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We advance the state-of-the art for zero-knowledge commit-and-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 -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 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 …