基于抽象解密结构的全同态加密构造方法分析

宋新霞; 陈智罡

doi:10.11999/JEIT170997

基于抽象解密结构的全同态加密构造方法分析

doi: 10.11999/JEIT170997

^①(浙江万里学院基础学院宁波 315100) ^②(浙江万里学院电子与计算机学院宁波 315100) ^③(中国科学院信息工程研究所信息安全国家重点实验室北京 100093)

基金项目:

浙江省科技厅公益性技术科研项目(2017C33079, LGG18F020001)，浙江省自然科学基金(LY17F020002)，密码科学技术国家重点实验室开放课题基金，宁波市自然科学基金(2017A610120)

详细信息

作者简介:
宋新霞：女，1973年生，副教授，研究方向为代数与编码. 陈智罡：男，1972年生，教授，研究方向为全同态加密与格密码.

中图分类号: TP309.7
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- 文章访问数: 1424
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- 被引次数: 0
出版历程
- 收稿日期: 2017-10-24
- 修回日期: 2018-04-03
- 刊出日期: 2018-07-19

Analysis of Constructing Fully Homomorphic Encryption Based on the Abstract Decryption Structure

SONG Xinxia^① CHEN Zhigang^②③

Funds:

The Public Projects of Zhejiang Province (2017C33079, LGG18F020001), The Natural Science Foundation of Zhejiang Province (LY17F020002), The Foundation of the State Key Laboratory of Cryptology, The Ningbo Natural Science Foundation (2017A610120)

摘要

摘要: 为什么能够在格上构造全同态加密?密文矩阵的本质及构造方法是什么?该文提出一个重要的概念：抽象解密结构。该文以抽象解密结构为工具，对目前全同态加密构造方法进行分析，得到抽象解密结构、同态性与噪音控制之间的关系，将全同态加密的构造归结为如何获得最终解密结构的问题，从而形式化地建立全同态加密构造方法。最后对GSW全同态加密方法分析，提出其密文矩阵是由密文向量堆叠而成。基于密文堆叠法，研究密文是矩阵的全同态加密的通用性原因，给出密文矩阵全同态加密与其它全同态加密之间的包含关系。
- 全同态加密 /
- 构造方法 /
- 抽象解密结构 /
- 密文堆叠 /
- 学习错误问题
Abstract: Why can fully homomorphic encryption be constructed based on lattice What is the essence and construction of the matrix An important concept is proposed: Abstract decryption structure. Based on the abstract decryption structure, the main factors related to the homomorphic encryption are analyzed and relationship between abstract decryption structure, homomorphism and noise control is studied. The construction of the homomorphic encryption is attributed to the problem of how to obtain the final decryption structure. So the formal method of homomorphic encryption can be established. Thus the essential law of the construction method of the homomorphic encryption construction is expounded, which provides the clue and clue for the construction of the new full homomorphic encryption. The general reason of the full homomorphic encryption of the ciphertext matrix from the point of view of the ciphertexts stack method is studied. The relation between the full homomorphic encryption and the other homomorphic encryption is obtained. Finally, this paper gives a general method of constructing fully homomorphic encryption.
- Fully homomorphic encryption、Construction method、Abstract decryption structure、Ciphertexts stack、Learning With Errors (LWE) /

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参考文献(22)

GENTRY C. Fully homomorphic encryption using ideal lattices[C]. Proceedings of the 41st Annual ACM Symposium on Theory of Computing, Bethesda, USA, 2009: 169-178. doi: 10.1145/1536414.1536440.

[2] SMART N P and VERCAUTEREN F. Fully homomorphic encryption with relatively small key and ciphertext sizes[C]. International Conference on Practice and Theory in Public- Key Cryptography, Berlin, Heidelberg, 2010: 420-443. doi: 10.1007/978-3-642-13013-7_25.

[3] DIJK M, GENTRY C, HALEVI S, et al. Fully homomorphic encryption over the integers[C]. Advances in Cryptology- EUROCRYPT 2010, Berlin, Heidelberg, 2010: 24-43.

[4] CORON J S, NACCACHE D, and TIBOUCHI M. Public key compression and modulus switching for fully homomorphic encryption over the integers[C]. Advances in Cryptology-EUROCRYPT 2012, Berlin, Heidelberg, 2012: 446-464. doi: 10.1007/978-3-642-29011-4_27.

[5] CORON J S, MANDAL A, NACCACHE D, et al. Fully homomorphic encryption over the integers with shorter public keys[C]. Advances in Cryptology-CRYPTO 2011, Berlin, Heidelberg, 2011: 487-504. doi: 10.1007/978-3-642- 22792-9_28.

