How to Compartment Secrets Trust Everybody, but Cut the Cards

摘要

Secret sharing splits a secret s into £ shares in such a way that k ≤ ℓ shares suffice to reconstruct s. Let ρ_(i,j) be the probability that shareholder i disclose their share to shareholder j, with 0 ≤ i, j < n. Given k ≤ ℓ ≤ n, to whom £ individuals should we hand shares, if we wish to minimize the probability that one of them reconstitutes s?