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More Efficient Commitments from Structured Lattice Assumptions

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Security and Cryptography for Networks (SCN 2018)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 11035))

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Abstract

We present a practical construction of an additively homomorphic commitment scheme based on structured lattice assumptions, together with a zero-knowledge proof of opening knowledge. Our scheme is a design improvement over the previous work of Benhamouda et al. in that it is not restricted to being statistically binding. While it is possible to instantiate our scheme to be statistically binding or statistically hiding, it is most efficient when both hiding and binding properties are only computational. This results in approximately a factor of 4 reduction in the size of the proof and a factor of 6 reduction in the size of the commitment over the aforementioned scheme.

Full version of the paper available at https://eprint.iacr.org/2016/997.

C. Baum—Supported by the BIU Center for Research in Applied Cryptography and Cyber Security in conjunction with the Israel National Cyber Bureau in the Prime Minister’s Office and COST Action IC1306.

I. Damgård—Supported by the European Research Council (ERC) under the European Unions’s Horizon 2020 research and innovation programme under grant agreement No 669255 (MPCPRO).

V. Lyubashevsky—Supported by the SNSF ERC Transfer Grant CRETP2-166734 – FELICITY.

S. Oechsner—Supported by the European Research Council (ERC) under the European Unions’s Horizon 2020 research and innovation programme under grant agreement No 669255 (MPCPRO); the Danish Independent Research Council under Grant-ID DFF-6108-00169 (FoCC); the European Union’s Horizon 2020 research and innovation programme under grant agreement No 731583 (SODA).

C. Peikert—Supported by the National Science Foundation under CAREER Award CCF-1054495 and CNS-1606362, the Alfred P. Sloan Foundation, and by a Google Research Award. The views expressed are those of the authors and do not necessarily reflect the official policy or position of the National Science Foundation, the Sloan Foundation, or Google.

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Notes

  1. 1.

    This was also the property in the commitment scheme of [9].

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Author information

Authors and Affiliations

  1. Department of Computer Science, Bar-Ilan University, Ramat Gan, Israel

    Carsten Baum

  2. Department of Computer Science, Aarhus University, Aarhus, Denmark

    Ivan Damgård & Sabine Oechsner

  3. IBM Research – Zurich, Rüschlikon, Switzerland

    Vadim Lyubashevsky

  4. Department of Computer Science and Engineering, University of Michigan, Ann Arbor, USA

    Chris Peikert

Authors
  1. Carsten Baum
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  2. Ivan Damgård
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  3. Vadim Lyubashevsky
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  4. Sabine Oechsner
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  5. Chris Peikert
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Correspondence to Vadim Lyubashevsky .

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Editors and Affiliations

  1. University of Catania, Catania, Italy

    Dario Catalano

  2. University of Salerno, Fisciano, Italy

    Roberto De Prisco

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Baum, C., Damgård, I., Lyubashevsky, V., Oechsner, S., Peikert, C. (2018). More Efficient Commitments from Structured Lattice Assumptions. In: Catalano, D., De Prisco, R. (eds) Security and Cryptography for Networks. SCN 2018. Lecture Notes in Computer Science(), vol 11035. Springer, Cham. https://doi.org/10.1007/978-3-319-98113-0_20

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