Arithmetic circuit for the first solution of distributed CSPs with cryptographic multi-party computations

A large class of problems like meeting scheduling, negotiation, or different types of coordination, can be formulated in terms of agents, variables, and constraints (i.e. predicates) on those variables. Distributed Constraint Satisfaction (DisCSP) is a framework addressing such general problems, namely defined in terms of a set of agents, variables, and constraints that the different agents enforce. Developing general algorithms for DisCSPs yield a basic solution for each of those problems. Each participant has its own constraint satisfaction problem, private concerns that should remain as secret as possible. Resources may be shared and cause the need for cooperation. We consider the case where privacy is an overwhelming requirement and we assume that any majority of the participants are incorruptible. Namely, given n participants, at least an n/2 unknown subset of them are trustworthy and not corrupted by attackers. This is a common assumption in cryptographic multi-party-computations, known as one of the threshold schemes. This work shows how a solution of a general DisCSP can be found securely by the owners of the problem without appealing to any trusted servers. The constraints are shared with Shamir's secret sharing scheme, transforming the DisCSP into a shared constraint satisfaction problem. An algorithm for such problems is developed.