Paper 2024/1671

Multi-party Setup Ceremony for Generating Multivariate zk-SNARK Parameters

Abstract

The development of succinct non-interactive arguments of knowledge (SNARKs), which maintain a constant proof size regardless of computational complexity, has led to substantial improvements in both the scalability and privacy of verifiable computations. By enabling efficient verification of complex computations without revealing sensitive data, SNARK systems underpin modern applications ranging from privacy-focused protocols to high-performance blockchain infrastructures. This work presents a generalised specification for a Multi-Party Computation (MPC) setup ceremony designed to generate structured reference strings for non-transparent, pairing-based zk-SNARKs. Building on the MMORPG framework of Bowe, Gabizon, and Miers, we design a unified MPC protocol that accommodates multi-dimensional parameter structures required by contemporary SNARK designs. While our methodology is applicable to a broad class of structured CRS constructions, the Tokamak zk-SNARK serves as a motivating example illustrating the need for such a generalisation. The proposed ceremony supports universal and circuit-specific parameter generation, enabling reuse of CRS components across multiple instantiations while maintaining strong soundness guarantees under the presence of at least one honest participant. The protocol operates in two phases: (i) a universal ``Powers of "tau''-style phase generating parameter sets independent of circuit topology; and (ii) a circuit-specialised phase derived from a subcircuit-based universal circuit paradigm. For both phases, we formalise complete computation and verification procedures, including proof-of-knowledge mechanisms, cross-parameter consistency checks, and structured multivariate parameter updates. Optional integration of a random beacon---as in the MMORPG construction---is supported to enhance unpredictability and public auditability without altering the core security assumptions. Overall, this work provides a modular, extensible, and publicly verifiable MPC framework suitable for SNARK systems requiring structured, multi-parameter CRS generation, while Tokamak serves as a practical motivating instance of the broader methodology.

Note: Updated version