计算机科学 ›› 2019, Vol. 46 ›› Issue (3): 209-216.doi: 10.11896/j.issn.1002-137X.2019.03.031
李孟天,胡斌
LI Meng-tian, HU Bin
摘要: 信息技术和网络通信的不断发展促使了大数据与云计算的产生,用户的数据安全和隐私保护逐渐成为学术界的研究重点。全同态加密是近年来新兴的一门研究学科,有着广阔的应用前景和重要的研究意义,能够支持在密文上做任意运算,且解密后等同于对明文做相同的操作,这一特性在云计算的安全性上有着重要应用。2011年,Lauter等提出了基于RLWE的同态加密方案,针对该方案,文中结合批处理技术设计了一种新的方案,利用中国剩余定理将多个“明文槽”打包到一个密文中,并进行同态运算操作。每次密文乘法操作后会造成噪声的指数增长,通过调用构造的密钥转换技术和模转换技术,来约减密文的噪声尺寸,保证能够正确解密且进行下一次同态运算。最后,对方案的安全性和效率进行了分析,结果表明在保证CPA安全的前提下,所提方案的加密效率是原始方案的n倍。
中图分类号:
[1]FENG D G,ZHANG M,ZHANG Y,et al.Study on Cloud Computing Security [J].Journal of Software,2011,22(1):71-83.(in Chinese) 冯登国,张敏,张妍,等.云计算安全研究[J].软件学报,2011,22(1):71-83. [2]RIVEST R L,ADLMAN L,DERTOUZOS M L.On data banks and privacy homomorphisms[J].Foundations of Secure Computation,1978,4(11):169-180. [3]GENTRY C.Fully homomorphic encryption using ideal lattices[C]∥Proc.of the 41st Annual ACM Symposium on Theory of Computing.New York:ACM Press,2009:169-178. [4]GENTRY C,HALEVI S.Implementing Gentry’s Fully-Homomorphic Encryption Scheme[C]∥EUROCRYPT.2011:129-148. [5]SMART N P,VERCAUTEREN F.Fully homomorphic SIMD operations[J].Designs,Codes and Cryptography,2014,71(1):57-81. [6]BRAKERSKI Z,VAIKUNTANATHAN V.Efficient Fully Ho- momorphic Encryption from (Standard) LWE[C]∥Foundations of Computer Science.IEEE,2011:97-106. [7]GENTRY C,HALEVI S,SMART N P.Fully homomorphic encryption with polylog overhead[C]∥Annual International Conference on the Theory and Applications of Cryptographic Techniques.Springer,Berlin,Heidelberg,2012:465-482. [8]NAEHRIG M,LAUTER K,VAIKUNTANATHAN V.Can homomorphic encryption be practical?[C]∥Proceedings of the 3rd ACM Workshop on Cloud Computing Security Workshop.ACM,2011:113-124. [9]LIDL R,NIEDERREITER H.Finite fields[M].Cambridge: Cambridge University Press,1997. [10]LYUBASHEVSKY V,PEIKERT C,REGEV O.On ideal lattices and learning with errors over rings[C]∥Annual International Conference on the Theory and Applications of Cryptographic Techniques.Springer,Berlin,Heidelberg,2010:1-23. [11]BRAKERSKI Z,GENTRY C,VAIKUNTANATHAN V.(Le- veled) fully homomorphic encryption without bootstrapping[J].ACM Transactions on Computation Theory (TOCT),2014,6(3):13. [12]MICCIANCIO D.The shortest vector in a lattice is hard to approximate to within some constant[J].SIAM Journal on Computing,2001,30(6):2008-2035. [13]GAMA N,NGUYEN P.Predicting lattice reduction[C]∥Advances in Cryptology-EUROCRYPT 2008.2008:31-51. [14]LINDNER R,PEIKERT C.Better Key Sizes (and Attacks) for LWE-Based Encryption[C]∥CT-RSA.2011:319-339. [15]GENTRY C.A fully homomorphic encryption scheme[D].Stanford University,2009. [16]CHEON J,KIM J,LEE M,et al.CRT-based fully homomorphic encryption over the integers[J].Information Sciences,2015,310:149-162. [17]REGEV O.On lattices,learning with errors,random linear codes,and cryptography[C]∥Acm Symposium on Theory of Computing.ACM,2005. |
[1] | 秦小月, 黄汝维, 杨波. 基于素数幂次阶分圆环的NTRU型全同态加密方案 NTRU Type Fully Homomorphic Encryption Scheme over Prime Power Cyclotomic Rings 计算机科学, 2022, 49(5): 341-346. https://doi.org/10.11896/jsjkx.210300089 |
[2] | 史经启,杨庚,孙彦珺,白双杰,闵兆娥. 支持浮点运算的高效并行全同态加密算法 Efficient Parallel Algorithm of Fully Homomorphic Encryption Supporting Operation of Floating-point Number 计算机科学, 2018, 45(5): 116-122. https://doi.org/10.11896/j.issn.1002-137X.2018.05.020 |
[3] | 毛和风, 胡斌. 基于整数的轻量级分组密码电路的同态运算 Homomorphic Evaluation of Lightweight Block Cipher over Integers 计算机科学, 2018, 45(11): 169-175. https://doi.org/10.11896/j.issn.1002-137X.2018.11.026 |
|