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Improved Threshold Signatures, Proactive Secret Sharing, and Input Certification from LSS Isomorphisms

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Progress in Cryptology – LATINCRYPT 2021 (LATINCRYPT 2021)

Part of the book series: Lecture Notes in Computer Science ((LNSC,volume 12912))

Abstract

In this paper we present a series of applications steming from a formal treatment of linear secret-sharing isomorphisms, which are linear transformations between different secret-sharing schemes defined over vector spaces over a field \(\mathbb {F}\) and allow for efficient multiparty conversion from one secret-sharing scheme to the other. This concept generalizes the folklore idea that moving from a secret-sharing scheme over \(\mathbb {F}_{p}\) to a secret sharing “in the exponent” can be done non-interactively by multiplying the share unto a generator of e.g., an elliptic curve group. We generalize this idea and show that it can also be used to compute arbitrary bilinear maps and in particular pairings over elliptic curves.

We include the following practical applications originating from our framework: First we show how to securely realize the Pointcheval-Sanders signature scheme (CT-RSA 2016) in MPC. Second we present a construction for dynamic proactive secret-sharing which outperforms the current state of the art from CCS 2019. Third we present a construction for MPC input certification using digital signatures that we show experimentally to outperform the previous best solution in this area.

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Notes

  1. 1.

    A verifiable secret-sharing scheme is one in which parties can verify that the dealer shared the secret correctly.

  2. 2.

    Note that the use of the vector \(\boldsymbol{r}_v\) here where all but one entries are random is similar to e.g., the choice of a random polynomial with a fixed 0-coefficient in Shamir’s secret sharing.

  3. 3.

    A downside of e.g., ECDSA signatures is that messages have to be hashed first, which creates a significant problem when messages are secret-shared, as hashing secret-shared data is quite expensive.

  4. 4.

    One caveat is that the shares on their own may not define the secret if the adversary is allowed to change the corrupt parties’ shares, which is the case for an active adversary. This is an issue for example with additive secret sharing and an dishonest majority (which can be fixed by adding homomorphic MACs), but not for Shamir secret sharing with an honest majority. We discuss this in detail in the full version.

  5. 5.

    For a more detailed derivation of this complexity, see the full version.

  6. 6.

    Notice that in the case the protocol does not succeed, nothing can be said about what caused it to abort. If this property is desired, then the protocol underlying \(\varPi _{\mathsf {CertInput}}\) have to support identifiable abort.

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Acknowledgments

The authors would like to thank Greg Zaverucha and the anonymous reviewers for useful feedback on earlier versions of this paper.

This work has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme under grant agreements No 669255 (MPCPRO) and No 803096 (SPEC), the Concordium Blockhain Research Center at Aarhus University (COBRA), the Carlsberg Foundation under the Semper Ardens Research Project CF18-112 (BCM), and the Danish Independent Research Council under Grant-ID DFF-6108-00169 (FoCC). The first and last authors are affiliated to the DIGIT Centre for Digitalisation, Big Data and Data Analytics at Aarhus University.

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Authors and Affiliations

  1. Aarhus University, Aarhus, Denmark

    Diego F. Aranha, Daniel Escudero & Claudio Orlandi

  2. Partisia, Aarhus, Denmark

    Anders Dalskov

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  1. Diego F. Aranha
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Correspondence to Diego F. Aranha .

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  1. Microsoft Research, Redmond, WA, USA

    Patrick Longa

  2. Universitat Pompeu Fabra, Barcelona, Spain

    Carla Ràfols

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Aranha, D.F., Dalskov, A., Escudero, D., Orlandi, C. (2021). Improved Threshold Signatures, Proactive Secret Sharing, and Input Certification from LSS Isomorphisms. In: Longa, P., Ràfols, C. (eds) Progress in Cryptology – LATINCRYPT 2021. LATINCRYPT 2021. Lecture Notes in Computer Science(), vol 12912. Springer, Cham. https://doi.org/10.1007/978-3-030-88238-9_19

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