# Non-interactively share secret with group without revealing to generator?

Imagine someone knows a set of $$n$$ ECC public keys $$\mathcal R = \{K_1, K_2, ... K_n\}$$ but they don't know the corresponding private keys $$k_1$$, $$k_2$$ ... $$k_n$$. They wish to create a public key $$sG$$ such that anyone with a private key $$k_i$$ belonging to a $$K_i \in \mathcal R$$ can retrieve/calculate $$s$$. This scheme should create $$sG$$ such that not even the executer of the scheme can retrieve $$s$$. Is this possible without having to interact with the private key holders?

• This question cannot be interpreted without the following typo being fixed: "No one else should be able to retrieve s not even the generator of sG." – Adrian Self Jun 10 at 0:00
• yes, I agree and took the liberty of fixing it. @philogy let us know if that is a problem – kodlu Jun 10 at 12:04
• which typo? I honestly don't know what you mean but thanks for fixing it anyway – philogy Jun 10 at 12:24
• What are the requirements on the private keys? As it stands I could simply have $k_1 = \dots, k_n$? – Cryptonaut Jun 11 at 13:25
• No the private keys are all different I'm afraid, otherwise it would be too easy – philogy Jun 11 at 22:10