This lecture discusses the intersection of Public Key Infrastructure (PKI) and provable security. It begins with an overview of symmetric and asymmetric cryptography, emphasizing their roles in secure communications. The instructor explains the significance of the X.509 standard and its evolution, including the adoption of PKIX and Certificate Transparency. The lecture highlights the architecture of PKI, detailing the roles of various entities such as Certificate Authorities (CAs) and the importance of accountability in certificate issuance. The instructor elaborates on the mechanisms for certificate revocation and the challenges posed by compromised keys. The discussion includes the modular security specification framework used to analyze PKI requirements, focusing on the need for transparency and the implications of potential attacks. The lecture concludes with a critical examination of the trust model inherent in PKI, addressing the reliance on CAs and the importance of verifying certificate validity in secure communications.