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This paper proposes a novel recursive polynomial commitment scheme (PCS) anda new polynomial interactive oracle proof (PIOP) protocol, which compile intoefficient and transparent zk-SNARKs (zero-knowledge succinct non-interactivearguments of knowledge). The Ethereum blockchain utilizes zero-knowledgeRollups (ZKR) to improve its scalability (the ability to handle a large numberof transactions), and ZKR uses zk-SNARKs to validate transactions. Thecurrently used zk-SNARKs rely on a trusted setup ceremony, where a group ofparticipants uses secret information about transactions to generate the publicparameters necessary to verify the zk-SNARKs. This introduces a security riskinto Ethereum's system. Thus, researchers have been developing transparentzk-SNARKs (which do not require a trusted setup), but those are not asefficient as non-transparent zk-SNARKs, so ZKRs do not use them. In thisresearch, I developed LUMEN, a set of novel algorithms that generatetransparent zk-SNARKs that improve Ethereum's security without sacrificing itsefficiency. Various techniques were creatively incorporated into LUMEN,including groups with hidden orders, Lagrange basis polynomials, and anamortization strategy. I wrote mathematical proofs for LUMEN that convey itscompleteness, soundness and zero-knowledgeness, and implemented LUMEN bywriting around $8000$ lines of Rust and Python code, which conveyed thepracticality of LUMEN. Moreover, my implementation revealed the efficiency ofLUMEN (measured in proof size, proof computation time, and verification time),which surpasses the efficiency of existing transparent zk-SNARKs and is on parwith that of non-transparent zk-SNARKs. Therefore, LUMEN is a promisingsolution to improve Ethereum's security while maintaining its efficiency.

Enhancing Ethereum's Security with LUMEN, a Novel Zero-Knowledge Protocol Generating Transparent and Efficient zk-SNARKs