Which data is communicated between participants in Distributed Key Generation

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I was asked recently if it is somehow possible to use already existing keypairs stored in HSMs for, e.g. ped-DKG.

Which ultimately led me to the question, which data is actually exchanged between parties when generating a shared key-pair? I was thinking surely there has to be some communication of the parties, e.g. agreeing on a threshold (degree of polynomial) before generating their private key fragment and public key?

My thoughts regarding using existing key-pairs: Even though the initially generated secret constant is random, so any existing private key could serve as a seed, the multiparty public key generated in DKG would have to match any polynomial of the defined order and degree, which would not apply to the already existing public key (matching the secret key on the HSMs). Overall my assumption is that without prior communication it is not possible to generate valid key-pairs among multiple parties, hence the name "distributed key generation". Is my understanding correct?

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