I am searching for a secret splitting scheme where the private key doesn't exist, since each party chooses their own secrets. The other parties should however still be able to calculate the public key.
For example everyone chooses their own plane and the intersection that - when calculated - would become the secret. We need the public key of that secret.
Basically such a scheme would amount to secret splitting without a dealer. It could use but some kind of algorithm that uses homomorphism. Such a scheme could allow the public key to be calculated.
It seems possible. It would be similar to an algorithm that allows three people to calculate the average salary without disclosing their individual salary.
If such an algorithm cannot exist then a explanation showing that it is impossible would be great.