Distributed Password for Quorum and Veto

A simple algorithm for sharing a secret with some nonmonotone access structures will be presented. This is achieved by splitting a secret password, represented by a large prime number, between n participants in such a way that only by pooling a qualified set of shares one can recover the original password. Executing the power of veto in addition to a qualified set provides a nonqualified (forbidden) superset. The cryptographic power of our algorithm is based on computational hardness of the integer factorization.