Foundations and Frontiers of Modern Cryptography

This lecture establishes the foundational concepts of computational hardness and pseudorandomness, essential for understanding the security assumptions underlying all cryptographic systems.

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

Expanding on interactive proofs, this lecture proves the fundamental IP=PSPACE equivalence, showcasing the immense power and scope of interactive verification systems in theoretical computer science.

Applying the principles of interactive proofs and cryptographic verification, this lecture explores their practical implications for ensuring the integrity and trustworthiness of AI systems.

Transitioning from classical to future-proof cryptography, this lecture introduces hash-based post-quantum cryptography, addressing the challenges posed by quantum computing to current cryptographic standards.

This final lecture delves into the efficiency limits of secure computation, integrating concepts of cryptographic primitives and complexity to explore advanced research frontiers in privacy-preserving technologies.