Efficient Blind Rotation in FHEW Using Refined Decomposition and NTT

In this paper, we propose two more efficient implementations for the FHEW scheme. First, for the gate bootstrapping case, we employ approximate gadget decomposition and refined Number Theoretic Transform (NTT) with AVX-512 instructions to improve the efficiency of blind rotation. Compared to the state-of-the-art implementation that uses FFT-based polynomial multiplication, our technique takes 4.7 ms, which is approximately 1.9 × faster than TFHEpp and 1.4 × faster than TFHE-rs. Furthermore, for the circuit bootstrapping case, we introduce the Residue Number System (RNS) to decompose the larger modulus. Experimental results demonstrate that the RNS decomposition is more efficient than the original numerical decomposition. Our optimized method is more applicable in scenarios involving prime moduli, such as homomorphic trace and automorphism.