Hybrid Number Theoretic Transform Architecture for Homomorphic Encryption

Fully homomorphic encryption (FHE) is an innovative cryptographic technology that has the potential to protect the privacy and confidentiality of data in the untrusted environments, such as public clouds or external parties. However, due to the inclusion of time-consuming polynomial arithmetic, FHE remains a challenge for computationally heavy applications. The number theoretic transform (NTT) is widely used in HE to reduce the complexity of polynomial multiplication. Therefore, implementing NTT in hardware for FHE has been explored in prior studies. However, due to the high hardware resource requirements, especially with a large number of moduli, hardware architecture supporting both NTT and its inverse transform (INTT) is still missing. This brief presents a hardware architecture for <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$2^{17}$</tex-math> </inline-formula> NTT and INTT suitable for high-circuit depth CKKS-based HE schemes, satisfying both criteria of high speed and affordability for various FPGA platforms. The implementation results highlight that this design is area-efficient compared to the most related work and hardware-friendly for practical HE-based applications on FPGA devices.