Paper 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.