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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.

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    $\begingroup$ Let me see if I understand. You are looking for an asymmetric crypto system that would allow multiple users to generate some private key, then jointly generate a public key. The public key is used to encrypt, and each party must use their private key (together) to decrypt. Something like that? Something like threshold cryptography? $\endgroup$ – mikeazo Aug 6 '15 at 17:00
  • $\begingroup$ I've created an extensive edit because the question was sub-optimal with regards to readability. Could you check if it still captures your question? $\endgroup$ – Maarten Bodewes Aug 6 '15 at 18:50
  • $\begingroup$ 'threshold cryptography' was exactly what I was looking for! Thanks @mikeazo !! $\endgroup$ – Kang Aug 6 '15 at 23:45

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