Distributing any Elliptic Curve Based Protocol: With an Application to MixNets
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 Fp 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.