I want to compute, in a distributed way, the following shared public keys on an elliptic curve:
being $x$ a secret scalar that no single party knows, $G$ the public generator point and $n$ a natural number. How can I do this?
One way that I can think of is that each party $i$ sends $(x_iG, x_i^2G,...,x_i^nG)$ and the public keys will be the sum of each component. But how to verify that each $x_i^nG$ is computed correctly?