FINAL: Faster FHE instantiated with NTRU and LWE

Since the introduction of the first fully homomorphic encryption (FHE) scheme by Gentry in 2009, various constructions have been proposed, primarily based on hard lattice problems, but many faced security challenges. Notably, schemes based on ideal lattices and NTRU assumptions were deemed insecure due to over-stretched parameters, while Learning-with-Errors (LWE) and its ring counterpart (Ring-LWE) form the basis of more secure schemes like BGV, BFV, CKKS, and GSW. Recent research by KU Leuven and Zama, presented at AsiaCrypt 2022, revisits NTRU-based constructions with a novel approach that avoids the parameter overstretching issue by integrating methods from GSW, FHEW, and TFHE systems. This new NTRU-based FHE scheme potentially restores the efficiency advantage of using a single ring element per ciphertext, although further optimization and research are required to determine if it can rival existing TFHE implementations.