基于矩阵的安全多方计算同态加密方案  

Matrix based secure multi-party computation homomorphic encryption scheme

作　　者：陈虹[1] 马博宇 金海波 武聪 Chen Hong;Ma Boyu;Jin Haibo;Wu Cong(College of Software,Liaoning Technical University,Fuxin Liaoning 123000,China;Science&Technology Research Institute,Liaoning Technical University,Fuxin Liaoning 123000,China)

机构地区：[1]辽宁工程技术大学软件学院,辽宁阜新123000 [2]辽宁工程技术大学科学技术研究院,辽宁阜新123000

出　　处：《计算机应用研究》2025年第4期1211-1216,共6页Application Research of Computers

基　　金：国家自然科学基金面上资助项目(62173171);辽宁省教育厅科研资助项目(LJKFZ20220198)。

摘　　要：针对现有同态加密方案效率低,同态运算噪声增长速率高影响解密正确性的问题进行了研究,提出了一种格上基于整数矩阵的安全多方计算同态加密方案。方案采用了矩阵存储方式来处理明文数据并减小了密钥尺寸,与传统的比特或向量存储方式相比,矩阵存储方法在处理大规模数据时更为高效。为了控制噪声增长并提高解密结果的准确性,引入了比例降噪技术,可以有效地减缓噪声的累积。运用密文打包并对自举技术进行改进削减了噪声增长速率,为实现安全多方计算提供了条件。通过严格的理论证明,验证了方案的正确性和安全性。实验结果表明本方案加密、解密时间相较于对比方案至少降低了66.97%、33.04%,表现出了显著的性能优势。A study has been conducted on the current issues of homomorphic encryption schemes,such as their low efficiency and high noise growth rate,which affects the accuracy of decryption.This paper proposed a novel homomorphic encryption scheme for secure multi-party computation based on integer matrices over lattices.This scheme utilized matrix storage to handle plaintext data,reducing the size of the encryption keys.Compared to traditional bit or vector storage methods,the matrix storage approach was more efficient when dealing with large-scale data.To control noise growth and enhance the accuracy of decryption results,it introduced proportional noise reduction technology,effectively mitigating the accumulation of noise.The scheme also employed ciphertext packing and improved the bootstrapping technique to reduce the noise growth rate,providing conditions for secure multi-party computation.It provided rigorous theoretical proofs to validate the correctness and security of the scheme.Experimental results demonstrate that the encryption and decryption times of this scheme are at least 66.97% and 33.04% lower than those of comparative schemes,respectively,showing a significant performance advantage.

关 键 词：同态加密 矩阵运算 安全多方计算 数据隐私 格 

分 类 号：TP309.7[自动化与计算机技术—计算机系统结构]