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Paper: Updatable and Universal Common Reference Strings with Applications to zk-SNARKs

Authors:
Jens Groth
Markulf Kohlweiss
Mary Maller
Sarah Meiklejohn
Ian Miers
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DOI: 10.1007/978-3-319-96878-0_24
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Conference: CRYPTO 2018
Abstract: By design, existing (pre-processing) zk-SNARKs embed a secret trapdoor in a relation-dependent common reference strings (CRS). The trapdoor is exploited by a (hypothetical) simulator to prove the scheme is zero knowledge, and the secret-dependent structure facilitates a linear-size CRS and linear-time prover computation. If known by a real party, however, the trapdoor can be used to subvert the security of the system. The structured CRS that makes zk-SNARKs practical also makes deploying zk-SNARKS problematic, as it is difficult to argue why the trapdoor would not be available to the entity responsible for generating the CRS. Moreover, for pre-processing zk-SNARKs a new trusted CRS needs to be computed every time the relation is changed.In this paper, we address both issues by proposing a model where a number of users can update a universal CRS. The updatable CRS model guarantees security if at least one of the users updating the CRS is honest. We provide both a negative result, by showing that zk-SNARKs with private secret-dependent polynomials in the CRS cannot be updatable, and a positive result by constructing a zk-SNARK based on a CRS consisting only of secret-dependent monomials. The CRS is of quadratic size, is updatable, and is universal in the sense that it can be specialized into one or more relation-dependent CRS of linear size with linear-time prover computation.
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BibTeX
@inproceedings{crypto-2018-28804,
  title={Updatable and Universal Common Reference Strings with Applications to zk-SNARKs},
  booktitle={Advances in Cryptology – CRYPTO 2018},
  series={Lecture Notes in Computer Science},
  publisher={Springer},
  volume={10993},
  pages={698-728},
  doi={10.1007/978-3-319-96878-0_24},
  author={Jens Groth and Markulf Kohlweiss and Mary Maller and Sarah Meiklejohn and Ian Miers},
  year=2018
}