# How to create a shared secret S from a subset of existing secrets n, such that k out of n secrets can recreate S? [duplicate]

In traditional secret sharing schemes, like Shamir's Secret Sharing, first a secret S is generated. Then it is divided into n parts, such that a subset k of the n parts are sufficient to reconstruct S.

My problem is that I already have n individual and independent secrets. Is there a way to come up with a shared secret S from these pre-existing n secrets, such that a subset k of the n parts are sufficient to reconstruct S?

• Questions like this are always difficult. I'm not aware of any way to do it, but I'm also not aware of a proof that no such thing exists. The simple case is when $k=n$, in which case use just use the XOR of the secrets. For $k<n$, my gut feeling is that this is impossible. – mikeazo Mar 9 '17 at 16:38