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This lecture covers the Diffie-Hellman key exchange protocol, focusing on the computational Diffie-Hellman problem, passive adversaries, and Decisional Diffie-Hellman problem. It explains the challenges with subgroups, group membership verification, and key wrapping in the context of RFC 2631. The instructor discusses the correct Diffie-Hellman key exchange steps, parameter generation, and validation, emphasizing the importance of group order and subgroup properties. The lecture concludes with a proof of the unique subgroup of prime order in the Diffie-Hellman protocol.