一种基于MLWE的同态内积方案

同态内积在安全多方几何计算、隐私数据挖掘、外包计算、可排序的密文检索等场景有广泛的应用.但现有的同态内积计算方案大多是基于RLWE的全同态加密方案，普遍存在效率不高的问题.在柯程松等人提出的基于MLWE的低膨胀率加密算法基础上，提出了一种同态内积方案.首先给出了密文空间上的张量积运算⊗，该密文空间上的运算对应明文空间上的整数向量内积运算；然后分析了方案的正确性与安全性；最后给出了两种优化的加密参数，对应计算两种不同大小的整数向量同态内积的应用场景.通过C++与大整数计算库NTL实现了该方案.对比其他同态加密方案，该方案能够比较高效地计算整数向量的同态内积.

MLWE-based Homomorphic Inner Product Scheme

The homomorphic inner product has a wide range of applications such as secure multi-geometry calculation, private data mining, outsourced computing, and sortable ciphertext retrieval. However, the existing schemes for calculating the homomorphism inner product are mostly based on FHE by RLWE with low efficiency. With MLWE, this study proposes a homomorphic inner product scheme by using a low expansion rate encryption algorithm proposed by Ke, et al. Firstly, the tensor product operation in the cipher space is given, which corresponds to the integer vector product operation in the plaintext space. Then, the correctness and security of the scheme are analyzed. At last, two sets of optimized encryption parameters are given, corresponding to the different application scenarios of homomorphic inner product. The scheme of this study is implemented by C++ and the large integer computation library NTL. Compared with other homomorphic encryption schemes, this scheme can efficiently calculate the homomorphism inner products of integer vectors.