This question already has an answer here:
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?