基于NTRU自举的多密钥全同态加密方案  

Multi-key fully homomorphic encryption scheme based on NTRU bootstrapping

作　　者：郑俊华[1] 江宏伟 刘荣 李沂修 李闻[1] 翁健[2] ZHENG Junhua;JIANG Hongwei;LIU Rong;LI Yixiu;LI Wen;WENG Jian(CNTC Guangdong Tobacco Corporation,China National Tobacco Corporation,Guangzhou 510610,China;College of Cyber Security,Jinan University,Guangzhou 510632,China)

机构地区：[1]中国烟草总公司广东省公司,广东广州510610 [2]暨南大学网络空间安全学院,广东广州510632

出　　处：《网络与信息安全学报》2024年第6期123-136,共14页Chinese Journal of Network and Information Security

基　　金：广东省烟草专卖局(公司)科技项目(粤烟科项202207);广州市科技计划项目(2024A03J0464)。

摘　　要：多密钥全同态加密(multi-key fully homomorphic encryption,MK-FHE)技术支持对不同密钥加密的密文进行同态运算,能够直接应用于现实中的多用户数据融合计算场景,如多方协同计算和联邦学习。目前,主流的多密钥全同态加密主要通过自举技术实现对LWE(learning with error)加密密文的多密钥同态计算。将单密钥密文扩展为多密钥密文的时间效率和存储开销与自举技术密切相关,通常需要大量的同态评估密钥以及复杂的运算。因此,如何结合更优的自举技术设计多密钥全同态加密方案,进而提升计算效率与降低存储开销成为研究的关键问题。基于NTRU(number theory research unit)自举技术,设计了一种针对LWE密文的高效多密钥全同态加密方案。与其他方案相比,所提方案在密文扩展过程中具有更高的计算效率。此外,对所提方案的正确性进行了详细阐述和分析,并在理论上将所提方案与现有主流的多密钥全同态加密方案进行了多维度对比,结果显示所提方案具有更优的计算效率。最后,探索了该方案在多行业多源销售数据跨部门监管场景中的潜在应用,在保护数据隐私的前提下帮助税务部门实现税务核验,有助于推动各行业的数字化转型和健康发展。Multi-key fully homomorphic encryption(MK-FHE)technology supports homomorphic operations on ciphertexts encrypted with different keys,and can be directly applied to real-world multi-user data fusion computing scenarios,such as multi-party collaborative computing and federated learning.At present,mainstream multi-key fully homomorphic encryption mainly uses bootstrapping technology to achieve multi-key homomorphic computing of LWE(learning with errors)encrypted ciphertexts.The time efficiency and storage overhead of expanding singlekey ciphertexts to multi-key ciphertexts are closely related to the bootstrapping technology,which usually requires a large number of homomorphic evaluation keys and complex operations.Therefore,designing a multi-key fully homomorphic encryption scheme in combination with a better bootstrapping technology to improve computational efficiency and reduce storage overhead had become a key research issue.Based on the NTRU(number theory research unit)bootstrapping technology,an efficient multi-key fully homomorphic encryption scheme for LWE ciphertexts was designed.Compared with other schemes,the proposed scheme exhibited higher computational efficiency in the ciphertext expansion process.In addition,the correctness of the proposed scheme was elaborated and analyzed in detail.The proposed scheme was compared with the existing mainstream multi-key fully homomorphic encryption scheme in theory.The results show that the proposed scheme has better computational efficiency.Finally,the potential application of the scheme in cross-departmental supervision scenarios of multi-industry and multi-source data sales data was explored,which helped the tax department to realize tax verification under the premise of protecting data privacy,and helped promote the digital transformation and healthy development of various industries.

关 键 词：多密钥全同态加密 协同计算 自举技术 加密技术 

分 类 号：TP309[自动化与计算机技术—计算机系统结构]