seIMC: A GSW-Based Secure and Efficient Integer Matrix Computation Scheme With Implementation
seIMC: A GSW-Based Secure and Efficient Integer Matrix Computation Scheme With Implementation
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seIMC：一种基于GSW的安全高效整数矩阵计算方案及实现
DOI：
10.1109/access.2020.2996000
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发表时间：
2020-01-01
期刊：
影响因子：
3.9
通讯作者：
Feng, Yong
中科院分区：
文献类型：
--
作者：
Bai, Yanan;Shi, Xiaoyu;Feng, Yong
作为原子操作，使用同型加密（HE）的基于矩阵的安全计算（HE）引起了基于云的机器学习的广泛关注。但是，大多数关注HE计划的现有安全矩阵计算解决方案作为矩阵的大小遭受效率损失，这极大地限制了其在大数据环境中的应用。为了解决这些问题，本文提出了SEIMC，这是一种基于绅士 - 撒哈拉 - 沃特斯（GSW）方案的整数矩阵计算方案，以应对隐私保护并确保对大规模数据的安全计算。详细说明，我们将GSW方案转换为加密整数矩阵模量（即大型正整数），并同派计算矩阵添加和乘法，这是HAO方案的自然扩展。此外，还显示了SEIMC的正确性和安全性分析，本研究还提供了复杂性分析。此外，提出的计划还将实施，包括公钥加密和私钥加密方案。与现有的安全矩阵计算方案相比，所提出的方案在执行时间上的性能更好。最后，将SEIMC应用于解决任何两个参与者通过加密社交网络中的步骤结交朋友的方式的问题。实验表明，当云服务器处理1000人的整数矩阵，安全级别为90，即100万个数据量时，每个同型矩阵乘法仅需大约1.9分钟。因此，在大数据环境下，拟议的SEIMC在隐私保护方面的实用性得到了高度证明。
As atomic operations, secure matrix-based computations using homomorphic encryption (HE) have attracted much attention in cloud-based machine learning. However, most existing secure matrix computation solutions that focus on HE schemes suffer efficiency loss as the size of the matrix, which greatly limits their applications in the big data environment. To address these issues, this paper proposes seIMC, an integer matrix computation scheme based on the Gentry-Sahai-Waters (GSW) scheme, to cope with privacy protection and secure computation of large-scale data. In detail, we translate the GSW scheme to encrypt an integer matrix modulo $q$ (i.e., a large positive integer), and homomorphically compute matrix addition and multiplication, which is a natural extension of HAO scheme. Besides, the correctness and security analysis of seIMC are shown, and complexity analysis is also given in this study. Furthermore, the proposed schemes are implemented, including public-key encryption and private-key encryption schemes. Compared with existing secure matrix computation schemes, the proposed scheme performs better in execution time. Finally, seIMC is applied to solve the problem of the number of ways in which any two participants make friends through $k$ steps in an encrypted social network. Experiments show that when the cloud server processes an integer matrix of 1000 people with a security level of 90, namely, 1 million data volumes, it only takes approximately 1.9 minutes for each homomorphic matrix multiplication. Hence, the practicality of the proposed seIMC in privacy protection under a big data environment is highly proven.