Suppose Alice and Bob are two entities (e.g. agents, organizations, etc.) that wish to negotiate a contract. A contract consists of several clauses, and each party has certain constraints on the acceptability and desirability (i.e., a private "utility" function) of each clause. If Bob were to reveal his constraints to Alice in order to find an agreement, then she would learn an unacceptable amount of information about his business operations or strategy. To alleviate this problem we propose the use of Secure Function Evaluation (SFE) to find an agreement between the two parties. There are two parts to this: ⅰ) determining whether an agreement is possible (if not then no other information should be revealed), and ⅱ) in case an agreement is possible, coming up with a contract that is valid (acceptable to both parties), fair (when many valid and good outcomes are possible one of them is selected randomly with a uniform distribution, without either party being able to control the outcome), and efficient (no clause is replaceable by another that is better for both parties). It is the fairness constraint in (ⅱ) that is the centerpiece of this paper as it requires novel techniques that produce a solution that is more efficient than general SFE techniques. We give protocols for all of the above in the semi-honest model, and we do not assume the Random Oracle Model.
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