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Two-Round Adaptively Secure MPC from Isogenies, LPN, or CDH
Authors: Navid Alamati, Hart Montgomery, Sikhar Patranabis, Pratik SarkarAbstract:
We present a new framework for building round-optimal (two-round) adaptively secure MPC. We show that a relatively weak notion of OT that we call indistinguishability \ OT \ with \ receiver \ oblivious \ sampleability (r-iOT) is enough to build two-round, adaptively secure MPC against malicious adversaries in the CRS model. We then show how to construct r-iOT from CDH, LPN, or isogeny-based assumptions that can be viewed as group actions (such as CSIDH and CSI-FiSh). This yields the first constructions of two-round adaptively secure MPC against malicious adversaries from CDH, LPN, or isogeny-based assumptions. We further extend our non-isogeny results to the plain model, achieving (to our knowledge) the first construction of two-round adaptively secure MPC against semi-honest adversaries in the plain model from LPN.
Our results allow us to build a two-round adaptively secure MPC against malicious adversaries from essentially all of the well-studied assumptions in cryptography. In addition, our constructions from isogenies or LPN provide the first post-quantum alternatives to LWE-based constructions for round-optimal adaptively secure MPC. Along the way, we show that r-iOT also implies non-committing encryption(NCE), thereby yielding the first constructions of NCE from isogenies or LPN.
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