Secret sharing refers to splitting a secret among multiple parties so that together they can reconstruct it. All parties, or just a threshold number of them, can be required for reconstruction. If fewer than the required number of parties participate, no information should be leaked about the ...

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Is there a secret sharing scheme which allows delegation/re-sharing without reconstructing the original secret?

EDIT: Ilmari Karonen's answer below well not exactly what I want, gives a very good idea of what I am trying to accomplish. Are there any known secret sharing schemes that allow new parties to be ...