2022

ECLIPSE: Enhanced Compiling Method for Pedersen-committed zkSNARK Engines

By Diego F. Aranha, Emil Madsen Bennedsen, Matteo Campanelli, Chaya Ganesh, Claudio Orlandi, Akira Takahashi
Background:
- Commit-and-prove SNARKs (CP-SNARKs), an important class of SNARKs, allow to efficiently combine different proof systems, e.g., general-purpose SNARKs for circuits and \(\Sigma\)-protocols for algebraic relations, where the statement to be proved is called composite statement.
Contributions:
- This paper advanced the state-of-the-art CP-SNARKs, and design the first construction of CP-SNARKs where the proof size is logarithmic in the number of commitments.
- This paper provided a compiler to compile Algebraic Holographic Proofs (AHP) (an underlying abstraction used in many modern SNARKs) with special “decomposition” properties into an efficient CP-SNARK.
- This paper gave three instantiations of their compiler, using the most efficient AHP constructions—Marlin, Plonk, and Sonic. The resulting CP-SNARKs achieve universal and updatable reference strings, instead of trusted ones.
Drawbacks:
- The verifier complexity is still linear in the number of commitments.
- All instantiations need "linking" protocols to prove the consistency among openings of different commitment schemes, which results in extra cost.
- The resulting CP-SNARKs don't support circuits with high-degree custom gates, which are more desirable in industry.