基于国密算法SM9的加法同态加密方案

doi:10.11896/jsjkx.241100188

计算机科学 ›› 2025, Vol. 52 ›› Issue (11): 408-414.doi: 10.11896/jsjkx.241100188

基于国密算法SM9的加法同态加密方案

谢振杰^1,2, 刘奕明³, 尹小康¹, 刘胜利¹, 张永光^4,5

1 信息工程大学网络空间安全教育部重点实验室郑州 450001
2 中国人民解放军78156部队重庆 400039
3 中国人民解放军92330部队山东青岛 266000
4 电磁空间安全全国重点实验室浙江嘉兴 314033
5 中国电子科技集团公司第三十六研究所浙江嘉兴 314033

收稿日期:2024-11-28 修回日期:2025-03-11 出版日期:2025-11-15 发布日期:2025-11-06
通讯作者: 尹小康(yxksjtu@sjtu.edu.cn)
作者简介:(jsonxie@126.com)
基金资助:
装备预先研究项目(30603010601)

Additively Homomorphic Encryption Scheme Based on Domestic Cryptographic Algorithm SM9

XIE Zhenjie^1,2, LIU Yiming³, YIN Xiaokang¹, LIU Shengli¹, ZHANG Yongguang^4,5

1 Key Laboratory of Cyberspace Security,Ministry of Education,Information Engineering University,Zhengzhou 450001,China
2 Troop 78156 of PLA,Chongqing 400039,China
3 Troop 92330 of PLA,Qingdao,Shandong 266000,China
4 National Key Laboratory of Electromagnetic Space Security,Jiaxing,Zhejiang 314033,China
5 The 36th Research Institute of China Electronics Technology Group Corporation,Jiaxing,Zhejiang 314033,China

Received:2024-11-28 Revised:2025-03-11 Online:2025-11-15 Published:2025-11-06
About author:XIE Zhenjie,born in 1995,Ph.D candidate.His main research interests include cloud security and cryptography applications.
YIN Xiaokang,born in 1993,Ph.D,lecturer.His main research interests include network security,binary code analysis and machine learning.
Supported by:
Equipment Pre Research Project(30603010601).

摘要/Abstract

摘要： 在云计算环境下,传统加密方案在保护数据机密性的同时,也使密文丧失了可计算性。同态加密解决了这一矛盾,已被广泛应用于数据聚合、安全多方计算、联邦学习等隐私计算领域。因此,以基于标识密码体制的国密算法SM9加密算法为基础,构造了具有加法同态性质的标识加密方案,细致推导了方案的正确性和加法同态性,从q-BCAA1和DDH困难问题出发证明了方案具有IND-CPA安全性,并对改进的消息恢复算法进行了详细描述。测试结果表明,提出的加法同态加密方案的加密效率相较于同类方案提升了42%,解密效率提升了20%~62%。

关键词: 国密算法, SM9, 加法同态加密, 隐私计算

Abstract: In the cloud computing environment,traditional encryption schemes not only protect data confidentiality but also cause the ciphertext to lose its computability.Homomorphic encryption solves this contradiction and has been widely applied in privacy computing fields such as data aggregation,secure multi-party computing,and federated learning.Based on the encryption algorithm of the domestic cryptographic algorithm SM9,an identity-based encryption scheme with additive homomorphism property is constructed.The correctness and additive homomorphism of the scheme are carefully derived.Starting from the q-BCAA1 and DDH difficulty problems,the scheme is proven to have IND-CPA security.And the improved message recovery algorithm is described in detail.Test results show that the encryption efficiency of the proposed additively homomorphic encryption scheme increases by 42% compared to the similar scheme,and the decryption efficiency increases by 20% to 62%.

Key words: Domestic cryptographic algorithm, SM9, Additively homomorphic encryption, Privacy computing

中图分类号:

TP309.7

谢振杰, 刘奕明, 尹小康, 刘胜利, 张永光. 基于国密算法SM9的加法同态加密方案[J]. 计算机科学, 2025, 52(11): 408-414. https://doi.org/10.11896/jsjkx.241100188

XIE Zhenjie, LIU Yiming, YIN Xiaokang, LIU Shengli, ZHANG Yongguang. Additively Homomorphic Encryption Scheme Based on Domestic Cryptographic Algorithm SM9[J]. Computer Science, 2025, 52(11): 408-414. https://doi.org/10.11896/jsjkx.241100188

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基于国密算法SM9的加法同态加密方案

Additively Homomorphic Encryption Scheme Based on Domestic Cryptographic Algorithm SM9

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