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Structure-Preserving Signatures on Equivalence Classes from Standard Assumptions

  • Mojtaba KhaliliEmail author
  • Daniel Slamanig
  • Mohammad Dakhilalian
Conference paper
  • 335 Downloads
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11923)

Abstract

Structure-preserving signatures on equivalence classes (SPS-EQ) introduced at ASIACRYPT 2014 are a variant of SPS where a message is considered as a projective equivalence class, and a new representative of the same class can be obtained by multiplying a vector by a scalar. Given a message and corresponding signature, anyone can produce an updated and randomized signature on an arbitrary representative from the same equivalence class. SPS-EQ have proven to be a very versatile building block for many cryptographic applications.

In this paper, we present the first EUF-CMA secure SPS-EQ scheme under standard assumptions. So far only constructions in the generic group model are known. One recent candidate under standard assumptions are the weakly secure equivalence class signatures by Fuchsbauer and Gay (PKC’18), a variant of SPS-EQ satisfying only a weaker unforgeability and adaption notion. Fuchsbauer and Gay show that this weaker unforgeability notion is sufficient for many known applications of SPS-EQ. Unfortunately, the weaker adaption notion is only proper for a semi-honest (passive) model and as we show in this paper, makes their scheme unusable in the current models for almost all of their advertised applications of SPS-EQ from the literature.

We then present a new EUF-CMA secure SPS-EQ scheme with a tight security reduction under the SXDH assumption providing the notion of perfect adaption (under malicious keys). To achieve the strongest notion of perfect adaption under malicious keys, we require a common reference string (CRS), which seems inherent for constructions under standard assumptions. However, for most known applications of SPS-EQ we do not require a trusted CRS (as the CRS can be generated by the signer during key generation). Technically, our construction is inspired by a recent work of Gay et al. (EUROCRYPT’18), who construct a tightly secure message authentication code and translate it to an SPS scheme adapting techniques due to Bellare and Goldwasser (CRYPTO’89).

Notes

Acknowledgments

We are grateful to the anonymous reviewers from ASIACRYPT 2019 and Romain Gay for their careful reading of the paper, their valuable feedback and suggestions to improve the presentation. We also thanks Carla Ràfols and Alonso González for their comments on earlier versions of this work. This work was supported by the EU’s Horizon 2020 ECSEL Joint Undertaking project SECREDAS under grant agreement n\(\circ \)783119 and by the Austrian Science Fund (FWF) and netidee SCIENCE project PROFET (grant agreement P31621-N38).

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Copyright information

© International Association for Cryptologic Research 2019

Authors and Affiliations

  • Mojtaba Khalili
    • 1
    Email author
  • Daniel Slamanig
    • 2
  • Mohammad Dakhilalian
    • 1
  1. 1.Isfahan University of TechnologyIsfahanIran
  2. 2.AIT Austrian Institute of TechnologyViennaAustria

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