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Black-Box Non-interactive Non-malleable Commitments

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Advances in Cryptology – EUROCRYPT 2021 (EUROCRYPT 2021)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 12698))

Abstract

There has been recent exciting progress on building non-interactive non-malleable commitments from judicious assumptions. All proposed approaches proceed in two steps. First, obtain simple “base” commitment schemes for very small tag/identity spaces based on a various sub-exponential hardness assumptions. Next, assuming sub-exponential non-interactive witness indistinguishable proofs (NIWIs), and variants of keyless collision resistant hash functions, construct non-interactive compilers that convert tag-based non-malleable commitments for a small tag space into tag-based non-malleable commitments for a larger tag space.

We propose the first black-box construction of non-interactive non-malleable commitments. Our key technical contribution is a novel implementation of the non-interactive proof of consistency required for tag amplification. Prior to our work, the only known approach to tag amplification without setup and with black-box use of the base scheme (Goyal, Lee, Ostrovsky and Visconti, FOCS 2012) added multiple rounds of interaction.

Our construction satisfies the strongest known definition of non-malleability, i.e., CCA (chosen commitment attack) security. In addition to being black-box, our approach dispenses with the need for sub-exponential NIWIs, that was common to all prior work. Instead of NIWIs, we rely on sub-exponential hinting PRGs which can be obtained based on a broad set of assumptions such as sub-exponential CDH or LWE.

This material is based on work supported in part by DARPA under Contract No. HR001120C0024. Any opinions, findings and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the United States Government or DARPA.

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Notes

  1. 1.

    The assumption that the commitment takes input a \(\mathsf {tag}\) is w.l.o.g when the tag space is exponential. As is standard with non-malleable commitments, tags can be generically removed from this construction by setting the tag as the verification key of a signature scheme, and signing the commitment string using the signing key.

  2. 2.

    This was recently further optimized by [23] but in this paper, we use the [11] technique for simplicity.

  3. 3.

    The choice of \(2^{2^{{\kappa }}}\) is somewhat arbitrary as the condition is in place so that the game is well defined on all P.

  4. 4.

    The constant \(\delta \) must be less than 1 in order to meet the requirement that the \(\mathsf {Equiv.Equivocate}\) algorithm runs in time polynomial in \(2^\kappa \).

  5. 5.

    \(\delta \) and \(\gamma \) are known from the security guarantees of \(\mathsf {Equiv},\mathsf {HPRG}\) respectively.

  6. 6.

    For brevity, \(\mathsf {ilog}(c,{\kappa })\) denotes \(\underbrace{\lg \lg \cdots \lg }_{c~ \mathrm {times}}({\kappa })\).

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Author information

Authors and Affiliations

  1. University of Texas at Austin, Austin, USA

    Rachit Garg, George Lu & Brent Waters

  2. University of Illinois Urbana-Champaign, Urbana, USA

    Dakshita Khurana

  3. NTT Research, Sunnyvale, USA

    Brent Waters

Authors
  1. Rachit Garg
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  2. Dakshita Khurana
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  3. George Lu
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  4. Brent Waters
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Correspondence to Rachit Garg .

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Editors and Affiliations

  1. Inria, Paris, France

    Anne Canteaut

  2. UCLouvain, Louvain-la-Neuve, Belgium

    François-Xavier Standaert

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Garg, R., Khurana, D., Lu, G., Waters, B. (2021). Black-Box Non-interactive Non-malleable Commitments. In: Canteaut, A., Standaert, FX. (eds) Advances in Cryptology – EUROCRYPT 2021. EUROCRYPT 2021. Lecture Notes in Computer Science(), vol 12698. Springer, Cham. https://doi.org/10.1007/978-3-030-77883-5_6

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  • DOI: https://doi.org/10.1007/978-3-030-77883-5_6

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