In this work we start from the following two results in the state-of-the art: 1.4-round non-malleable zero knowledge (NMZK): Goyal et al. in FOCS 2014 showed the first 4-round one-one NMZK argument from one-way functions (OWFs). Their construction requires the prover to know the instance and the witness already at the 2nd round.2.4-round multi-party coin tossing (MPCT): Garg et al. in Eurocrypt 2016 showed the first 4-round protocol for MPCT. Their result crucially relies on 3-round 3-robust parallel non-malleable commitments. So far there is no candidate construction for such a commitment scheme under standard polynomial-time hardness assumptions. We improve the state-of-the art on NMZK and MPCT by presenting the following two results: 1.a delayed-input 4-round one-many NMZK argument IINMZKfrom OWFs; moreover IINMZKis also a delayed-input many-many synchronous NMZK argument.2.a 4-round MPCT protocol IIMPCTfrom one-to-one OWFs; IIMPCTuses IINMZKas subprotocol and exploits the special properties (e.g., delayed input, many-many synchronous) of IINMZK. Both IINMZKand IIMPCTmake use of a special proof of knowledge that offers additional security guarantees when played in parallel with other protocols. The new technique behind such a proof of knowledge is an additional contribution of this work and is of independent interest.
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