  Threshold schemes have been used to protect secrets by distributing shares to
participants. To protect two secrets, we can use two separate traditional
schemes, say, a (t1, n1) scheme and a (t2, n2) scheme. If there are u
(<=min(t1, t2)) participants involved in both schemes, each of these u
participants must keep two different shares. This paper proposes a method that
allows each common participant to keep only one share. Our method constructs
two polynomials with u common crossover points. We give theoretical details and
two demonstrative examples. This algorithm can also handle the collaboration
between more than two schemes.
