基于RLWE的全同态加密方案

doi:10.3969/j.issn.1000-436x.2014.01.020

通信学报 ›› 2014, Vol. 35 ›› Issue (1): 173-182.doi: 10.3969/j.issn.1000-436x.2014.01.020

基于RLWE的全同态加密方案

汤殿华¹,祝世雄¹,王林¹,杨浩淼²,范佳¹

¹ 保密通信重点实验室，四川成都 610041
² 电子科技大学计算机学院，四川成都 610054

出版日期:2014-01-25 发布日期:2017-06-17
基金资助:
国家自然科学基金资助项目

Fully homomorphic encryption scheme from RLWE

Dian-hua TANG¹,Shi-xiong ZHU¹,Lin WANG¹,Hao-miao YANG²,Jia FAN¹

¹ Science and Technology on Communication Security Laboratory,Chengdu 610041,China
² College of Computer Science ＆ Engineering,UEST of China,Chengdu 610054,China

Online:2014-01-25 Published:2017-06-17

摘要/Abstract

摘要：

基于Kristin Lauter等人的somewhat同态方案，提出“带密钥转换的重线性化技术”。结合该技术与“模转换”，设计了一个基于RLWE的非自举的层次化全同态加密方案。该方案的同态操作简单，而且给出的平凡门操作使得电路层结构更清晰。最后利用自举技术作为优化提升了方案的同态运算能力。

关键词: 全同态加密, 重线性化, 模转换

Abstract:

Based on the somewhat homomorphic scheme of Kristin Lauter et al.a new technique,called Relinearization with key switching was presented.Combining this technique with modulus switching,a (leveled) fully homomorphic encryption scheme without bootstrapping from RLWE were designed.Homomorphic operations of this scheme is simple,and trivial gate operation given in the scheme can make level structure of circuit clearer.Finally,bootstrapping was used as optimization to evaluate capability of the proposed scheme.

Key words: fully homomorphic encryption, relinearization, modulus switching

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.

Dian-hua TANG,Shi-xiong ZHU,Lin WANG,Hao-miao YANG,Jia FAN. Fully homomorphic encryption scheme from RLWE[J]. Journal on Communications, 2014, 35(1): 173-182.

图/表 1

参考文献 19

[1]	RIVEST R L , ADLEMAN L , DERTOUZOS M L . On data banks and privacy homomorphisms[A]. Foundations of Secure Computation[C]. 1978. 169-180.
[2]	PAILLIER P . Public-key cryptosystems based on composite degree residuosity classes[A]. EUROCRYPT'99[C]. Spring, 1999. 223-238.
[3]	RIVEST R L , SHAMIR A , ADLEMAN L . A method for obtaining digital signatures public key cryptosystem[J]. Communication of ACM, 1978,21(1): 120-126.
[4]	BONEH D , GOH E J , NISSIM K . Evaluating 2-DNF formulas on ciphertexts[A]. Proceedings of Theory of Cryptography Conference 2005[C]. 2005. 325-342.
[5]	GENTRY C . Fully homomorphic encryption using ideal lattices[A]. The 41st ACM Symposium on Theory of Computing (STOC)[C]. 2009. 169-178.
[6]	GENTRY C . A Fully Homomorphic Encryption Scheme[D]. Standford:Stanford University, 2009.
[7]	DIJK M , GENTRY C , HALEVI S ,et al. Fully homomorphic encryptionover the integers[A]. Cryptology-EUROCRYPT’10[C]. 2010. 24-43.
[8]	SMART N , VERCAUTEREN F . Fully homomorphic encryption with relatively small key and ciphertext sizes[A]. PKC 2010[C]. 2010. 420-443.
[9]	GENTRY C , HALEVI S . Implementing gentry’s fully-homomorphic encryption scheme[A]. EUROCRYPT,Lecture Notes in Computer Science[C]. 2011. 129-148.
[10]	GENTRY C , HALEVI S . Fully homomorphic encryption without squashing using depth-3 arithmetic circuits[EB/OL]. , 2011.
[11]	BRAKERSKI Z , VAIKUNTANATHAN V . Efficient fully homomorphic encryption from (standard)lwe[EB/OL]. , 2011.
[12]	BRAKERSKI Z , GENTRY C . Fully homomorphic encryption without bootstrapping[EB/OL]. , 2011.
[13]	LAUTER K , NAEHRIG M , VAIKUNTANATHAN V . Can homo morphic encryption be practical?[EB/OL]. , 2011.
[14]	LYUBASHEVSKY V , PEIKERT C , REGEV O . On ideal lattices and learning with errors over rings[A]. EUROCRYPT,Lecture Notes in Computer Science[C]. 2010. 1-23.
[15]	MICCIANCIO D , REGEV O . Worst-case to average-case reductions based on gaussian measures[J].SIAM J Comput,2007.37(1):267-302.　　　　　　　SIAM J Comput, 2007,37(1): 267-302.
[16]	KARP R M , RAMACHANDRAN V . A Survey of Parallel Algorithms for Shared-Memory Machines[R]. Technical Report CSD-88-408,UC Berkeley, 1988.
[17]	LINDNER R , PEIKERT C . Better key sizes (and attacks) for LWE-based encryption[A]. Cryptology-CT-RSA 2011,Lecture Notes in Computer Science[C]. 2011. 319-339.
[18]	BANASZCZYK W . New bounds in some transference theorems in the geometry of numbers[J]. Mathematische Annalen, 1993,296(4): 625-635.
[19]	GAMA N , NGUYEN P Q . Predicting lattice reduction[A]. Cryptology-EUROCRYPT 2008,Lecture Notes in Computer Science[C]. Springer, 2008. 31-51.

基于RLWE的全同态加密方案

Fully homomorphic encryption scheme from RLWE

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 1

参考文献 19

相关文章 8

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]	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.
[4]	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.
[5]	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.
[6]	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.
[7]	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.
[8]	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.