# Compute shared public keys

I want to compute, in a distributed way, the following shared public keys on an elliptic curve:

$$(xG, x^2G,...,x^nG)$$,

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?

• Huh? What kind of relation does $x_i$ have with the secret scalar $x$? – Maarten Bodewes Dec 7 '19 at 13:35