AI memory systems are evolving toward unified context layers that enable efficient cross-agent collaboration and multi-tool workflows, facilitating better accumulation of personal data and learning of user preferences. However, centralization creates a trust crisis where users must entrust cloud providers with sensitive digital memory data. We identify a core tension between personalization demands and data sovereignty: centralized memory systems enable efficient cross-agent collaboration but expose users' sensitive data to cloud provider risks, while private deployments provide security but limit collaboration. To resolve this tension, we aim to achieve local-equivalent security while enabling superior maintenance efficiency and collaborative capabilities. We propose a five-layer architecture abstracting common functional components of AI memory systems: Storage, Extraction, Learning, Retrieval, and Governance. By applying TEE protection to each layer, we establish a trustworthy framework. Based on this, we design MemTrust, a hardware-backed zero-trust architecture that provides cryptographic guarantees across all layers. Our contributions include the five-layer abstraction, "Context from MemTrust" protocol for cross-application sharing, side-channel hardened retrieval with obfuscated access patterns, and comprehensive security analysis. The architecture enables third-party developers to port existing systems with acceptable development costs, achieving system-wide trustworthiness. We believe that AI memory plays a crucial role in enhancing the efficiency and collaboration of agents and AI tools. AI memory will become the foundational infrastructure for AI agents, and MemTrust serves as a universal trusted framework for AI memory systems, with the goal of becoming the infrastructure of memory infrastructure.