Cryptology ePrint Archive: Report 2018/280

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

Jens Groth and Markulf Kohlweiss and Mary Maller and Sarah Meiklejohn and Ian Miers

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.

Category / Keywords: public-key cryptography / zero-knowledge, common reference strings, subvertability, zk-SNARKs

Original Publication (with minor differences): IACR-CRYPTO-2018

Date: received 22 Mar 2018, last revised 22 Jun 2018

Contact author: mkohlwei at ed ac uk

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Version: 20180622:091705 (All versions of this report)

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