  In the first part of the paper, we have studied the computational privacy
risks in distributed computing protocols against local or global dynamics
eavesdroppers, and proposed a Privacy-Preserving-Summation-Consistent (PPSC)
mechanism as a generic privacy encryption subroutine for consensus-based
distributed computations. In this part of this paper, we show that the
conventional deterministic and random gossip algorithms can be used to realize
the PPSC mechanism over a given network. At each time step, a node is selected
to interact with one of its neighbors via deterministic or random gossiping.
Such node generates a random number as its new state, and sends the subtraction
between its current state and that random number to the neighbor; then the
neighbor updates its state by adding the received value to its current state.
We establish concrete privacy-preservation conditions by proving the
impossibility for the reconstruction of the network input from the output of
the gossip-based PPSC mechanism against eavesdroppers with full network
knowledge, and by showing that the PPSC mechanism can achieve differential
privacy at arbitrary privacy levels. The convergence is characterized
explicitly and analytically for both deterministic and randomized gossiping,
which is essentially achieved in a finite number of steps. Additionally, we
illustrate that the proposed algorithms can be easily made adaptive in
real-world applications by making realtime trade-offs between resilience
against node dropout or communication failure and privacy preservation
capabilities.
