The transition from isolated distributed ledgers to a unified “Internet of Value” is hindered by the lack of efficient, verifiable, and privacy-preserving cross-chain data retrieval mechanisms. While asset bridging has matured, generalized data indexing remains a critical bottleneck, constrained by the semantic gap between heterogeneous storage layouts and the prohibitive verification tax of cryptographic proofs. In this paper, we present HyperCross, a novel semantic-aware zero-knowledge indexing framework designed to bridge this divide. We first formalize the heterogeneous cross-chain storage optimization problem (HCCSOP) and prove its NP-completeness. To tackle this, HyperCross employs a synergistic tri-layered architecture. At the semantic layer, we introduce a unified data abstraction (UDA) that leverages category-theoretic functors and schema morphisms to ensure mathematically rigorous state mapping for both simple assets and complex smart contract logic. At the indexing layer, a zero-knowledge learning index (ZKLI) shifts prediction intelligence to the client side, integrating zk-SNARKs with silent oblivious transfer to achieve constant-time verification (O(1)) while concealing access patterns. Finally, a multi-level cache (MLC) utilizes predictive prefetching with Δ-bounded staleness to mask network latency. Extensive evaluations demonstrate that HyperCross reduces query latency by 2.4× and storage overhead by 40% compared to state-of-the-art baselines, establishing a scalable foundation for data-intensive inter-chain applications.
Hao et al. (Mon,) studied this question.