Delayed-Input Non-Malleable Zero Knowledge and Multi-Party Coin Tossing in Four Rounds

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 $\Pi_{nmzk}$ from OWFs; moreover $\Pi_{nmzk}$ is also a delayed-input many-many synchronous NMZK argument. 2) a 4-round MPCT protocol $\Pi_{mpcf}$ from one-to-one OWFs; $\Pi_{mpcf}$ uses $\Pi_{nmzk}$ as subprotocol and exploits the special properties (e.g., delayed input, many-many synchronous) of $\Pi_{nmzk}$. $\Pi_{mpcf}$ makes 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