With the ecological conversion from single-chain collaboration to multi-chain expansion in blockchain， cross-chain technology becomes key path for driving application innovation and enhancing system capabilities. However， the absence of a unified identity authentication scheme in distributed ledgers with multi-chain architecture may pose potential privacy risks during asset cross-chain transactions. In response， a privacy-preserving random consensus asset cross-chain scheme was proposed. In the proposed scheme， the Random Notary Multiple Signature （RNMS） architecture-based cross-chain model was introduced， and secure negotiation of shared keys by the two parties of transaction was insured through the Elliptic Curve Diffie-Hellman （ECDH） key negotiation algorithm. Furthermore， considering the intermediate trust problem， an algorithm for random notary selection based on enhanced Algorand approach was designed. In this algorithm， the roulette-style labeling method for random notary selection was improved to a verifiable pseudo-random method， thereby reducing the risks associated with pseudo-random selection and ensuring the security and decentralization of cross-chain interactions. After that， Byzantine Agreement （BA） was improved to reduce the communication cost of consensus， and algorithmic simulations on BFT simulation platform were performed. Experimental results demonstrate that compared to Algorand algorithm， the proposed scheme achieves higher node privacy verification， enhances cross-chain message consensus efficiency by 89%， and reduces node message communication cost by 80% through notary mechanism verification. The above show that the proposed scheme can improve cross-chain security effectively.