Recent advancements in blockchain technology have heightened interest in enabling information transfer and value exchange across different blockchains. To tackle asset and data interoperability challenges, cross-chain technology has emerged, though it often risks transaction privacy leakage. This paper presents a relay chain-based cross-chain model that facilitates operations through the relay chain while storing generated information on-chain, ensuring traceability. A privacy protection scheme and a verifiable multi-node key-sharing method are proposed, employing cryptographic techniques to safeguard transaction privacy. In case of disputes, privacy information can be decrypted via the relay chain for auditability. The paper includes a detailed analysis and performance testing of the proposed solution, comparing it with other existing privacy-preserving relay chain solutions, and evaluates the delay performance of the key-sharing algorithm, showcasing its security and feasibility advantages.