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Somewhere Statistically Binding Commitment Schemes with Applications

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Financial Cryptography and Data Security (FC 2021)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 12674))

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Abstract

We define a new primitive that we call a somewhere statistically binding (SSB) commitment scheme, which is a generalization of dual-mode commitments but has similarities with SSB hash functions (Hubacek and Wichs, ITCS 2015) without local opening. In (existing) SSB hash functions, one can compute a hash of a vector v that is statistically binding in one coordinate of v. Meanwhile, in SSB commitment schemes, a commitment of a vector v is statistically binding in some coordinates of v and is statistically hiding in the other coordinates. The set of indices where binding holds is predetermined but known only to the commitment key generator. We show that the primitive can be instantiated by generalizing the succinct Extended Multi-Pedersen commitment scheme (González et al., Asiacrypt 2015). We further introduce the notion of functional SSB commitment schemes and, importantly, use it to get an efficient quasi-adaptive NIZK for arithmetic circuits and efficient oblivious database queries.

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Notes

  1. 1.

    One cannot construct zk-SNARKs in a black-box way from falsifiable assumptions [21], hence any black-box construction from falsifiable assumptions will not be fully succinct.

  2. 2.

    The properties of SSB and local opening are orthogonal: it is possible to construct efficient SSB hashes without local opening [33] and efficient vector commitments [5, 31] (which have a local opening) without the SSB property.

  3. 3.

    González et al. [24] mostly considered the case \(q= 1\); they also did not formalize its security by using notions like ISH.

  4. 4.

    We add \(+1\) to the dimension (e.g., \(q+ 1\)) to accommodate the randomizer in EMP.

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Acknowledgments

We would like to thank Carla Ràfols and Janno Veeorg for useful discussions. The authors were supported by the Estonian Research Council grant (PRG49) and by Dora Plus Grant funded by the European Regional Development Fund, Republic of Estonia and Archimedes Foundation. Janno Siim was additionally supported by the European Union’s Horizon 2020 research and innovation programme under grant agreement No. 780477 (project PRIViLEDGE). Part of this work was done while Janno Siim was affiliated with the University of Edinburgh.

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Authors and Affiliations

  1. Simula UiB, Bergen, Norway

    Prastudy Fauzi & Helger Lipmaa

  2. University of Tartu, Tartu, Estonia

    Helger Lipmaa & Janno Siim

  3. Universitat Pompeu Fabra, Barcelona, Spain

    Zaira Pindado

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  1. Prastudy Fauzi
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Correspondence to Janno Siim .

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  1. University of Illinois at Urbana-Champaign, Urbana, IL, USA

    Nikita Borisov

  2. KU Leuven, Leuven, Belgium

    Claudia Diaz

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Fauzi, P., Lipmaa, H., Pindado, Z., Siim, J. (2021). Somewhere Statistically Binding Commitment Schemes with Applications. In: Borisov, N., Diaz, C. (eds) Financial Cryptography and Data Security. FC 2021. Lecture Notes in Computer Science(), vol 12674. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-64322-8_21

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