LUMEN's Efficiency

This shows an example run of LUMEN and its efficiency in computation time, verification time, and proof size ran 100 times under the parameters of alpha = 512, d = 16, p = 64. LUMEN is a novel set of algorithms generating efficient and transparent zk-SNARKs: LUMEN consists of 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. Mathematical proofs were written to show LUMEN's completeness, soundness, and zero-knowledge, and we implemented LUMEN in Python and Rust. LUMEN's efficiency, measured in proof size, surpasses DARK and zk-STARK (two of the most efficient transparent zk-SNARKs) by 8 and 37 times, respectively, and LUMEN is only 2 times less efficient than Plonk, the most commonly used non-transparent zk-SNARKs. This dataset shows an example run of how LUMEN's efficiency was obtained.