As the blockchain ecosystem evolves from single-chain systems to multi-chain collaboration, decentralized cross-chain identity authentication has become a critical challenge for ensuring system interoperability and privacy protection. Existing identity verification schemes often suffer from identity fragmentation, privacy leakage risks, and insufficient data consistency. To address these issues, we propose zkHARPS, a decentralized method for cross-chain identity aggregation and privacy proof that integrates secure multi-party computation with zero-knowledge proofs. Specifically, we design a novel cross-chain identity aggregation protocol that enables secure global identity computation from distributed fragments via multi-party computation. In addition, we develop HARPS, a recursive hash-based ZKP framework that compactly encodes multi-attribute identity proofs using zkSNARK. Furthermore, to ensure consistent and efficient identity synchronization across heterogeneous blockchains, we design a lightweight cross-chain verification mechanism that leverages event-driven listeners and embedded light clients. The proposed method is implemented and validated on both Hyperledger Fabric and Ganache, and compared with mainstream zero-knowledge proof methods, including Bulletproofs, Scalable zk, and ZK-STARK. Experimental results demonstrate that zkHARPS achieves significant advantages in proof generation time, verification latency, gas cost, storage overhead, and identity aggregation stability, making it well-suited for privacy-preserving applications in complex multi-chain environments.