Rapid advancements in large language models (LLMs) require secure and efficient mechanisms for sharing insights between different models, particularly when handling sensitive data. Addressing these needs, the presented research develops and evaluates a comprehensive framework incorporating differential privacy, homomorphic encryption, and secure multi-party computation to ensure the integrity and confidentiality of data shared between commercial large language models such as Gemini 1.5 and ChatGPT-4. Key results demonstrate that the implementation of these cryptographic methods effectively protects data privacy and security, allowing for collaborative enhancements in model intelligence without compromising data integrity. Extensive testing confirms the framework's robustness against sophisticated cyber threats and its practical viability for real-time applications. The findings provide a solid foundation for further optimization of security measures, aiming to enhance the scalability and efficiency of knowledge sharing among AI systems in sensitive and critical environments.