With the widespread adoption of blockchain technology, the privacy issues arising from its public transparency have become increasingly prominent. Ring signature technology, through its anonymity and untraceability, can enhance system security while protecting user privacy. The study proposes a ring signature algorithm based on novel mathematical challenges, significantly improving computational efficiency and security, and designs an adaptive integration architecture of ring signatures and blockchain to optimize privacy protection. Experimental validation demonstrates that the solution performs excellently in various application scenarios, providing theoretical support and practical guidance for the development of blockchain privacy protection technology. Future research directions include exploring quantum-resistant ring signature algorithms and integrating with other privacy-preserving technologies to further enhance the security and scalability of blockchain.