Proposals for ultralarge-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 (SCs), and zero-knowledge-proofs (ZKs) address the increasing topological, behavioral, and data-processing challenges. In this context, the aggregation and verification of aggregated, ZK Kate-Zaverucha–Goldberg (KZG) constant-sized polynomials commitments are a bottleneck limiting deployment to Internet of Things (IoT) nodes used by the EMS due to high $O(b\;\mathcal {G}+b\log ^{2}b\;\mathcal {F})$ computation incurred 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 $O(\ell)$ computation, where $\ell $ 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.

中文翻译：

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通过有效验证和聚合 KZG 承诺来扩展以太坊 2.0 的跨分片交易


随着以太坊区块链通过分片、汇总、智能合约 (SC) 支持隐私保护、加密、去中心化计算，关于超大规模系统 (ULSS)，特别是电网能源管理系统 (EMS) 采用以太坊区块链的提案越来越多和零知识证明 (ZK) 解决了日益增长的拓扑、行为和数据处理挑战。在这种情况下，由于 $O(b\ ;\mathcal {G}+b\log ^{2}b\;\mathcal {F})$通过重新聚合或验证时产生的计算量。另一种昂贵的配对检查涉及两次配对、三次求幂 (Exp)、三次乘法 (Mul) 和一次加法 (Add)，对于 n 个聚合 KZG 来说安全系数为 S 倍。所提出的配对检查显着降低了两者的成本：1）验证者：两个配对，无 Exp，一个 Mul 和一个 Add，2）证明者：一个配对检查，无 Exp，四个 Mul 和一个 Add。基于多维差分加法链的聚合方法仅花费$O(\ell)$计算，其中$\ell$是标量的位长度。这种方法证明了在物联网网络上通过 KZG 汇总操作以 KZG 为中心的区块链的可行性，标志着 ULSS 的重大进步。