  We study algorithms in the distributed message-passing model that produce
secured output, for an input graph $G$. Specifically, each vertex computes its
part in the output, the entire output is correct, but each vertex cannot
discover the output of other vertices, with a certain probability. This is
motivated by high-performance processors that are embedded nowadays in a large
variety of devices. In such situations, it no longer makes sense, and in many
cases it is not feasible, to leave the whole processing task to a single
computer or even a group of central computers. As the extensive research in the
distributed algorithms field yielded efficient decentralized algorithms for
many classic problems, the discussion about the security of distributed
algorithms was somewhat neglected. Nevertheless, many protocols and algorithms
were devised in the research area of secure multi-party computation problem
(MPC or SMC). However, the notions and terminology of these protocols are quite
different than in classic distributed algorithms. As a consequence, the focus
in those protocols was to work for every function $f$ at the expense of
increasing the round complexity, or the necessity of several computational
assumptions. In this work, we present a novel approach, which rather than
turning existing algorithms into secure ones, identifies and develops those
algorithms that are inherently secure (which means they do not require any
further constructions). This approach yields efficient secure algorithms for
various locality problems, such as coloring, network decomposition, forest
decomposition, and a variety of additional labeling problems. Remarkably, our
approach does not require any hardness assumption, but only a private
randomness generator in each vertex. This is in contrast to previously known
techniques in this setting that are based on public-key encryption schemes.
