Enhancing Ethereum's Security with LUMEN, Novel Zero -Knowledge Algorithms Generating Transparent and Efficient SNARKs Based on Hidden Order Groups

Overview

Zero-knowledge rollups (ZKR), the best scalability solution for the cryptocurrency Ethereum, 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. These zk-SNARKs rely on a trusted setup procedure, where a group of participants uses secret information about transactions to generate public information used by zk -SNARKs. However, this process 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, we developed LUMEN, a novel set of algorith ms 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, a new amortization strategy, and auxiliary polynomials. Mathematical proofs were written to show LUMEN's completeness, soundness, and zero -knowledge, and we impl emented 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. LUMEN is a promising solution to improve Ethereum's security while maintaining its efficiency and can significantly benefit the Ethereum market worth of 308 billion USD. ANOMaLY: A Real-time Globalized System for Effective Regional Mitigation of Agricultural Nitrous Oxide Emissions Nikhil Vemuri North Carolina School of Science and Mathematics, Durham, NC Nitrous oxide (N 2O) is one of the largest contributors to the greenhouse effect (265x more greenhouse forcing than CO 2) and is the largest contributor to ozone depletion in the 21st century. Over 70% of anthropogenic N2O is emitted directly from agriculture and soil management, and previous studies have observed that these emissions spike in localized spatiotemporal events. The system developed in this project identifies these events in real -time across the globe, allowi ng for fast and effective mitigation measures to be put in place to quickly reduce total emissions. Sentinel-2 imagery was correlated with soil chemical data gathered by the author from 7 farms across North Carolina over 6 months (1200+ samples taken) and used to extract novel spectral indices that approximate soil NH 4+ and NO3- (R2 = 0.53, 0.46). Existing data was paired with soil chemical data using the new spectral indices and was used to build an informed model that integrated partial differential equations modeling microbial nitrogen kinetics into a neural network architecture. This informed model explained ~80% of variation in regional N 2O a large improvement over previous models explaining only ~30% of variation. Due to this system using real -time satellite and climate data, localization of regional -scale flux hotspots can be achieved at nearly any place and time on Earth. At maximum capa city, this system can localize over 55% of total anthropogenic N 2O emissions and is generalizable to various agricultural gas -based pollutants. Additionally, the world’s first spatiotemporally linked soil nitrate and ammonium dataset was developed for this project.