## Cryptology ePrint Archive: Report 2019/768

Distributing any Elliptic Curve Based Protocol

Nigel P. Smart and Younes Talibi Alaoui

Abstract: We show how to perform a full-threshold $n$-party actively secure MPC protocol over a subgroup of order $p$ of an elliptic curve group $E(K)$. This is done by utilizing a full-threshold $n$-party actively secure MPC protocol over $\mathbb{F}_p$ in the pre-processing model (such as SPDZ), and then locally mapping the Beaver triples from this protocol into equivalent triples for the elliptic curve. This allows us to transform essentially any one-party protocol over an elliptic curve, into an $n$-party one. As an example we show how to transform the shuffle protocol of Abe into an $n$-party protocol. This application requires us to also give an MPC protocol to derive the switches in a Waksman network from a generic permutation, which may be of independent interest.

Category / Keywords: cryptographic protocols /

Original Publication (with major differences): IMACC 2019

Date: received 1 Jul 2019, last revised 18 Sep 2019

Contact author: nigel smart at kuleuven be,younes talibialaoui@kuleuven be

Available format(s): PDF | BibTeX Citation

Short URL: ia.cr/2019/768

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