Is it possible to have a shared secret without any party knowing all the parts?

Question

I believe with Shamir’s Secret Sharing Scheme, I can create an n-part secret and distribute each of those parts to n parties. But the weakness is that I still know all the parts.

Is there a mechanism in which n parties can each have a secret that none of the other parties know, but yet have the public key be known in advance?

In asymmetric cryptography, if I have a private key, I can share the public key freely and then I can digitally sign a message proving that I have the private key for that public one. I assume something similar can be done with Samir’s SSS, but what I’m seeking is a way to do it in a distributed fashion.

Thanks in advance!

The keyword is dealer dupe of Shamir secret sharing with no dealer and Secret sharing - no dealer, modifiable, verifiable — kelalaka, Dec 04 '21 at 16:57
Are you trying to have a well known (publicized) public key, and a secret-shared private key (so that no set of $t-1$ individuals ever know the private key)? If so, yes, that's doable... — poncho, Dec 04 '21 at 17:38
If there is a shared public key, and your goal is to have a scheme such that a threshold k of n signers are required to sign for the public key, then what you are looking for is a threshold multi-signature scheme. Is that your goal? — knaccc, Dec 05 '21 at 13:49

Is it possible to have a shared secret without any party knowing all the parts?

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