GAPP: Generic Aggregation of Polynomial Protocols

We propose a generic framework called GAPP for aggregation of polynomial protocols. This allows proving n instances of a polynomial protocol using a single aggregate proof that has O(log n) size, and can be verified using O(log2 n) operations. The satisfiability of several univariate polynomial identities over a domain is reduced to the satisfiability of a single bivariate polynomial identity over a related domain, where the bivariate polynomials interpolate a batch of univariate polynomials over the domain. We construct an information-theoretic protocol for proving the satisfiability of the bivariate polynomial identity, which is then compiled using any bivariate polynomial commitment scheme (PCS) to yield an argument of knowledge for the aggregation relation. GAPP can be applied to several popular SNARKs over bilinear groups that are modeled as polynomial protocols in a black-box way. We present a new bivariate polynomial commitment scheme, bPCLB, with succinct verification that yields an efficient instantiation of GAPP. Towards this, we show a new folding technique that we call Lagrangian folding. The bivariate PCS bPCLB and the Lagrangian folding scheme are of independent interest. We implement bPCLB and experimentally validate the practical efficiency of our GAPP instantiation. For the popular PLONK proof system, we achieve 25-30% faster proof generation than the na ̈ıve baseline of generating n separate PLONK proofs. Compared to all existing aggregation schemes that incur additional prover overheads on top of the baseline, we achieve significantly more efficient proving, while retaining succinct verification. We demonstrate the versatility of our proposed GAPP framework by out- lining applications of practical interest: tuple lookups that significantly outperform existing lookup arguments in terms of prover overheads; and proofs for non-uniform computation with “à la carte” prover cost.