Twiddle-Factor Generation Using Reused Butterfly Array for Fully Homomorphic Encryption

초록

The Number Theoretic Transform (NTT) and its inverse (INTT) are essential operations in Fully Homomorphic Encryption (FHE), converting expensive polynomial convolution into element-wise multiplication in O(n) time while each transform itself costs O(n log n). However, these transformations require storing O(n) twiddle factors (TF). As the polynomial degree increases, storing these TFs imposes significant memory overhead, limiting available resources for ciphertexts and intermediate data in hardware accelerators. Prior work has used a separate TF generation datapath, leading to higher additional resource overhead. To address this, we propose an on-the-fly TF generation method using a reused butterfly array, which eliminates the need for dedicated TF logic. The design reduces memory usage from 12.09 MB to only 0.38 MB, a 96.9% reduction, with zero DSP overhead. Compared to prior designs, it achieves up to 9.6 × better resource efficiency in terms of equivalent normalized slices (ENS), enabling more area- and memory-efficient FHE hardware accelerators. © 2025 IEEE.

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