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 in the privacy-preserving computation literature. 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 {\em 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 parties and no honest non-colluding servers. Privacy protection is offered for an extended period after the query executions.

翻译：一系列关于安全计算的研究早已证实，任何可计算的内容均可通过一组无合谋参与方实现安全计算。事实上，这种无合谋假设使许多问题得以解决，同时降低了计算开销，绕过了计算复杂性理论的极限，并在隐私保护计算文献中普遍存在。然而，该假设极易受到计算方之间隐蔽的、不可检测的合谋攻击的影响。本文源于一个观察：若可用计算方的数量远高于执行安全计算任务所需的参与方数量，则隐私保护计算中的合谋企图可能被遏制。我们聚焦于多服务器$1$-隐私信息检索（PIR）这一典型的隐私保护计算任务，该任务固有地假设无两两合谋。对于PIR应用场景（例如区块链轻客户端），当可用服务器数量充足时，单个服务器的偏离行为对其自身而言并无巨大收益。我们可通过少量奖励与惩罚使偏离行为不受欢迎，从而显著{\em 提高合谋抵抗的门槛}。我们在具有支付执行功能的公共公告板上设计并实现了一种合谋缓解机制，仅考虑理性参与方，且无诚实无合谋服务器。查询执行后，隐私保护将在延长的时间段内持续提供。