Abstract
We give the first construction of three-round non-malleable commitments from the almost minimal assumption of injective one-way functions. Combined with the lower bound of Pass (TCC 2013), our result is almost the best possible w.r.t. standard polynomial-time hardness assumptions (at least w.r.t. black-box reductions). Our results rely on a novel technique which we call 'bidirectional Goldreich-Levin extraction'. Along the way, we also obtain the first rewind secure delayed-input witness indistinguishable (WI) proofs from only injective one-way functions. We also obtain the first construction of an epsilon-extractable commitment scheme from injective one-way functions. We believe both of these to be of independent interest. In particular, as a direct corollary of our rewind secure WI construction, we are able to obtain a construction of 3-round promise zero-knowledge from only injective one-way functions.
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