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. Furthermore, sensor networks were established to monitor physical areas for scientific research, smart-cities control, and other purposes. 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.