Ben Fisch (Stanford University)
We construct a new interactive polynomial commitment scheme using groups of unknown order. The interactive evaluation argument is public-coin and has logarithmic communication in the degree of the polynomial. The scheme does not require a trusted setup if instantiated with class groups. We apply this as a cryptographic compiler to polynomial IOPs in order to obtain preprocessing public-coin interactive arguments of knowledge with succinct online communication (without trusted setup). Instantiated with the IOP from Sonic (Maller et al, CCS 2019), the argument has logarithmic online communication/verification, quasi-linear prover time and preprocessing.
More generally, we provide a compiler for algebraic linear IOPs, such as one based on QAPs, but with less practical prover time (i.e. quadratic).