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Home > Archive>Volume 27, Issue 6, 2016 >1487-1497. DOI:10.13328/j.cnki.jos.004991
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Identity-Based Fully Homomorphic Encryption from Eigenvector
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The Province Foundation for Science Innovation Distinguished Young Scholars of He’nan (134100510002); He’nan Province foundation and Advanced Technology Study (142300410002); State Key Laboratory of Mathematical Engineering and Advanced Computing Open Foundation

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    Abstract:

    Fully homomorphic encryption allows valid operation on encrypted data without decrypting, providing a new solution to data confidentiality and privacy protection. However, current fully homomorphic encryption schemes are faced with challenges like large size of public key or low efficiency in calculation. To achieve an efficient fully homomorphic encryption scheme, this work provides an identity-based fully homomorphic encryption scheme employing the idea of eigenvector and arbitrary cyclotomic rings. Compared with existing scheme, this identity-based fully homomorphic encryption with eigenvector is able to successfully avoid the evaluation key, resulting a true identity-based scheme. Compared with special cyclotomic rings whose degree is power of 2, utilizing arbitrary cyclotomic rings may double the efficiency of encryption schemes and further improve the efficiency of calculation and memory using SIMD technique.

    Reference
    [1] Rivest RL, Adleman L, Dertouzos ML. On data banks and privacy homomorphisms. Foundations of Secure Computation, 1978, 4(11):169-180.
    [2] Gentry C. Fully homomorphic encryption using ideal lattices. 2009,9:169-178. http://www.cs.cmu.edu/~odonnell/hits09/gentry- homomorphic-encryption.pdf [doi: 10.1145/1536414.1536440]
    [3] Smart NP, Vercauteren F. Fully homomorphic encryption with relatively small key and ciphertext sizes. In: Proc. of the Public Key Cryptography (PKC 2010). Berlin, Heidelberg: Springer-Verlag, 2010. 420-443. [doi: 10.1007/978-3-642-13013-7_25]
    [4] Van Dijk M, Gentry C, Halevi S, Vaikuntanathan V. Fully homomorphic encryption over the integers. In: Proc. of the Advances in Cryptology (EUROCRYPT 2010). Berlin, Heidelberg: Springer-Verlag, 2010. 24-43. [doi: 10.1007/978-3-642-13190-5_2]
    [5] Smart NP, Vercauteren F. Fully homomorphic SIMD operations. Designs, Codes and Cryptography, 2014,71(1):57-81. [doi: 10.1007/s10623-012-9720-4]
    [6] Shoup V. A Computational Introduction to Number Theory and Algebra. Cambridge University Press, 2009. [doi: 10.1017/ CBO 9781139165464]
    [7] Stehlé D, Steinfeld R. Faster fully homomorphic encryption. In: Proc. of the Advances in Cryptology (ASIACRYPT 2010). Berlin, Heidelberg: Springer-Verlag, 2010. 377-394. [doi: 10.1007/978-3-642-17373-8_22]
    [8] Brakerski Z, Vaikuntanathan V. Efficient fully homomorphic encryption from (standard) LWE. SIAM Journal on Computing, 2014, 43(2):831-871. [doi: 10.1109/focs.2011.12]
    [9] Regev O. On lattices, learning with errors, random linear codes, and cryptography. Journal of the ACM, 2009,56(6):34. [doi: 10. 1145/1060590.1060603]
    [10] Peikert C. Public-Key cryptosystems from the worst-case shortest vector problem. In: Proc. of the 41st Annual ACM Symp. on Theory of Computing. ACM Press, 2009. 333-342. [doi: 10.1145/1536414.1536461]
