Delegating large-scale computations to service providers is a common practice which raises privacy concerns. This paper studies information-theoretic privacy-preserving delegation of data to a service provider, who may further delegate the computation to auxiliary worker nodes, in order to compute a polynomial over that data at a later point in time. We study techniques which are compatible with robust management of distributed computation systems, an area known as coded computing. Privacy in coded computing, however, has traditionally addressed the problem of colluding workers, and assumed that the server that administrates the computation is trusted. This viewpoint of privacy does not accurately reflect real-world privacy concerns, since normally, the service provider as a whole (i.e., the administrator and the worker nodes) form one cohesive entity which itself poses a privacy risk. This paper aims to shift the focus of privacy in coded computing to safeguarding the privacy of the user against the service provider as a whole, instead of merely against colluding workers inside the service provider. To this end, we leverage the recently defined notion of perfect subset privacy, which guarantees zero information leakage from all subsets of the data up to a certain size. Using known techniques from Reed-Muller decoding, we provide a scheme which enables polynomial computation with perfect subset privacy in straggler-free systems. Furthermore, by studying information super-sets in Reed-Muller codes, which may be of independent interest, we extend the previous scheme to tolerate straggling worker nodes inside the service provider.

翻译：将大规模计算委托给服务提供商是常见做法，但会引发隐私问题。本文研究基于信息论的隐私保护数据委托方法——数据被委托给服务提供商后，可能进一步转交给辅助工作节点，以便后续对数据进行多项式计算。我们研究与分布式计算系统鲁棒管理相兼容的技术，该领域被称为编码计算。然而，编码计算中的隐私问题传统上关注共谋工作节点，并假设管理计算的服务器是可信的。这种隐私观点未能准确反映现实世界的隐私顾虑，因为通常服务提供商整体（即管理员与工作节点）构成一个统一的实体，其本身即构成隐私风险。本文旨在将编码计算中的隐私焦点转向保护用户免受服务提供商整体的侵害，而非仅针对服务提供商内部的共谋工作节点。为此，我们利用新近定义的完美子集隐私概念，该概念保证数据中任意不超过特定大小的子集均无信息泄露。通过运用里德-穆勒译码的已知技术，我们提出一种方案，可在无掉队者系统中实现具有完美子集隐私的多项式计算。此外，通过研究里德-穆勒码中的信息超集（该结果可能具有独立研究价值），我们将前述方案扩展至可容忍服务提供商内部掉队工作节点的场景。