Fully homomorphic encryption (FHE) is a post-quantum secure cryptographic technology that enables privacy-preserving computing on an untrusted platform without divulging any secret or sensitive information. The core of FHE is the bootstrapping algorithm, which is the intermediate refreshing procedure of a processed ciphertext. However, this step has been the computational bottleneck that prevents real-world deployments among various FHE schemes. This paper, to the best of our knowledge, for the first time, presents a scalable and ultra-highly parallel design for the number theoretic transform (NTT)-based polynomial multiplier with a variable number of reconfigurable processing elements (PEs). Hence, the highest degree of acceleration can be achieved for any targeted hardware platform by implementing as many PEs as possible under the resource constraint. The corresponding addressing and scheduling schemes are also proposed to avoid memory access conflict for the PEs, which yields an extremely high utilization ratio of 99.18% on average. In addition, the latency of the proposed design with the general negative wrapped convolution algorithm is reduced by 59.20% compared to prior works.

完全同态加密（FHE）是一种后量子安全密码技术，可在不泄露任何机密信息或敏感信息的情况下，在不受信任的平台上实现隐私保护计算。FHE的核心是自举算法，它是处理后的密文的中间刷新过程。但是，此步骤已成为阻止各种FHE方案之间实际部署的计算瓶颈。据我们所知，本文首次为具有可变数量的可重配置处理元素（PE）的基于数字理论变换（NTT）的多项式乘法器提供了一种可扩展的超高度并行设计。因此，通过在资源限制下实现尽可能多的PE，可以对任何目标硬件平台实现最高程度的加速。还提出了相应的寻址和调度方案，以避免PE的内存访问冲突，这会产生平均99.98％的极高利用率。此外，与先前的工作相比，采用通用负包裹卷积算法的拟议设计的等待时间减少了59.20％。