Scaling Ethereum 2.0’s Cross-Shard Transactions With Efficient Verification and Aggregation of KZG Commitments

Proposals for Ultra-Large-Scale-System (ULSS), particularly the grid’s energy management systems (EMSs), to adopt the Ethereum blockchain are increasing as its support for privacy-preserving, encrypted, decentralized computing via sharding, rollups, Smart-Contracts (SC), and Zero-Knowledge-proofs (ZK) address the increasing topological, behavioral, and data-processing challenges. In this context, the aggregation and verification of aggregated, ZK Kate-Zaverucha-Goldberg constant-sized polynomials commitments (KZG) are a bottleneck limiting deployment to Internet-of-Things (IoT) nodes used by the EMS due to high O(b G+blog2b F) computationincurred when aggregating or verifying by recreation. The alternative, expensive pairing checks involve two pairings, three exponentiations (Exp), three multiplications (Mul), and one addition (Add), a security factor S times for the n aggregated KZG. The proposed pairing checks significantly reduce costs for both: 1) Verifiers: two pairings, no Exp, one Mul, and one Add, and 2) Provers: one pairing check, no Exp, four Mul, and one Add. The aggregation method, based on multidimensional differential addition chains, costs only O(ℓ) computation, where ℓ is the bit length of the scalars. This approach demonstrates the feasibility of operating a KZG-centric blockchain with KZG rollups on IoT networks, marking a significant advancement in ULSS.