SudoZKu: implementation and evaluation of the Groth16 zk-SNARK protocol

Abstract

This project explores the Groth16 zero-knowledge succinct non-interactive argument of knowledge (zk-SNARK) protocol, with an emphasis on accessibility and practical understanding. It begins with a review of zero-knowledge proofs, non-interactive zero-knowledge proofs, and zk-SNARKs, followed by a structured explanation of the Groth16 construction, from Rank-1 Constraint System (R1CS) and Quadratic Arithmetic Program (QAP) representations, to the full formulation incorporating trapdoor elements and zero-knowledge randomness that is supported with a working Python implementation over the BN254 elliptic curve. These theoretical concepts are then applied in SudoZKu, a browser-based Sudoku game that demonstrates a complete end-to-end zk-SNARK real-world implementation pipeline. This system uses Circom for circuit design and snarkjs for Groth16 proof generation and verification, illustrating how high-level computations can be translated into succinct, verifiable proofs within a practical setting. Experimental evaluation then compares Groth16 and another zk-SNARK known as Permutations over Lagrange-bases for Oecumenical Non-interactive arguments of Knowledge (PLONK). Results show that Groth16 achieves approximately 1.9x smaller proofs and up to 16x faster proof generation than PLONK, while both are able to complete verification under 65 milliseconds. The project then concludes by analysing the key trade-offs for Groth16, including trusted setup requirements and a lack of post-quantum security, and outlines future research directions such as on-chain verification and privacy-preserving uses of Groth16.