环上基于属性的全同态加密体制设计

doi:10.11959/j.issn.1000-436x.2017077

通信学报 ›› 2017, Vol. 38 ›› Issue (4): 55-63.doi: 10.11959/j.issn.1000-436x.2017077

环上基于属性的全同态加密体制设计

郑永辉^1,²,康元基³,顾纯祥^1,²,董辉³

¹ 信息工程大学，河南郑州 450002
² 数学工程与先进计算国家重点实验室，江苏无锡 214125
³ 中国人民解放军66136部队，北京 100043

修回日期:2017-02-23 出版日期:2017-04-01 发布日期:2017-07-20
作者简介:郑永辉（1976-），男，江西乐平人，博士，信息工程大学讲师，主要研究方向为密码学。|康元基（1992-），男，辽宁凤城人， 66136部队助理工程师，主要研究方向为全同态加密。|顾纯祥（1976-），男，安徽霍山人，博士，信息工程大学副教授，主要研究方向为密码学。|董辉（1982-），男，河北丰南人，66136部队工程师，主要研究方向为模拟计算。
基金资助:
河南省科技创新杰出青年基金资助项目(134100510002);河南省基础与前沿技术研究基金资助项目(142300410002);数学工程与先进计算国家重点实验室开放基金资助项目

Attribute-based fully homomorphic encryption scheme over rings

Yong-hui ZHENG^1,²,Yuan-ji KANG³,Chun-xiang GU^1,²,Hui DONG³

¹ Information Engineering University,Zhengzhou 450002,China
² State Key Laboratory of Mathematical Engineering and Advanced Computing,Wuxi 214125,China
³ 66136 Troop of PLA,Beijing 100043,China

Revised:2017-02-23 Online:2017-04-01 Published:2017-07-20
Supported by:
The Province Foundation for Science Innovation Distinguished Young Scholars of Henan Province(134100510002);Henan Province Foundation and Advanced Technology Study(142300410002);State Key Laboratory of Mathematical Engineering and Advanced Computing Open Foundation

摘要/Abstract

摘要：

全同态加密在云计算的数据和隐私安全领域有重要应用，但现有全同态加密体制普遍存在密钥、密文尺寸偏大的弊端，严重制约其实用性。为此，以环上容错学习问题为基础，提出环上重编码体制与基于属性加密体制，并与全同态加密体制结合，构造基于属性的全同态加密体制，该体制无需公钥证书，可实现对加密数据细粒度访问控制，与已有同类成果相比，大大缩短了密钥与密文尺寸。

关键词: RLWE问题, 重编码, 基于属性加密, 全同态加密

Abstract:

The fully homomorphic encryption has important applications in the area of data security and privacy security of cloud computing,but the size of secret keys and ciphertext in most of current homomorphic encryption schemes were too large,which restricted its practical.To improve these drawbacks,a recoding scheme and a attribute-based encryption scheme based on learning with errors problem over rings were provided,then a attribute-based fully homomorphic encryption was constructed.The new scheme overcame the above mentioned drawbacks,because it did't need public key certificate,meanwhile,it can achieve the fine-grained access control to the ciphertext.Compared with similar results,proposed method decreases the size of keys and ciphertext greatly.

Key words: RLWE problem, recode, attribute-based encryption, fully homomorphic encryption

中图分类号:

TP309

郑永辉,康元基,顾纯祥,董辉. 环上基于属性的全同态加密体制设计[J]. 通信学报, 2017, 38(4): 55-63.

Yong-hui ZHENG,Yuan-ji KANG,Chun-xiang GU,Hui DONG. Attribute-based fully homomorphic encryption scheme over rings[J]. Journal on Communications, 2017, 38(4): 55-63.

图/表 3

参考文献 18

[1]	RIVEST R L , ADLEMAN L , DERTOUZOS M L . On data banks and privacy homomorphisms[J]. Foundations of Secure Computation, 1978,4(11): 169-180.
[2]	GENTRY C , . Fully homomorphic encryption using ideal lattices[C]// STOC, 2009,9: 169-178.
[3]	DUK M V , GENTRY C , HALEVI S ,et al. Fully homomorphic encryption over the integers[C]// The 29th Annual Eurocrypt Conference. Riviera,French, 2010: 24-43.
[4]	SMART N P , VERCAUTEREN F . Fully homomorp-hic encryption with relatively small key and cipher-ext sizes[C]// The 13th International Conference on Practive and Theory in Public Key Cryptography(PKC2010). Paris,France, 2010: 420-443.
[5]	GENTRY C , HALEVI S . Implementing gentry's fully homomorphic encryption scheme[C]// EUROCRYP-T,Lecture Notes in Computer Science. 2011: 129-148.
[6]	BRAKERSKI Z , VAIKUNTANATHAN V . Efficient fully homomorphic encryption from (standard) LWE[J]. SIAM Journal on Computing, 2014,43(2): 831-871.
[7]	BRAKERSKI Z , VAIKUNTANATHAN V . Fully homomorphic encryption from ring-LWE and security for key dependent messages[M]. Advances in Cryptology CRYPTO 2011. Springer Berlin Heidelberg, 2011: 505-524.
[8]	REGEV O . On lattices,learning with errors,random linear codes,and cryptography[J]. Journal of the ACM (JACM), 2009,56(6): 34.
[9]	LYUBASHEVSKY V , PEIKERT C , REGEV O . On ideal lattices and learning with errors over rings[J]. Journal of the ACM (JACM), 2013,60(6): 43.
[10]	BRAKERSKI Z , Gentry C , VAIKUNTANATHAN V . (Leveled) fully homomorphic encryption without bootstrapping[C]// The 3rd Innovations in Theoretical Computer Science Conference. ACM, 2012: 309-325.
[11]	SAHAI A , WATERS B . Fuzzy identity-based encryption[M]. Advances in Cryptology–EUROCRYPT 2005. Springer Berlin Heidelberg, 2005: 457-473.
[12]	GOYAL V , PANDEY O , SAHAI A ,et al. Attribute-based encryption for fine-grained access control of encrypted data[C]// Proceedings of the 13th ACM Conference on Computer and Communications Security. ACM, 2006: 89-98.
[13]	SHAMIR A , . Identity-based cryptosystems and signa-ture schemes[C]// Advances in Cryptology. Springer Berlin Heidelberg, 1985: 47-53.
[14]	GORBUNOY S , VAIKUNTANATHAN V , WEE H . Attribute-based encryption for circuits[J]. Journal of the ACM (JACM), 2015,62(6): 45.
[15]	GENTRY C , SAHAI A , WATERS B . Homomorphic encryption from learning with errors:conceptually-simpler,asymptotically-faster,attribute-based[M]. Advances in Cryptology–CRYPTO 2013. Springer Berlin Heidelberg, 2013: 75-92.
[16]	LYUBASHEVSKY V , PEIKERT C , REGEV O . A toolkit for ring-LWE cryptography[M]. Advances in Cryptology–EUROCRYPT 2013. Springer Berlin Heidelberg, 2013: 35-54.
[17]	KANG Y J , GU C X , ZHENG Y H ,et al. Identity-based fully homomorphism encryption from eigenvector[J]. Journal of Software,doi:10.13328/j.cnki.jos.004991.
[18]	GENTRY C , PEIKERT C , VAIKUNTANATHAN V . Trapdoors for hard lattices and new cryptographic constructions[C]// The 40th Annual ACM Symposium on Theory of Computing. ACM, 2008: 197-206.

