Explore a comprehensive talk from Asiacrypt 2016 on partitioning via non-linear polynomial functions and compact identity-based encryption (IBE) schemes from ideal lattices. Delve into adaptive security, template construction, and simulation techniques presented by Shuichi Katsumata and Shota Yamada. Learn about Fourier IBE, modulus size considerations, and simulation results. Examine obstacles in implementation and discover how various components are integrated. Investigate the polynomial ring concept, scalar properties, and potential issues. Gain insights into linear maps, hardcore functions, and mental experiments. Compare the presented approach with existing methods and grasp the key takeaways from this cutting-edge cryptographic research.