Fairness with an Honest Minority and a Rational Majority.

Shien Jin Ong, David C. Parkes, Alon Rosen +1 more

Steven Gordon, Jonathan I. Katz

Jie Wang

In the setting of ( , ) mn rational secret sharing, n rational players wish to share a secret s , arbitrarily m players can reconstruct it, they always choose the strategies which can bring them more utilities.The security requirement includes privacy, correctness and fairness.Fairness is a central objective of the rational secret sharing scheme, complete fair means either all players get the secret s or none of them get it, but most existing schemes do not meet this nature.In this work, a rational secret sharing protocol is proposed, which neither need particular communication channel, nor assume the existence of honest minority, in addition, the scheme can resist the collusion attack with () k k m  players, and can achieve sequential equilibrium.Theoretical analysis shows that the proposed protocol is complete fair.

Pedro Branco, Pratik Soni, Sri Aravinda Krishnan Thyagarajan +1 more

Secure coin-tossing is typically modeled as an input-less functionality, where parties with no private inputs jointly generate a fair coin. In the dishonest majority setting, however, a strongly fair coin-tossing protocol is impossible. To circumvent this barrier, recent work has adopted the weaker notion of game-theoretic fairness, where adversaries are rational parties with preferences for specific outcomes, seeking to bias the coin in their favor. Yet these preferences may encode secret information, making prior protocols that assume preferences are public, fundamentally incompatible with privacy. We initiate a comprehensive study of privacy-preserving game-theoretically fair coin-tossing, where the preferences of honest parties remain private. We propose a simulation-based security framework and a new ideal functionality that reconciles both preference-privacy and game-theoretic fairness. A key ingredient is a certifying authority that authenticates each party’s preference and publishes only aggregate statistics, preventing misreporting while hiding parties' preferences. The functionality guarantees that every honest party receives an output: either a uniform coin; or, if an adversary deviates, a coin that does not increase the adversarial coalition's expected utility. Within this framework, we construct a protocol realizing our ideal functionality under standard cryptographic assumptions that works for both binary and general m -sided coin-tossing. Our binary scheme matches the corruption threshold of Wu-Asharov-Shi (EUROCRYPT '22); our multi-sided scheme builds on Thyagarajan-Wu-Soni (CRYPTO '24) with a corruption guarantee depending on the coalition's preference counts. Technically, our protocols combine authenticated preferences with an anonymous communication layer that decouples identities from preference-dependent actions, together with a deviation-penalty mechanism that enforces game-theoretic fairness. Our work is the first to reconcile game-theoretic fairness with preference privacy, offering new definitional tools and efficient protocols for rational multi-party computation in dishonest majority settings.

A.A. Tyapkin

Ran Cohen, Yehuda Lindell

In the setting of secure multiparty computation, a set of parties wish to compute a joint function of their private inputs. The computation should preserve security properties such as privacy, correctness, independence of inputs, fairness and guaranteed output delivery. In the case of no honest majority, fairness and guaranteed output delivery cannot always be obtained. Thus, protocols for secure multiparty computation are typically of two disparate types: protocols that assume an honest majority (and achieve all properties including fairness and guaranteed output delivery), and protocols that do not assume an honest majority (and achieve all properties except for fairness and guaranteed output delivery). In addition, in the two-party case, fairness and guaranteed output delivery are equivalent. As a result, the properties of fairness (which means that if corrupted parties receive output then so do the honest parties) and guaranteed output delivery (which means that corrupted parties cannot prevent the honest parties from receiving output in any case) have typically been considered to be the same. In this paper, we initiate a study of the relation between fairness and guaranteed output delivery in secure multiparty computation. We show that in the multiparty setting these proper-ties are distinct and proceed to study under what conditions fairness implies guaranteed output delivery (the opposite direction always holds). We also show the existence of non-trivial func-tions for which complete fairness is achievable (without an honest majority) but guaranteed output delivery is not, and the existence of non-trivial functions for which complete fairness and guaranteed output delivery are achievable. Our study sheds light on the role of broadcast in fairness and guaranteed output delivery, and shows that these properties should sometimes be considered separately.