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Explore the fundamental concepts and techniques of security proofs in cryptography through this comprehensive lecture. Delve into the essential methodologies used to establish the security of cryptographic protocols and systems. Learn how to construct rigorous mathematical arguments that demonstrate the robustness of security measures against potential attacks. Gain insights into the importance of formal security proofs in ensuring the reliability and trustworthiness of cryptographic implementations. Examine real-world examples and case studies to understand the practical applications of security proofs in modern cryptography.