Explore lattice-based cryptography and its applications in post-quantum cryptography through this comprehensive lecture. Delve into the New Hope algorithm, a key encapsulation mechanism for PQC, and examine the costs associated with pre- and post-processing Negative Wrapped Convolution. Discover a new lattice-based hardware design featuring an innovative binary-search CDT sampler. Investigate the experimental setup for TESLA on FPGA and learn about NTT-based polynomial multipliers. Gain insights into speed and memory optimizations, including reduced storage for secrets. Analyze performance results, bottlenecks, and various accelerator types, including Ring Arithmetic and Sampling Accelerators. Conclude with a thorough understanding of the latest advancements in lattice-based cryptography and their implications for future secure communication systems.