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This lecture covers the establishment of trust in the context of cryptography and security, focusing on topics such as setting up secure channels, trusted third parties, and trust management. It delves into the challenges of certificate verification, the PKI model, and the chain of trust in real-life scenarios. The instructor discusses various approaches to trust infrastructure, including Kerberos, PKI, identity-based encryption, and certificateless encryption. The lecture also explores the vulnerabilities in the current PKI landscape and the efforts to enhance security through improved PKI schemes. Additionally, it addresses the importance of human factors, trust management, and the need for diverse cryptographic models.