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?

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

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