Cake-cutting algorithms, which aim to fairly allocate a continuous resource based on individual agent preferences, have seen significant progress over the past two decades. Much of the research has concentrated on fairness, with comparatively less attention given to other important aspects. Chen et al. (2010) introduced an algorithm that, in addition to ensuring fairness, was strategyproof -- meaning agents had no incentive to misreport their valuations. However, even in the absence of strategic incentives to misreport, agents may still hesitate to reveal their true preferences due to privacy concerns (e.g., when allocating advertising time between firms, revealing preferences could inadvertently expose planned marketing strategies or product launch timelines). In this work, we extend the strategyproof algorithm of Chen et al. by introducing a privacy-preserving dimension. To the best of our knowledge, we present the first private cake-cutting protocol, and, in addition, this protocol is also envy-free and strategyproof. Our approach replaces the algorithm's centralized computation with a novel adaptation of cryptographic techniques, enabling privacy without compromising fairness or strategyproofness. Thus, our protocol encourages agents to report their true preferences not only because they are not incentivized to lie, but also because they are protected from having their preferences exposed.

翻译：蛋糕分割算法旨在基于个体代理人偏好公平分配连续资源，该领域在过去二十年中取得了显著进展。多数研究聚焦于公平性，而相对较少关注其他重要方面。Chen等人（2010）提出了一种算法，该算法除了确保公平性外，还具备策略证明性——即代理人不具备虚报自身估值动机。然而，即便缺乏策略性虚报激励，代理人仍可能因隐私顾虑而犹豫是否透露真实偏好（例如，在企业间分配广告时段时，透露偏好可能无意中暴露既定营销策略或产品发布时间线）。本研究通过引入隐私保护维度，对Chen等人的策略证明算法进行了扩展。据我们所知，我们提出了首个私有蛋糕分割协议，且该协议同时具备无嫉妒性与策略证明性。我们的方法将算法中的集中式计算替换为密码学技术的创新改编，在不牺牲公平性与策略证明性的前提下实现了隐私保护。因此，本协议不仅因代理人缺乏欺骗动机，更因其偏好免受暴露的保护机制，鼓励代理人报告真实偏好。