Optimum secret sharing scheme secure against cheating

Abstract

Tompa and Woll considered a problem of cheaters in (k, n) threshold secret sharing schemes. We first derive a tight lower bound on the size of shares |Vi| for this problem: |Vi| ≥ (|S| − 1)/δ + 1, where Vi denotes the set of shares of participant Pi, S denotes the set of secrets, and δ denotes the cheating probability. We next present an optimum scheme which meets the equality of our bound by using “difference sets.”