基于NTRU自举的多密钥全同态加密方案

郑俊华; 江宏伟; 刘荣; 李沂修; 李闻; 翁健

doi:10.11959/j.issn.2096-109x.2024085

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基于NTRU自举的多密钥全同态加密方案

学术论文 | 更新时间：2025-02-06

- 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
- 网络与信息安全学报 2024年10卷第6期页码：123-136
- 作者机构：
  
  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
- 作者简介：
  
  [ "郑俊华（1978- ），男，浙江金华人，中国烟草总公司广东省公司信息中心工程师，主要研究方向为计算机软件与信息安全。" ]
  [ "江宏伟（1980- ），男，河南信阳人，中国烟草总公司广东省公司信息中心高级工程师，主要研究方向为网络和数据安全防护。" ]
  [ "刘荣（1982- ），男，广东省韶关人，中国烟草总公司广东省公司信息中心高级工程师，主要研究方向为云平台、大数据。" ]
  [ "李沂修（2000- ），男，河北邯郸人，暨南大学硕士生，主要研究方向为密码学与信息安全。" ]
  [ "李闻（1981- ），男，江西鄱阳人，中国烟草总公司广东省公司信息中心高级工程师，主任科员，主要研究方向为计算机应用技术。" ]
  [ "翁健（1976- ），男，广东茂名人，暨南大学教授、博士生导师，主要研究方向为密码学、云计算安全、区块链与信息安全。" ]
- 基金信息：
  
  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)
- DOI：10.11959/j.issn.2096-109x.2024085
  中图分类号： TP309
- 收稿：2024-08-05，
  
  修回：2024-11-06，
  
  纸质出版：2024-12-25
- 稿件说明：
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郑俊华, 江宏伟, 刘荣, 等. 基于NTRU自举的多密钥全同态加密方案[J]. 网络与信息安全学报, 2024, 10(6): 123-136.

ZHENG J H, JIANG H W, LIU R, et al. Multi-key fully homomorphic encryption scheme based on NTRU bootstrapping[J]. Chinese Journal of Network and Information Security, 2024, 10(6): 123-136.
郑俊华, 江宏伟, 刘荣, 等. 基于NTRU自举的多密钥全同态加密方案[J]. 网络与信息安全学报, 2024, 10(6): 123-136. DOI： 10.11959/j.issn.2096-109x.2024085.

ZHENG J H, JIANG H W, LIU R, et al. Multi-key fully homomorphic encryption scheme based on NTRU bootstrapping[J]. Chinese Journal of Network and Information Security, 2024, 10(6): 123-136. DOI： 10.11959/j.issn.2096-109x.2024085.

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。

Abstract

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 single-key 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

Keywords

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