We consider the problem of fair two-party computation, where fairness (informally) means that both parties should learn the correct output. A seminal result of Cleve (STOC 1986) shows that fairness is, in general, impossible to achieve for malicious parties. Here, we treat the parties as rational and seek to understand what can be done. Asharov et al. (Eurocrypt 2011) recently considered this problem and showed impossibility of rational fair computation for a particular function and a particular set of utilities. We observe, however, that in their setting the parties have no incentive to compute the function even in an ideal world where fairness is guaranteed. Revisiting the problem, we show that rational fair computation is possible (for arbitrary functions and utilities) as long as the parties have a strict incentive to compute the function in the ideal world. This gives a new example where game theory can be used to circumvent impossibility results in cryptography.
Rational secure multi-party computation means two or more rational parties complete a function on private inputs. Unfortunately, players sending false information can prevent the protocol from executing correctly, which will destroy the fairness of the protocol. To ensure the fairness of the protocol, the existing works on achieving fairness by specific utility functions. In this paper, we leverage game theory to propose the direction entropy-based solution. To this end, we utilize the direction entropy to examine the player's strategy uncertainty and quantify its strategy from different dimensions. Then, we provide mutual information to construct a new utility for the players. What's more, we measure the mutual information of players to appraise their strategies. By analyzing and proofing of protocol, we show that the protocol reaches a Nash equilibrium when players choose a cooperative strategy. Furthermore, we solve the fairness of the protocol. Compared to the previous approaches, our protocol is not required deposits and design-specific utility functions.
Complete fairness means that either all parties learn the output of the function or none of them does. It was deemed as an impossible task in general in secure two party computation by Cleve (STOC 1986). However, a seminal result of complete fairness between two parties was achieved by Gordorn et al. (STOC 2008). Recently Groce and Katz (Euro crypt 2012) corrected the insufficient assumptions and gave some positive results of fairness. Here we revisit this problem and introduce the Tit-for-Tat (TFT) strategy into rational two-party computation. To the best of our knowledge, it is the first secure two-party computation protocol with constant rounds that allows both parties to know the terminal round.
The field of rational cryptography considers the design of cryptographic protocols in the presence of rational agents seeking to maximize local utility functions. This departs from the standard secure multiparty computation setting, where players are assumed to be either honest or malicious. We detail the construction of both a two-party and a multiparty game theoretic framework for constructing rational cryptographic protocols. Our framework specifies the utility function assumptions necessary to realize the privacy, correctness, and fairness guarantees for protocols. We demonstrate that our framework correctly models cryptographic protocols, such as rational secret sharing, where existing work considers equilibrium concepts that yield unreasonable equilibria. Similarly, we demonstrate that cryptography may be applied to the game theoretic domain, constructing an auction market not realizable in the original formulation. Additionally, we demonstrate that modeling players as rational agents allows us to design a protocol that destabilizes coalitions. Thus, we establish a mutual benefit from combining the two fields, while demonstrating the applicability of our framework to real-world market environments. We also give an application of game theory to adversarial interactions where cryptography is not necessary. Specifically, we consider adversarial machine learning, where the adversary is rational and reacts to the presence of a data miner. We give a general extension to classification algorithms that returns greater expected utility for the data miner than existing classification methods.