Parameter Optimization & Larger Precision for (T)FHE

The blog post outlines two significant advancements in improving the efficiency of Fully Homomorphic Encryption (FHE), as detailed in the scientific paper BBB+23 published in the Journal of Cryptology. The first contribution involves an optimization framework for the TFHE scheme, aiming to minimize computational costs while maintaining precision, security, and correctness by carefully selecting macro and micro parameters. The second contribution introduces the Without Bit of Padding Programmable Bootstrapping (WoP-PBS), which eliminates the need for a padding bit, thereby enhancing the speed and scalability of processing higher precision messages compared to the standard Programmable Bootstrapping (PBS). This innovation allows for the efficient evaluation of multivariate lookup tables on messages exceeding 10 bits, outperforming previous methods such as the tree-PBS, particularly in terms of scalability and speed as precision increases. The discussion highlights the importance of these advancements in optimizing homomorphic computations and selecting optimal parameters, contributing to the broader field of cryptographic research and application.