Explore the foundations and advancements in lattice-based cryptography in this comprehensive lecture. Delve into the world of lattices and encrypted computation, focusing on fully homomorphic encryption (FHE) and its historical breakthroughs. Learn about key concepts such as Vika encryption, key switching, modular computation, short ciphertexts, circular encryption, and multi-key encryption. Gain insights into the algorithms, complexity, and cryptographic applications of lattices from MIT expert Vinod Vaikuntanathan. Discover how these advanced techniques are shaping the future of secure computation and data privacy.