Disjunctive Multi-Level Secret Sharing

A disjunctive multi-level secret sharing scheme divides users into different levels. Each level L is associated with a threshold tL, and a group of users can only recover the secret if, for some L, there are at least tL users at levels 0....L in the group. We present a simple ideal disjunctive multi-level secret sharing scheme – in fact, the simplest and most direct scheme to date. It is the first polynomial-time solution that allows the dealer to add new users dynamically. Our solution is by far the most efficient; the dealer must perform O(t) field operations per user, where t is the highest threshold in the system. We demonstrate the simplicity of our scheme by extending our construction into a distributed commitment scheme using standard techniques.