###### tags: `Reading sessions`

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# 2022

<https://pkc.iacr.org/2022/acceptedpapers.php/>

## [ECLIPSE: Enhanced Compiling Method for Pedersen-committed zkSNARK Engines](https://eprint.iacr.org/2021/934.pdf)
* 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.

###### tags: `CP-SNARKs` `Composite Statement`