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.

中文翻译：

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无硬度假设的安全分布式算法

我们研究了分布式消息传递模型中的算法，该模型为输入图 $G$ 产生安全输出。具体来说，每个顶点计算它在输出中的部分，整个输出是正确的，但每个顶点都不能发现其他顶点的输出，有一定的概率。这是由当今嵌入在各种设备中的高性能处理器驱动的。在这种情况下，将整个处理任务留给单个计算机甚至一组中央计算机已不再有意义，并且在许多情况下是不可行的。由于分布式算法领域的广泛研究为许多经典问题产生了高效的分散算法，因此对分布式算法的安全性的讨论有些被忽视。尽管如此，在安全多方计算问题（MPC 或 SMC）的研究领域设计了许多协议和算法。然而，这些协议的概念和术语与经典的分布式算法有很大不同。因此，这些协议的重点是以增加轮次复杂性或几个计算假设的必要性为代价来为每个函数 $f$ 工作。在这项工作中，我们提出了一种新方法，该方法不是将现有算法转变为安全算法，而是识别和开发那些本质上安全的算法（这意味着它们不需要任何进一步的构造）。这种方法为各种局部问题产生了高效的安全算法，例如着色、网络分解、森林分解和各种附加标签问题。值得注意的是，我们的方法不需要任何硬度假设，而只需要每个顶点中的私有随机生成器。这与此设置中基于公钥加密方案的先前已知技术形成对比。