[1] SHAMIR A.Identity-based cryptosystems and signature schemes[C]//Proceedings of CRYPTO'84.Berlin,Germany:Springer,1985:47-53. [2] GENTRY C,SILVERBERG A.Hierarchical ID-based crypto-graphy[C]//Proceedings of International Conference on the Theory and Application of Cryptology and Information Security.Berlin,Germany:Springer,2002:236-250. [3] HORWITZ J,LYNN B.Toward hierarchical identity-based encryption[C]//Proceedings of International Conference on the Theory and Applications of Cryptographic Techniques.Berlin,Germany:Springer,2002:466-481. [4] GENTRY C,HALEVI S.Hierarchical identity based encryption with polynomially many levels[C]//Proceedings of Theory of Cryptography Conference.Berlin,Germany:Springer,2009:437-456. [5] YAN Xixi,LIU Yuan,HU Mingxing,et al.LWE-based multi-authority attribute-based encryption scheme in cloud environment[J].Netinfo Security,2017(9):128-133.(in Chinese) 闫玺玺,刘媛,胡明星,等.云环境下基于LWE的多机构属性基加密方案[J].信息网络安全,2017(9):128-133. [6] YAN Xixi,LIU Yuan,LI Zichen,et al.A privacy-preserving multi-authority attribute-based encryption scheme on ideal lattices in the cloud environment[J].Netinfo Security,2017(8):19-25.(in Chinese) 闫玺玺,刘媛,李子臣,等.云环境下理想格上的多机构属性基加密隐私保护方案[J].信息网络安全,2017(8):19-25. [7] YAN Xixi,LIU Yuan,LI Zichen,et al.A privacy-preserving multi-authority attribute-based encryption scheme on ideal lattices in the cloud environment[J].Netinfo Security,2017(8):19-25. [8] GENTRY C,PEIKERT C,VAIKUNTANATHAN V.Trapdoors for hard lattices and new cryptographic constructions[C]//Proceedings of the 40th Annual ACM Symposium on Theory of Computing.New York,USA:ACM Press,2008:17-20. [9] CASH D,HOFHEINZ D,KILTZ E,et al.Bonsai trees,or how to delegate a lattice basis[C]//Proceedings of the 29th Annual International Conference on Theory and Applications of Cryptographic Techniques.Berlin,Germany:Springer,2010:523-552. [10] AGRAWAL S,BONEH D,BOYEN X.Lattice basis delegation in fixed dimension and shorter-ciphertext hierarchical IBE[C]//Proceedings of the 30th Annual Conference on Advances in Cryptology.Berlin,Germany:Springer,2010:98-115. [11] AGRAWAL S,DAN B,BOYEN X.Efficient lattice (H)IBE in the standard model[C]//Proceedings of International Conference on Theory and Applications of Cryptographic Techniques.Berlin,Germany:Springer,2010:553-572. [12] SINGH K,PANDURANGAN C,BANERJEE A K.Adaptively secure efficient lattice (H)IBE in standard model with short public parameters[M]//CHAKRABORTY R S.Security,privacy,and applied cryptography engineering.Berlin,Germany:Springer,2012:153-172. [13] YANG Chunli,ZHENG Shihui,WANG Licheng,et al.Hierarchical identity-based broadcast encryption scheme from LWE[J].Journal of Communications and Networks,2014,16(3):258-263. [14] MICCIANCIO D,PEIKERT C.Trapdoors for lattices:simpler,tighter,faster,smaller[C]//Proceedings of Annual International Conference on the Theory and Applications of Cryptographic Techniques.Berlin,Germany:Springer,2012:700-718. [15] GENTRY C,PEIKERT C,VAIKUNTANATHAN V.How to use a short basis:trapdoors for hard lattices and new cryptographic constructions[EB/OL].[2018-11-05].https://eprint.iacr.org/2007/432.pdf. [16] YE Qing,HU Mingxing,TANG Yongli,et al.Novel hierarchical identity-based encryption scheme from lattice[J].Journal on Communications,2017,38(11):54-64.(in Chinese) 叶青,胡明星,汤永利,等.新的格上基于身份的分级加密方案[J].通信学报,2017,38(11):54-64. [17] YE Qing,HU Mingxing,TANG Yongli,et al.Efficient hierarchical identity-based encryption scheme from learning with errors[J].Journal of Computer Research and Development,2017,54(10):2193-2204.(in Chinese)叶青,胡明星,汤永利,等.基于LWE的高效身份基分级加密方案[J].计算机研究与发展,2017,54(10):2193-2204. [18] HOFHEINZ D,KILTZ E.Programmable hash functions and their applications[J].Journal of Cryptology,2012,25(3):484-527. [19] CATALANO D,FIORE D,NIZZARDO L.Programmable hash functions go private:constructions and applications to (homomorphic) signatures with shorter public keys[C]//Proceedings of Annual Cryptology Conference.Berlin,Germany:Springer,2015:84-85. [20] ZHANG Jiang,CHEN Yu,ZHANG Zhenfeng.Programmable hash functions from lattices:short signatures and IBEs with small key sizes[C]//Proceedings of Annual International Cryptology Conference.Berlin,Germany:Springer,2016:303-332. [21] CASH D,HOFHEINZ D,KILTZ E.How to delegate a lattice basis[J].Manuscript,2009,25(4):601-639. |