A long line of research on secure computation has confirmed that anything that can be computed, can be computed securely using a set of non-colluding parties. Indeed, this non-collusion assumption makes a number of problems solvable, as well as reduces overheads and bypasses computational hardness results, and it is pervasive across different privacy-enhancing technologies. However, it remains highly susceptible to covert, undetectable collusion among computing parties. This work stems from an observation that if the number of available computing parties is much higher than the number of parties required to perform a secure computation task, collusion attempts in privacy-preserving computations could be deterred. We focus on the prominent privacy-preserving computation task of multi-server $1$-private information retrieval (PIR) that inherently assumes no pair-wise collusion. For PIR application scenarios, such as those for blockchain light clients, where the available servers can be plentiful, a single server's deviating action is not tremendously beneficial to itself. We can make deviations undesired via small amounts of rewards and penalties, thus significantly raising the bar for collusion resistance. We design and implement a collusion mitigation mechanism on a public bulletin board with payment execution functions, considering only rational and malicious parties with no honest non-colluding servers. Privacy protection is offered for an extended period after the query executions.

翻译：安全计算领域的一系列研究已证实，任何可计算的问题均能通过一组非共谋参与方安全地完成计算。事实上，这种非共谋假设不仅使诸多问题变得可解，还能降低计算开销并绕过计算复杂性理论中的困难性结论，在各类隐私增强技术中得到广泛应用。然而，该假设极易受到计算方之间难以察觉的隐蔽共谋攻击。本工作的出发点是：当可用计算方数量远超执行安全计算任务所需数量时，隐私保护计算中的共谋尝试可被有效遏制。我们聚焦于多服务器$1$-隐私信息检索（PIR）这一典型隐私计算任务——该任务本质要求服务器间不存在两两共谋。在PIR应用场景（如区块链轻客户端场景）中，当可用服务器数量充足时，单个服务器的违规行为对其自身收益极为有限。通过设置小额奖惩机制即可抑制违规动机，从而显著提升抗共谋能力。我们设计并实现了一种基于公共公告板的共谋缓解机制（含支付执行功能），仅考虑理性参与方与恶意参与方（不依赖诚实非共谋服务器），且查询执行后仍能提供长期隐私保护。