On-the-Fly Twiddle Factor Generator Design for Efficient Memory Management of Negative Wrapped Convolution

Efficient designs of Negative Wrapper Convolution (NWC) and its inverse (INWC) are crucial for handling large-sized polynomial multiplication in lattice-based cryptosystems such as fully homomorphic encryption and post-quantum cryptography. This paper explores a systematic approach of reducing the storage requirement for twiddle factors, which will contribute a large portion of memory requirement if not properly handled. Moreover, we integrate correction factors with twiddle factors along with the scaling factors necessary for performing INWC, leading to a more streamlined data flow. Experimental results show that generating twiddle factors on-the-fly can significantly reduce the memory size for storing seed factors. Taking a 65536-point INWC as an example, the proposed scheme only needs to store less than 3% of twiddle factors, generating others on-the-fly. The overall INWC implementation results also demonstrate the effectiveness of our approach when compared with related works.