[6] CHEON J H and STEHL D. Fully homomophic encryption over the integers revisited[C]. Advances in Cryptology- EUROCRYPT 2015, Sofia, Bulgaria, 2015: 513-536. doi: 10.1007/978-3-662-46800-5_20.

[7] BRAKERSKI Z and VAIKUNTANATHAN V. Efficient fully homomorphic encryption from (standard) LWE[C]. IEEE 52nd Annual Symposium on Foundations of Computer Science, Los Alamitos, 2011: 97-106. doi: 10.1109/FOCS. 2011.12.

[8] BRAKERSKI Z. Fully homomorphic encryption without modulus switching from classical gapsvp[C]. Advances in Cryptology-CRYPTO 2012, Berlin, Heidelberg, 2012: 868-886. doi: 10.1007/978-3-642-32009-5_50.

[9] BRAKERSKI Z, GENTRY C, and VAIKUNTANATHAN V. (Leveled) Fully homomorphic encryption without bootstrapping[C]. The 3rd Innovations in Theoretical Computer Science Conference, Cambridge, Massachusetts, 2012: 1-36. doi: 10.1145/2090236.2090262.

[10] GENTRY C, SAHAI A, and WATERS B. Homomorphic encryption from learning with errors: conceptually-simpler, asymptotically-faster, attribute-Based[C]. Advances in Cryptology – CRYPTO 2013, Berlin, Heidelberg, 2013: 75-92. doi: 10.1007/978-3-642-40041-4_5.

[11] REGEV O. On lattices, learning with errors, random linear codes, and cryptography[C]. The 37th Annual ACM Symposium on Theory of Computing, Baltimore, 2005: 84-93. doi: 10.1145/1060590.1060603.

[12] COSTACHE A and SMART N P. Which ring based somewhat homomorphic encryption scheme is best?[C]. CT-RSA 2016, San Francisco, CA, 2016: 325-340. doi: 10.1007/978-3-319-29485-8_19.

[13] GENTRY C, HALEVI S, and SMART N. Fully homomorphic encryption with polylog overhead[C]. Advances in Cryptology-EUROCRYPT 2012, Berlin, Heidelberg, 2012: 465-482. doi: 10.1007/978-3-642-29011-4_28.

[14] OZTURK E, DOROZ Y, SAVAS E, et al. A custom accelerator for homomorphic encryption applications[J]. IEEE Transactions on Computers, 2017, 66(1): 3-16. doi: 10.1109/TC.2016.2574340.

[15] CANETTI R, RAGHURAMAN S, RICHELSON S, et al. Chosen-ciphertext secure fully homomorphic encryption[C]. International Conference on Practice and Theory in Public- Key Cryptography, Amsterdam, 2017: 213-240. doi: 10.1007/ 978-3-662-54388-7_8.

[16] GAVIN G. An efficient somewhat homomorphic encryption scheme based on factorization[C]. The 15th International Conference Cryptology and Network Security, Milan, 2016: 451-464. doi: 10.1007/978-3-319-48965-0_27.

[17] BENARROCH D, BRAKERSKI Z, and LEPOINT T. FHE over the integers: decomposed and batched in the post-quantum regime[C]. International Conference on Practice and Theory in Public-Key Cryptography, Amsterdam, Netherlands, 2017: 271-301. doi: 10.1007/978- 3-662-54388-7_10.

[18] CHILLOTTI I, GAMA N, GEORGIEVA M, et al. Faster fully homomorphic encryption: Bootstrapping in less than 0.1 seconds[C]. International Conference on the Theory and Application of Cryptology and Information Security, Hanoi, Vietnam, 2016: 3-33. doi: 10.1007/978-3-662-53887-6_1.

[19] HALEVI S and SHOUP V. Algorithms in HElib[C]. Advances in Cryptology-CRYPTO 2014, Santa Barbara, CA, 2014: 554-571. doi: 10.1007/978-3-662-44371-2_31.

[20] CHEN H, LAINE K, PLAYER R, et al. Simple encrypted arithmetic library-SEAL v2.1[C]. Proceedings of the Financial Cryptography and Data Security, Sliema, Malta, 2017: 3-18. doi: 10.1007/978-3-319-70278-0_1.

[21] CROCKETT E and PEIKERT C. : Functional lattice cryptography[C]. Proceedings of the 2016 ACM SIGSAC Conference on Computer and Communications Security, Vienna, Austria, 2016: 993-1005. doi: 10.1145/2976749. 2978402.

[22] L PEZ-ALT A, TROMER E, and VAIKUNTANATHAN V. On-the-fly multiparty computation on the cloud via multikey fully homomorphic encryption[C]. Proceedings of the 44th Symposium on Theory of Computing, New York, USA, 2012: 1219-1234. doi: 10.1145/2213977.2214086.

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