JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2017, Vol. 52 ›› Issue (5): 85-94.doi: 10.6040/j.issn.1671-9352.0.2017.090

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An efficient multi-identity-based fully homomorphic encryption scheme

WANG Wei-li, HU Bin, ZHAO Xiu-feng   

  1. School of Cryptography Engineering, The PLA Information Engineering University, Zhengzhou 450001, Henan, China
  • Received:2017-03-07 Online:2017-05-20 Published:2017-05-15

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Abstract: An efficient identity-based encryption scheme is constructed by efficient trapdoor generation algorithm. The security of the scheme can be reduced to the standard LWE problem, which greatly reduces the lattic security dimension and reduces the key scale and computational complexity. In order to convert single-identity-based FHE scheme, the approximate singular vectors, original image matrix and sub Gaussian variable were utilized. Whats more, the noise expansion rate is reduced from O(n) to O(n0.5). Finally, we took advantage of extended cipher in conjunction with the masking scheme to construct an efficient multi-identity-based fully homomorphic encryption scheme.

Key words: identity-based encryption, identity-based fully homomorphic encryption, fully homomorphic encryption, LWE problem

CLC Number: 

  • TN918
[1] GENTRY C. Fully homomorphic encryption using ideal lattices[C] // Proceedings of the 2009 ACM Symposium on Theory of Computing. New York: Assoc Computing Machinery, 2009: 169-178.
[2] BONEH D, FRANKLIN M. Identity-based encryption from the Weil pairing[C] // Advances in Cryptology-CRYPTO 2001, Heidelberger: Springer-Verlag Berlin, 2001: 213-229.
[3] COCKS C. An identity based encryption scheme based on quadratic residues[C] // Proceedings of IMA International Conference on Cryptography and Coding. Heidelberger: Springer-Verlag Berlin, 2001: 360-363.
[4] GENTRY C, SAHAI A, WATERS B. Homomorphic encryption from learning with errors: conceptually-simpler, asymptotically-faster, attribute-based [C] //Advances in Cryptology-CRYPTO 2013. Heidelberger: Springer-Verlag Berlin, 2013: 75-92.
[5] 光焱,祝跃飞,费金龙,等. 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,2014,02:111-117. GUANG Yan, ZHU Yuefei, FEI Jinlong, et al. Identity-based fully homomorphic encryption from learning with error problem[J]. Journal on Communications, 2014(2):111-117.
[6] CLEAR M, MCGOLDRICK C. Bootstrappable identity-based fully homomorphic encryption[C] // Proceedings of International Conference on Cryptology and Network Security. Switzerland: Springer International Publishing AG, 2014: 1-19.
[7] GARG S, GENTRY C, HALEVI S,et al. Candidate indistinguishability obfuscation and functional encryption for all circuits[J]. SIAM Journal on Computing, 2016, 45(3):882-929.
[8] CLEAR M, MCGOLDRICK C. Multi-identity and multi-key leveled FHE from learning with errors[C] // Advances in Cryptology - CRYPTO 2015. Berlin: Springer, 2015: 630-656.
[9] 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.
[10] MICCIANCIO D, PEIKERT C.Trapdoors for lattices: simpler, tighter, faster, smaller[C] // Advances in Cryptology—EUROCRYPT 2012. Heidelberger: Springer-Verlag Berlin, 2012: 700-718.
[11] AGRAWAL S, BONEH D, BOYEN X. Efficient lattice(H)IBE in the standard model[C] // Advances in Cryptology—EUROCRYPT 2010. Heidelberger: Springer-Verlag Berlin, 2010: 553-572.
[12] REGEV O. On lattices, learning with errors, random linear codes, and cryptography[J]. ACM Symposium on Theory of Computing, 2005, 56(6):84-93.
[13] ELDAR Y C, KUTYNIOK G. Compressed sensing: theory and applications[M]. Cambridge: Cambridge University Press, 2012.
[14] 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: ACM, 2008: 197-206.
[15] SHOUP V. A computational introduction to number theory and algebra[M]. Cambridge: Cambridge University Press, 2009.
[16] MUKHERJEE P, WICHS D. Two round MPC from LWE via multi-key FHE[J]. IACR Cryptology ePrint Archive, 2015, 2015:345.
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