation with the help of a computationally powerful party, namely the "Cloud". Their protocols are simultaneously efficient in a number of metrics: rounds, communication and computation. In the semi-honest case, their protocol relies on the "Ring Learning With Errors" (RLWE) assumption, whereas in the malicious case, security is shown under the Ring LWE assumption as well as the existence of simulation-extractable NIZK proof systems and succinct non-interactive arguments. In the malicious setting, they also relax the communication and computation requirements above, and only require that they be "Small" - polylogarithmic in the computation size and linear in the size of the joint size of the inputs.
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