改进的格上基于多身份全同态加密方案

doi:10.13190/j.jbupt.2017-163

北京邮电大学学报 ›› 2018, Vol. 41 ›› Issue (1): 125-133.doi: 10.13190/j.jbupt.2017-163

改进的格上基于多身份全同态加密方案

汤永利, 胡明星, 叶青, 秦攀科, 于金霞

河南理工大学计算机科学与技术学院, 河南焦作 454000

收稿日期:2017-08-14 出版日期:2018-02-28 发布日期:2018-01-04
作者简介:胡明星(1994-),男,硕士生,E-mail:18236885186@163.com;叶青(1981-),女,硕士生导师.
基金资助:
"十三五"国家密码发展基金项目（MMJJ20170122）；河南省科技厅项目（142300410147）；河南省教育厅项目（12A520021，16A520013）；河南理工大学博士基金项目（B2014-044）

Improved Multi-Identity Based Fully Homomorphic Encryption Scheme over Lattices

TANG Yong-li, HU Ming-xing, YE Qing, QIN Pan-ke, YU Jin-xia

School of Computer Science and Technology, Henan Polytechnic University, Henan Jiaozuo 454000, China

Received:2017-08-14 Online:2018-02-28 Published:2018-01-04

摘要/Abstract

摘要： 针对格上基于多身份的全同态加密方案（mIBFHE）中陷门函数低效的问题，提出一种改进的格上mIBFHE方案.首先利用MP12陷门函数结合对偶Regev算法构造出一种可转化的基于身份的加密（IBE）方案，并构造出一种支持标准模型下IBE方案转化的Mask系统；然后基于该系统利用特征向量思想将构造出的IBE方案转化为mIBFHE方案.对比分析结果表明，新方案较同类方案在陷门生成和原像采样阶段均有效率提升，且格的维数、密文和运算密文尺寸等明显缩短.在标准模型下，方案的安全性归约至格上容错学习问题的难解性，并包含严格的安全性证明.

关键词: 格, 基于多身份的加密, 全同态加密, 标准模型, 容错学习问题

Abstract: Aiming at low efficiency of trapdoor function in multi-identity based fully homomorphic encryption (mIBFHE) schemes, a new mIBFHE scheme was proposed. Firstly, the MP12 trapdoor function with Dual-Regev algorithm was combined to construct a transformable identity-based encryption (IBE) scheme, and a Mask system which supports to transform IBE scheme presented to mIBFHE scheme under standard model. Then, based on presented Mask system and eigenvector idea, the IBE schemes was transformed to mIBFHE scheme. Comparing with the similar schemes, the efficiency of the scheme is improved in trapdoor generation and preimage sampling stage, and the lattice dimension, the size of ciphertext and evaluated ciphertext, etc. are obviously reduced. The security of the presented scheme strictly is reduced to the hardness of learning with errors problem in the standard model.

Key words: lattices, multi-identity based encryption, fully homomorphic encryption, standard model, learning with errors

中图分类号:

TP309

汤永利, 胡明星, 叶青, 秦攀科, 于金霞. 改进的格上基于多身份全同态加密方案[J]. 北京邮电大学学报, 2018, 41(1): 125-133.

TANG Yong-li, HU Ming-xing, YE Qing, QIN Pan-ke, YU Jin-xia. Improved Multi-Identity Based Fully Homomorphic Encryption Scheme over Lattices[J]. JOURNAL OF BEIJING UNIVERSITY OF POSTS AND TELECOM, 2018, 41(1): 125-133.