参数	TOR	RTOR
n	256	256
lbq	80	107
d	4	4
公钥尺寸	40 MB	856 KB
重编码密钥尺寸	6.25 GB	3.34 MB
重编码复杂度	8.39×10⁷次乘8.39×10⁷次加	8.39×10⁶次乘8.42×10⁶次加

参数	GVW	RABE
n	256	256
lb q	80	107
公钥尺寸	320 MB	6.79 MB
密文尺寸	640 KB	883 KB
ReKeyGen算法复杂度	5.04×10⁸次乘5.04×10⁸次加	5.04×10⁷次乘5.06×10⁷次加
是否可使用SIMD技术	否	是

参数	GSW	RABFHE
n	256	256
l′	81	107
N	6 553 680	3 531
公钥尺寸	320 MB	6.79 MB
私钥尺寸	6.33 MB	883 KB
密文尺寸	22.26 GB	2.97 GB

环上基于属性的全同态加密体制设计

Attribute-based fully homomorphic encryption scheme over rings

在线阅读

PDF下载

可视化

被引次数

摘要/Abstract

引用本文

使用本文

图/表 3

参考文献 18

相关文章 15

Metrics

推荐阅读 0

[1]	杨亚涛, 刘德莉, 刘培鹤, 曾萍, 肖嵩. BFV-Blockchainvoting：支持BFV全同态加密的区块链电子投票系统[J]. 通信学报, 2022, 43(9): 100-111.
[2]	田有亮,李秋贤,张铎,王琳杰. 可证明安全的理性委托计算协议[J]. 通信学报, 2019, 40(7): 135-143.
[3]	冯朝胜,罗王平,秦志光,袁丁,邹莉萍. 支持多种特性的基于属性代理重加密方案[J]. 通信学报, 2019, 40(6): 177-189.
[4]	丁晟,曹进,李晖. 基于OBDD访问结构的无配对CP-ABE方案[J]. 通信学报, 2019, 40(12): 1-8.
[5]	汤永利,胡明星,刘琨,叶青,闫玺玺. 新的格上基于身份的全同态加密方案[J]. 通信学报, 2017, 38(5): 39-47.
[6]	段然,顾纯祥,祝跃飞,郑永辉,陈莉. 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.
[7]	孙泽栋,祝跃飞,顾纯祥,郑永辉. 基于RLWE的密钥策略属性加密体制[J]. 通信学报, 2016, 37(Z1): 125-131.
[8]	马海英,曾国荪,陈建平,王金华,王占君. 适应性安全的可追踪叛徒的基于属性加密方案[J]. 通信学报, 2016, 37(1): 76-87.
[9]	魏江宏，刘文芬，胡学先. 前向安全的密文策略基于属性加密方案[J]. 通信学报, 2014, 35(7): 5-45.
[10]	马海英，曾国荪，王占君，王伟. 高效可证明安全的基于属性的在线/离线加密机制[J]. 通信学报, 2014, 35(7): 13-112.
[11]	魏江宏,刘文芬,胡学先. 前向安全的密文策略基于属性加密方案[J]. 通信学报, 2014, 35(7): 38-45.
[12]	马海英,曾国荪,王占君,王伟. 高效可证明安全的基于属性的在线/离线加密机制[J]. 通信学报, 2014, 35(7): 104-112.
[13]	光焱,祝跃飞,费金龙,顾纯祥,郑永辉. 利用容错学习问题构造基于身份的全同态加密体制[J]. 通信学报, 2014, 35(2): 111-117.
[14]	光焱1,2，祝跃飞1，费金龙1,2，顾纯祥1,2，郑永辉1,2. 利用容错学习问题构造基于身份的全同态加密体制[J]. 通信学报, 2014, 35(2): 15-117.
[15]	汤殿华,祝世雄,王林,杨浩淼,范佳. 基于RLWE的全同态加密方案[J]. 通信学报, 2014, 35(1): 173-182.