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Explore the foundations of cryptography in this comprehensive tutorial on proof systems presented by Abhishek Jain from Johns Hopkins University. Delve into the concept of minimal complexity assumptions and their crucial role in cryptographic protocols. Gain insights into the intricate relationship between proof systems and secure communication methods. Examine the latest advancements in the field and understand how these theoretical concepts translate into practical applications. Enhance your knowledge of cryptographic fundamentals and their implications for modern security systems in this hour-long lecture from the Simons Institute.