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Zero-Knowledge Elementary Databases with More Expressive Queries

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Public-Key Cryptography – PKC 2019 (PKC 2019)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 11442))

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Abstract

Zero-knowledge elementary databases (ZK-EDBs) are cryptographic schemes that allow a prover to commit to a set \(\mathsf {D}\) of key-value pairs so as to be able to prove statements such as “x belongs to the support of \(\mathsf {D}\) and \(\mathsf {D}(x)=y\)” or “x is not in the support of \(\mathsf {D}\)”. Importantly, proofs should leak no information beyond the proven statement and even the size of \(\mathsf {D}\) should remain private. Chase et al. (Eurocrypt’05) showed that ZK-EDBs are implied by a special flavor of non-interactive commitment, called mercurial commitment, which enables efficient instantiations based on standard number theoretic assumptions. On the other hand, the resulting ZK-EDBs are only known to support proofs for simple statements like (non-)membership and value assignments. In this paper, we show that mercurial commitments actually enable significantly richer queries. We show that, modulo an additional security property met by all known efficient constructions, they actually enable range queries over keys and values – even for ranges of super-polynomial size – as well as membership/non-membership queries over the space of values. Beyond that, we exploit the range queries to realize richer queries such as \(k\)-nearest neighbors and revealing the \(k\) smallest or largest records within a given range. In addition, we provide a new realization of trapdoor mercurial commitment from standard lattice assumptions, thus obtaining the most expressive quantum-safe ZK-EDB construction so far.

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Acknowledgements

Part of this research was funded by Singapore Ministry of Education under Research Grant MOE2016-T2-2-014(S). Another part was funded by BPI-France in the context of the national project RISQ (P141580). This work was also supported in part by the European Union PROMETHEUS project (Horizon 2020 Research and Innovation Program, grant 780701). Khoa Nguyen was also supported by the Gopalakrishnan – NTU Presidential Postdoctoral Fellowship 2018. Huaxiong Wang was also supported by the National Research Foundation, Prime Minister’s Office, Singapore under its Strategic Capability Research Centres Funding Initiative.

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Authors and Affiliations

  1. CNRS, Laboratoire LIP, Lyon, France

    Benoît Libert

  2. ENS de Lyon, Laboratoire LIP (U. Lyon, CNRS, ENSL, Inria, UCBL), Lyon, France

    Benoît Libert

  3. School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore, Singapore

    Khoa Nguyen, Benjamin Hong Meng Tan & Huaxiong Wang

  4. Institute for Infocomm Research, A*STAR, Singapore, Singapore

    Benjamin Hong Meng Tan

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  1. Benoît Libert
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  2. Khoa Nguyen
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  3. Benjamin Hong Meng Tan
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  4. Huaxiong Wang
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Correspondence to Benjamin Hong Meng Tan .

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Editors and Affiliations

  1. SKLOIS, Institute of Information Engineering, Chinese Academy of Sciences, Beijing, China

    Dongdai Lin

  2. Security Research Laboratories, NEC Corporation, Kawasaki, Japan

    Kazue Sako

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Libert, B., Nguyen, K., Tan, B.H.M., Wang, H. (2019). Zero-Knowledge Elementary Databases with More Expressive Queries. In: Lin, D., Sako, K. (eds) Public-Key Cryptography – PKC 2019. PKC 2019. Lecture Notes in Computer Science(), vol 11442. Springer, Cham. https://doi.org/10.1007/978-3-030-17253-4_9

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  • DOI: https://doi.org/10.1007/978-3-030-17253-4_9

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  • Online ISBN: 978-3-030-17253-4

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