Page 270 - 《软件学报》2021年第11期

软件学报 ISSN 1000-9825, CODEN RUXUEW E-mail: jos@iscas.ac.cn
Journal of Software,2021,32(11):3596−3605 [doi: 10.13328/j.cnki.jos.006032] http://www.jos.org.cn
©中国科学院软件研究所版权所有. Tel: +86-10-62562563

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一种基于 MLWE 的同态内积方案

1,2
1
柯程松 , 吴文渊 , 冯 勇 1
1
(自动推理与认知重庆市重点实验室(中国科学院 重庆绿色智能技术研究院),重庆 400714)
2
(重庆邮电大学 计算机科学与技术学院,重庆 400065)
通讯作者: 吴文渊, E-mail: wuwenyuan@cigit.ac.cn

摘 要: 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.
关键词: MLWE;同态内积;安全多方计算
中图法分类号: TP309

中文引用格式: 柯程松,吴文渊,冯勇.一种基于 MLWE 的同态内积方案.软件学报,2021,32(11):3596−3605. http://www.jos.org.
cn/1000-9825/6032.htm
英文引用格式: Ke CS, Wu WY, Feng Y. MLWE-based homomorphic inner product scheme. Ruan Jian Xue Bao/Journal of
Software, 2021,32(11):3596−3605 (in Chinese). http://www.jos.org.cn/1000-9825/6032.htm
MLWE-based Homomorphic Inner Product Scheme

1,2
1
KE Cheng-Song , WU Wen-Yuan , FENG Yong 1
1
(Chongqing Key Laboratory of Automated Reasoning and Cognition (Chongqing Institute of Green and Intelligent Technology, Chinese
Academy of Sciences), Chongqing 400714, China)
2
(College of Computer Science and Technology, Chongqing University of Posts and Telecommunications, Chongqing 400065, China)
Abstract: 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.
Key words: MLWE; homomorphic inner product; secure multi-party computation

[1]
安全多方计算最早由 Yao 提出,指的是解决一组互不信任的参与方之间保护隐私的协同计算问题.随着云
计算与大数据技术的广泛应用,越来越多的场景需要安全高效的计算两方所输入向量的内积,如安全多方几何

∗ 基金项目: 国家自然科学基金(11671377); 重庆市院士专项(cstc2017zdcy-yszxX0011, cstc2018jcyj-yszxX0002)
Foundation item: National Natural Science Foundation of China (11671377); Research Project of Chongqing Science and
Technology Commission (cstc2017zdcy-yszxX0011, cstc2018jcyj-yszxX0002)
收稿时间: 2018-07-02; 修改时间: 2019-01-06, 2019-10-08; 采用时间: 2020-02-28