  A distributed computing protocol consists of three components: (i) Data
Localization: a network-wide dataset is decomposed into local datasets
separately preserved at a network of nodes; (ii) Node Communication: the nodes
hold individual dynamical states and communicate with the neighbors about these
dynamical states; (iii) Local Computation: state recursions are computed at
each individual node. Information about the local datasets enters the
computation process through the node-to-node communication and the local
computations, which may be leaked to dynamics eavesdroppers having access to
global or local node states. In this paper, we systematically investigate this
potential computational privacy risks in distributed computing protocols in the
form of structured system identification, and then propose and thoroughly
analyze a Privacy-Preserving-Summation-Consistent (PPSC) mechanism as a generic
privacy encryption subroutine for consensus-based distributed computations. The
central idea is that the consensus manifold is where we can both hide node
privacy and achieve computational accuracy. In this first part of the paper, we
demonstrate the computational privacy risks in distributed algorithms against
dynamics eavesdroppers and particularly in distributed linear equation solvers,
and then propose the PPSC mechanism and illustrate its usefulness.