    [11] Brakerski Z, Gentry C, Vaikuntanathan V. (Leveled) fully homomorphic encryption without bootstrapping. In: Proc. of the 3rd Innovations in Theoretical Computer Science Conf. ACM Press, 2012. 309-325. [doi: 10.1145/2090236.2090262]
    [12] Lyubashevsky V, Peikert C, Regev O. On ideal lattices and learning with errors over rings. Journal of the ACM, 2013, 60(6):43. [doi: 10.1145/2535925]
    [13] Brakerski Z, Vaikuntanathan V. Fully homomorphic encryption from ring-LWE and security for key dependent messages. In: Proc. of the Advances in Cryptology (CRYPTO 2011). Berlin, Heidelberg: Springer-Verlag, 2011. 505-524. [doi: 10.1007/978-3-642- 22792-9_29]
    [14] Lyubashevsky V, Peikert C, Regev O. A toolkit for ring-LWE cryptography. In: Proc. of the Advances in Cryptology (EUROCRYPT 2013). Berlin, Heidelberg: Springer-Verlag, 2013. 35-54. [doi: 10.1007/978-3-642-38348-9_3]
    [15] Shamir A. Identity-Based cryptosystems and signature schemes. In: Proc. of the Advances in Cryptology. Berlin, Heidelberg: Springer-Verlag,1985. 47-53. [doi: 10.1007/3-540-39568-7_5]
    [16] Boneh D, Lynn B, Shacham H. Short signatures from the Weil pairing. In: Proc. of the Advances in Cryptology (ASIACRYPT 2001). Berlin, Heidelberg: Springer-Verlag, 2001. 514-532. [doi: 10.1007/3-540-45682-1_30]
    [17] Cocks C. An identity based encryption scheme based on quadratic residues. In: Proc. of the Cryptography and Coding. Berlin, Heidelberg: Springer-Verlag, 2001. 360-363. [doi: 10.1007/3-540-45325-3_32]
    [18] Gentry C, Peikert C, Vaikuntanathan V. Trapdoors for hard lattices and new cryptographic constructions. In: Proc. of the 40th Annual ACM Symp. on Theory of Computing. ACM Press, 2008. 197-206. [doi: 10.1145/1374376.1374407]
    [19] Guang Y, Gu CX, Zhu YF, Zheng YH, Fei JL. Identity-Based fully homomorphic encryption from learning with error problem. Journal on Communications, 2014,35(2):111-117 (in Chinese with English abstract).
    [20] Gentry C, Sahai A, Waters B. Homomorphic encryption from learning with errors: Conceptually-Simpler, asymptotically-faster, attribute-based. In: Proc. of the Advances in Cryptology (CRYPTO 2013). Berlin, Heidelberg: Springer-Verlag, 2013. 75-92. [doi: 10.1007/978-3-642-40041-4_5]
    [21] Gentry C, Halevi S, Smart NP. Fully homomorphic encryption with polylog overhead. In: Proc. of the Advances in Cryptology (EUROCRYPT 2012). Berlin, Heidelberg: Springer-Verlag, 2012. 465-482. [doi: 10.1007/978-3-642-29011-4_28]
    [22] Brakerski Z, Gentry C, Halevi S. Packed ciphertexts in LWE-based homomorphic encryption. In: Proc. of the Public-Key Cryptography (PKC 2013). Berlin, Heidelberg: Springer-Verlag, 2013. 1-13. [doi: 10.1007/978-3-642-36362-7_1]
    [23] Gentry C, Halevi S, Smart NP. Homomorphic evaluation of the AES circuit. In: Proc. of the Advances in Cryptology (CRYPTO 2012). Berlin, Heidelberg: Springer-Verlag, 2012. 850-867. [doi: 10.1007/978-3-642-32009-5_49]
    [24] Gentry C, Halevi S. Implementing Gentry's fully-homomorphic encryption scheme. In: Proc. of the EUROCRYPT 2011. 2011. 129-148. [doi:10.1007/978-3-642-20465-4_9]
    附中文参考文献:
    [19] 光焱,顾纯祥,祝跃飞,郑永辉,费金龙.利用容错学习问题构造基于身份的全同态加密体制.通信学报,2014,35(2):111-117.
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康元基,顾纯祥,郑永辉,光焱.利用特征向量构造基于身份的全同态加密体制.软件学报,2016,27(6):1487-1497

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History
  • Received:August 08,2015
  • Revised:October 09,2015
  • Online: January 22,2016
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