Mathematics and Computation: The Landscape of P vs. NP

Avi Wigderson · 1:02:49

This lecture establishes the foundational concepts of computational hardness and the P vs. NP problem, which are essential for understanding the security assumptions underlying all cryptographic systems.

Proofs, Knowledge, and Computation: Zero-Knowledge Interactive Systems

Silvio Micali · 1:03:26

Building on the concept of computational hardness, this lecture introduces interactive proof systems and the revolutionary idea of zero-knowledge proofs, demonstrating how interaction can verify knowledge without revealing it.

The Birch-Swinnerton-Dyer Conjecture: A Millennium Prize Problem at 25

Chris Skinner · 52:16

Transitioning from theoretical complexity, this lecture introduces elliptic curves through the Birch-Swinnerton-Dyer Conjecture, providing the mathematical foundation for modern public-key cryptography, including ECC.

Introduction to Hash-based Post-quantum Cryptography (PQC)

Christof Paar · 1:40:59

Following the mathematical foundations of public-key cryptography, this lecture addresses the critical challenge of quantum computing by introducing hash-based post-quantum cryptography, preparing learners for future cryptographic paradigms.

What Can the Theory of Cryptography Tell Us About AI Verification?

Shafi Goldwasser · 1:02:15

Finally, this lecture applies cryptographic principles to the cutting-edge domain of AI verification, demonstrating how interactive proofs and adversarial guarantees can ensure the security and trustworthiness of machine learning systems.