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

In this paper we present the concept of linear secret-sharing homomorphisms, which are linear transformations between different secretsharing schemes defined over vector spaces over a field F and allow for efficient multiparty conversion from one secret-sharing scheme to the other. This concept generalizes the observation from (Smart and Talibi, IMACC 2019) and (Dalskov et al., ESORICS 2020) that moving from a secret-sharing scheme over Fp to a secret sharing over an elliptic curve group G of order p can be done non-interactively by multiplying the share unto a generator of G. 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 present several practical applications using our techniques: 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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