ECLIPSE: Enhanced Compiling Method for Pedersen-Committed zkSNARK Engines

We advance the state-of-the art for zero-knowledge commitand-prove SNARKs (CP-SNARKs). CP-SNARKs are an important class of SNARKs which, using commitments as "glue" , allow to efficiently combine proof systems-e.g., general-purpose SNARKs (an efficient way to prove statements about circuits) and Sigma-protocols (an efficient way to prove statements about group operations). Thus, CP-SNARKs allow to efficiently provide zero-knowledge proofs for composite statements such as h = H(g(x)) for some hash-function H. Our main contribution is providing the first construction of CP-SNARKs where the proof size is succinct in the number of commitments. We achieve our result by providing a general technique to compile Algebraic Holographic Proofs (AHP) (an underlying abstraction used in many modern SNARKs) with special "decomposition" properties into an efficient CP-SNARK. We then show that some of the most efficient AHP constructions-Marlin, PLONK, and Sonic-satisfy our compilation requirements. Our resulting SNARKs achieve universal and updatable reference strings, which are highly desirable features as they greatly reduce the trust needed in the SNARK setup phase.