  We investigate channel synthesis in a cascade setting where nature provides
an iid sequence $X^n$ at node 1. Node 1 can send a message at rate $R_1$ to
node 2 and node 2 can send a message at rate $R_2$ to node 3. Additionally, all
3 nodes share bits of common randomness at rate $R_0$. We want to generate
sequences $Y^n$ and $Z^n$ along nodes in the cascade such that $(X^n,Y^n,Z^n)$
appears to be appropriately correlated and iid even to an eavesdropper who is
cognizant of the messages being sent. We characterize the optimal tradeoff
between the amount of common randomness used and the required rates of
communication. We also solve the problem for arbitrarily long cascades and
provide an inner bound for cascade channel synthesis without an eavesdropper.
