Three Round Non-Malleable Commitment from Non-Malleable Codes
We present a new non-malleable commitment protocol. Our protocol has the following features:
Our techniques depart significantly from the techniques used previously to construct non-malleable commitment schemes. As a main technical tool, we rely on non-malleable codes in the split state model. Our proofs of security are combinatorial.
- The protocol has only three rounds of interaction. Pass (TCC 2013) showed an impossibility result for a two-round non-malleable commitment scheme w.r.t. a black-box reduction to any "standard" intractability reduction. Thus, this resolves the round complexity of non-malleable commitment at least w.r.t. black-box security reductions. Our construction is secure as per the standard notion of non-malleability w.r.t. commitment.
Our protocol is truly efficient. In our basic protocol, the entire computation of the committer is dominated by just three invocations of a non-interactive statically binding commitment scheme, while, the receiver computation (in the commitment stage) is limited to just sampling a random string. Unlike many previous works, we directly construct a protocol for large tags and hence avoid any non-malleability amplification steps.
- Our protocol is based on a black-box use of any non-interactive statistically binding commitment scheme. Such schemes, in turn, can be based on any one-to-one one-way function (or any one-way function at the cost of an extra initialization round). Previously, the best known black-box construction of non-malleable commitments required a larger (constant) number of rounds.
- Our construction is public-coin and makes use of only black-box simulation. Prior to our work, no public-coin constant round non-malleable commitment schemes were known based on black-box simulation.