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Leveled Strongly-Unforgeable Identity-Based Fully Homomorphic Signatures

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Information Security (ISC 2015)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 9290))

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Abstract

Recently, Gorbunov, Vaikuntanathan and Wichs proposed a new powerful primitive: (fully) homomorphic trapdoor function (HTDF) based on small integer solution (SIS) problem in standard lattices, from which they constructed the first leveled existentially-unforgeable fully homomorphic signature (FHS) schemes.

In this paper, we first extend the notion of HTDF to identity-based setting with stronger security and better parameters. The stronger security requires that the identity-based HTDF (IBHTDF) is not only claw-free, but also collision-resistant. And the maximum noise comparing to Gorbunov-Vaikuntanathan-Wichs’ HTDF roughly reduces from \(O(m^d\beta )\) to \(O(4^dm\beta )\), which will result in polynomial modulus \(q=\mathrm {poly}(\lambda )\) when \(d=O(\log \lambda )\), where \(\lambda \) is the security parameter and d is the depth bound of circuit. We then define and construct the first leveled strongly-unforgeable identity-based fully homomorphic signature (IBFHS) schemes.

This work is supported in part by the National Nature Science Foundation of China under award No. 61272040 and No. 61379137, and in part by the National 973 Program of China under award No. 2013CB338001.

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Notes

  1. 1.

    Here \( \widetilde{\mathbf {G}}^{-1}\) is not the inverse matrix of \(\widetilde{\mathbf {G}}\) but a deterministic algorithm.

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Acknowledgement

We are very grateful to the anonymous ISC reviewers for valuable comments and constructive suggestions that helped to improve the presentation of this work.

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Authors and Affiliations

  1. State Key Laboratory of Information Security, Institute of Information Engineering, Chinese Academy of Sciences, Beijing, China

    Fuqun Wang, Kunpeng Wang, Bao Li & Yuanyuan Gao

  2. Data Assurance and Communication Security Research Center, Chinese Academy of Sciences, Beijing, China

    Fuqun Wang, Kunpeng Wang, Bao Li & Yuanyuan Gao

  3. University of Chinese Academy of Sciences, Beijing, China

    Fuqun Wang

  4. School of Science, Sichuan University of Science and Engineering, Zigong, China

    Yuanyuan Gao

Authors
  1. Fuqun Wang
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  2. Kunpeng Wang
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  3. Bao Li
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  4. Yuanyuan Gao
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Corresponding author

Correspondence to Fuqun Wang .

Editor information

Editors and Affiliations

  1. University of Malaga, Malaga, Spain

    Javier Lopez

  2. Royal Holloway University of London, Egham, United Kingdom

    Chris J. Mitchell

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Wang, F., Wang, K., Li, B., Gao, Y. (2015). Leveled Strongly-Unforgeable Identity-Based Fully Homomorphic Signatures. In: Lopez, J., Mitchell, C. (eds) Information Security. ISC 2015. Lecture Notes in Computer Science(), vol 9290. Springer, Cham. https://doi.org/10.1007/978-3-319-23318-5_3

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  • DOI: https://doi.org/10.1007/978-3-319-23318-5_3

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  • Online ISBN: 978-3-319-23318-5

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