Improving Function-Hiding Functional Commitments

Function-hiding functional commitment schemes allow one party to commit to a private function f and later prove f(x)=y for public x and y without revealing additional information about the function. We construct efficient function-hiding functional commitment schemes for arithmetic circuits of bounded size that achieve proof sizes below 1.6 kB—over an order of magnitude smaller than previous constructions—while simultaneously reducing proving and verification times. We achieve these results by introducing a novel information-theoretic interactive proof system called Polynomial Interactive Oracle Proofs with Randomized Indexer (rPHPs). By compiling rPHPs with commit-and-prove zkSNARKs, we are able to leverage relaxed zero-knowledge notions for our building blocks. This approach eliminates the overhead of strict privacy requirements of prior work, directly translating into improved efficiency in both communication and computation.