Paper 2020/691

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

Diego Aranha, Anders Dalskov, Daniel Escudero, and Claudio Orlandi


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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Cryptographic protocols
Publication info
Preprint. MINOR revision.
Multiparty ComputationElliptic CurvesPairingsProactive-Secret-SharingSecure Signatures
Contact author(s)
dfaranha @ cs au dk
anderspkd @ cs au dk
orlandi @ cs au dk
escudero @ cs au dk
2021-08-10: last of 4 revisions
2020-06-09: received
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      author = {Diego Aranha and Anders Dalskov and Daniel Escudero and Claudio Orlandi},
      title = {Improved Threshold Signatures, Proactive Secret Sharing, and Input Certification from LSS Isomorphisms},
      howpublished = {Cryptology ePrint Archive, Paper 2020/691},
      year = {2020},
      note = {\url{}},
      url = {}
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