In recent years, several studies proposed privacy-preserving algorithms for solving Distributed Constraint Optimization Problems (DCOPs). Those studies were based on existing DCOP solving algorithms, which they strengthened by implementing cryptographic weaponry that enabled performing the very same computation while protecting sensitive private data. All of those studies assumed that agents do not collude. In this study we propose the first privacy-preserving DCOP algorithm that is immune to coalitions. Our basic algorithm is secure against any coalition under the assumption of an honest majority (namely, the number of colluding agents is $<n/2$, where n is the overall number of agents). We then proceed to describe two variants of that basic algorithm: a more efficient variant that is secure against coalitions of size ≤c, for some constant $c<(n-1)/2$; and another variant that is immune to agent coalitions of any size, but relies on an external committee of mediators with an honest majority. Our algorithm – PC-SyncBB – is based on the classical Branch and Bound DCOP algorithm. It offers constraint, topology and decision privacy. We evaluate its performance on different benchmarks, problem sizes, and constraint densities. We show that achieving security against coalitions is feasible. Our experiments indicate that PC-SyncBB can run in reasonable time on problems involving up to 19 agents. As all existing privacy-preserving DCOP algorithms base their security on assuming solitary conduct of the agents, we view this study as an essential first step towards lifting this potentially harmful assumption in all those algorithms.

近年来，一些研究提出了用于解决分布式约束优化问题（DCOP）的隐私保护算法。这些研究是基于现有的DCOP解决算法的，这些算法通过实施加密武器得以加强，该加密武器能够执行相同的计算，同时保护敏感的私有数据。所有这些研究都假定代理人之间不会共谋。在这项研究中，我们提出了第一个不受联盟保护的隐私保护DCOP算法。在诚实多数的假设下，我们的基本算法对于任何联盟都是安全的（即，共谋代理的数量为$<ñ/\mathrm{2个}$，其中n是代理的总数）。然后我们继续描述基本算法的两个变种：一个更有效的变体是对大小≤的联盟安全Ç，对于某一常数$C<（ñ-\mathrm{1个}）/\mathrm{2个}$; 另一个变体不受任何规模的特工联盟影响，但要依靠诚实多数的调解员外部委员会。我们的算法PC-SyncBB基于经典的Branch and Bound DCOP算法。它提供了约束，拓扑和决策隐私。我们在不同的基准，问题大小和约束密度下评估其性能。我们表明，实现针对联盟的安全是可行的。我们的实验表明，PC-SyncBB可以在合理的时间内解决涉及多达19个代理的问题。由于所有现有的保护隐私的DCOP算法的安全性都基于假设代理人的单独行为，因此，我们认为本研究是在所有这些算法中取消这一潜在有害假设的必不可少的第一步。