参考文献

[1] Gentry C, Sahai A, Waters B. Homomorphic encryption from learning with errors:conceptually-simpler, asymptotically-faster, attribute-based[C]//Proceedings of CRYPTO 2013. Santa Barbara:Springer, 2013:75-92.
[2] Clear M, McGoldrick C. Bootstrappable identity-based fully homomorphic encryption[C]//Proceedings of International Conference on Cryptology and Network Security. New York:Springer, 2014:1-19.
[3] 康元基, 顾纯祥, 郑永辉, 等. 利用特征向量构造基于身份的全同态加密体制[J]. 软件学报, 2016, 27(6):1487-1497. Kang Yuanji, Gu Chunxiang, Zheng Yonghui, et al. Identity-based fully homomorphic encryption from eigenvector[J]. Journal of Software, 2016, 27(6):1487-1497.
[4] 段然, 顾纯祥, 祝跃飞, 等. NTRU格上高效的基于身份的全同态加密体制[J]. 通信学报, 2017, 38(1):66-75. Duan Ran, Gu Chunxiang, Zhu Yuefei, et al. Efficient identity-based fully homomorphic encryption over NTRU[J]. Journal on Communications, 2017, 38(1):66-75.
[5] Clear M, McGoldrick C. Multi-identity and multi-key leveled FHE from learning with errors[C]//Proceedings of CRYPTO 2015. Santa Barbara:Springer, 2015:630-656.
[6] Ajtai M. Generating hard instances of the short basis problem[C]//Proceedings of Automata, Languages and Programming.[S.l.]:Springer, 1999:1-9.
[7] 来齐齐, 胡予濮, 陈原, 等. 辅助输入安全的损耗陷门函数的构造[J]. 北京邮电大学学报, 2014, 37(6):6-10. Lai Qiqi, Hu Yupu, Chen Yuan, et al. Construction of auxiliary-input secure lossy trapdoor functions[J]. Journal of Beijing University of Posts and Telecommunications, 2014, 37(6):6-10.
[8] Alwen J, Peikert C. Generating shorter bases for hard random lattices[C]//Proceedings of the 26^th International Symposium on Theoretical Aspects of Computer Science. Freiburg:Springer, 2009:535-553.
[9] Gentry C, Peikert C, Vaikuntanathan V. Trapdoors for hard lattices and new cryptographic constructions[C]//Proceeding of the 40^th ACM Symposium on Theory of Computing. Victoria:ACM, 2008:197-206.
[10] Micciancio D, Peikert C. Trapdoors for lattices:simpler, tighter, faster, smaller[C]//Proceeding of EUROCRYPT 2012. Cambridge:Springer, 2012:700-718.
[11] Agrawal S, Boneh D, Boyen X. Efficient lattice (H)IBE in the standard model[C]//Proceeding of EUROCRYPT 2010. Riviera:Springer, 2010:553-572.
[12] Regev O. On lattices, learning with errors, random linear codes, and cryptography[C]//Proceedings of the 37^th Annual ACM Symposium on Theory of Computing. New York:Springer, 2005:84-93.
[13] Cash D, Hofheinz D, Kiltz E, et al. Bonsai trees, or how to delegate a lattice basis[C]//Proceeding of EUROCRYPT 2010. Riviera:Springer, 2010:523-552.
[14] 王威力, 胡斌. 利用混淆器构造多身份的全同态加密体制[J]. 密码学报, 2017, 4(2):165-175. Wang Weili, Hu Bin. Multi-identity-based fully homomorphic encryption from obfuscation[J]. Journal of Cryptologic Research, 2017, 4(2):165-175.

[1]	李震东谭振庭方萍. 具有长程相互作用正方晶格的色散关系和热容[J]. 北京邮电大学学报, 2022, 45(5): 60-65.
[2]	李端玲, 成苈委, 于功敬, 张忠海, 于淑月. 融合小波包和神经网络的脑电信号处理方法[J]. 北京邮电大学学报, 2021, 44(3): 94-99.
[3]	邓筱, 徐梦秋, 吴铭, 张闯. 基于语义分割的织锦类自适应风格迁移算法[J]. 北京邮电大学学报, 2021, 44(1): 117-123.
[4]	李增鹏, 王九如, 张问银, 马春光. 一种基于对偶Regev加密的门限公钥加密方案[J]. 北京邮电大学学报, 2020, 43(4): 83-87.
[5]	何倩, 李双富, 黄焕, 徐红. 一种海量数据快速聚类算法[J]. 北京邮电大学学报, 2020, 43(3): 118-124.
[6]	叶晓彤, 刘周斌, 邵苏杰, 亓峰. 基于博弈论的WiFi接入资源动态分配算法[J]. 北京邮电大学学报, 2020, 43(2): 10-15,58.
[7]	管焱然, 奥利弗·范凯克, 管有庆. 基于重心映射的三角形网格参数化方法研究与实现[J]. 北京邮电大学学报, 2019, 42(5): 83-90.
[8]	段治健, 谢公南, 张迎春. 隐式超松弛LU-SGS间断Galerkin算法[J]. 北京邮电大学学报, 2019, 42(5): 8-14.
[9]	付卫红, 胡展. 一种混合网台跳频参数盲估计算法[J]. 北京邮电大学学报, 2019, 42(4): 57-63.
[10]	李志沛, 王曦朔, 刘博, 张琦, 忻向军. 一种适用于概率成形光传输系统的调制格式识别方法[J]. 北京邮电大学学报, 2019, 42(3): 79-82,126.
[11]	赵海英, 谭欣, 王亮亮. 基于E-OEM的SWF半结构化模型建立[J]. 北京邮电大学学报, 2017, 40(5): 129-134.
[12]	谭志远, 陈磊, 李曦, 纪红. 异构蜂窝网络中用户非均匀分布的CRE和eICIC优化[J]. 北京邮电大学学报, 2017, 40(2): 11-15.
[13]	谢显中, 李传文, 杨和林. 认知D2D通信中基于博弈论的动态频谱分配方案[J]. 北京邮电大学学报, 2017, 40(2): 43-48.
[14]	马英杰, 李亚, 谢绒娜. 立体网格多涡卷混沌系统及其电路实现[J]. 北京邮电大学学报, 2017, 40(2): 84-87.
[15]	冯筠, 刘飞鸿, 李盼, 卜起荣, 王红玉. 基于格式塔认知框架的腹腔CT多目标分割算法[J]. 北京邮电大学学报, 2016, 39(5): 51-55.

改进的格上基于多身份全同态加密方案

Improved Multi-Identity Based Fully Homomorphic Encryption Scheme over Lattices

PDF

可视化

摘要/Abstract

引用本文

使用本文

参考文献

相关文章 15

编辑推荐

Metrics

本文评价