Homomorphic encryption (HE) allows computations to be directly carried out on ciphertexts and is essential to privacy-preserving computing, such as neural network inference, medical diagnosis, and financial data analysis. Only addition and 2-input multiplication are defined over ciphertexts in popular HE schemes. However, many HE applications involve non-linear functions and they need to be approximated using high-order polynomials to maintain precision. To reduce the complexity of these computations, this paper proposes 3-input ciphertext multiplication. One extra evaluation key is introduced to carry out the relinearization step of ciphertext multiplication, and new formulas are proposed to combine computations and share intermediate results. Compared to using two consecutive 2- input multiplications, computing the product of three ciphertexts utilizing the proposed scheme leads to almost a half of the latency, 29% smaller silicon area, and lower noise without scarifying the throughput.

翻译：同态加密（HE）允许直接在密文上执行计算，对于隐私保护计算（如神经网络推理、医疗诊断和金融数据分析）至关重要。在流行的HE方案中，密文上仅定义了加法与二输入乘法运算。然而，许多HE应用涉及非线性函数，需要借助高阶多项式进行近似以维持精度。为降低此类计算的复杂度，本文提出了三输入密文乘法方案。该方案引入一个额外的评估密钥来执行密文乘法的重线性化步骤，并提出了新的计算公式以合并计算并共享中间结果。与使用两次连续的二输入乘法相比，利用所提方案计算三个密文的乘积，在保持吞吐量的同时，实现了近一半的延迟降低、29%的硅面积缩减以及更低的噪声水平。