Enhancing Ethereum's Security with LUMEN: Transparent and Efficient Zk-SNARKs

Overview

The cryptocurrency Ethereum currently utilizes zero-knowledge rollups (ZKR) to improve its scalability. ZKRs processes thousands of Ethereum transactions in a batch and uses zk-SNARKs (zero-knowledge succinct non-interactive arguments of knowledge) to verify the validity of those transactions. zk-SNARKs rely on a trusted setup ceremony, where a group of participants uses secret information about transactions to generate public information used by zk-SNARKs. However, This introduces a security risk to Ethereum. Thus, researchers have been developing transparent zk-SNARKs that do not require a trusted setup. However, those transparent zk-SNARKs are often not as efficient as non-transparent zk-SNARKs. In this research, I developed LUMEN, a novel set of algorithms that includes a recursive polynomial commitment scheme and a new interactive polynomial oracle proof protocol, which is compiled into efficient and transparent zk-SNARKs with linear proof computation and verification time. Various techniques were creatively incorporated into LUMEN, including groups with hidden orders, Lagrange basis polynomials, and an amortization strategy. I wrote mathematical proofs for LUMEN that convey its completeness, soundness, and zero knowledge, and I implemented LUMEN by writing 8000 lines of Python and Rust code, which conveyed the practicality of LUMEN. LUMEN's efficiency, measured in proof size, is 1.22 kilobytes and surpasses DARK and zk-STARK (two of the most efficient transparent zk-SNARKs) by 8 and 37 times, respectively, and LUMEN is on par with the efficiency of non-transparent zk-SNARKs. LUMEN is a promising solution to improve Ethereum's security without sacrificing its efficiency.