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.