General Constructions of Rational Secret Sharing with Expected Constant-Round Reconstruction: Table 1.

Abstract

We present a general construction of a rational secret-sharing protocol that converts any rational secret-sharing protocol to a protocol with an expected constant-round reconstruction. Our construction can be applied to protocols for synchronous channels, and preserves a strict Nash equilibrium of the original protocol. Combining with an existing protocol, we obtain the first expected constant-round protocol that achieves a strict Nash equilibrium with the optimal coalition resilience ⌈ n 2 ⌉ − 1, where n is the number of players. Our construction can be extended to a construction that preserves the immunity to unexpectedly behaving players. Then, for any constant m ≥ 1, we obtain an expected constant-round protocol that achieves a Nash equilibrium with the optimal coalition resilience ⌈ n 2 ⌉ − m − 1 in the presence of m unexpectedly behaving players. The same protocol also achieves a strict Nash equilibrium with coalition resilience 1. We show that our protocol with immunity achieves the optimal coalition resilience among constant-round protocols with immunity with respect to both Nash and strict Nash equilibria.

Realistic versus Rational Secret Sharing

“…Halpern and Teague and followers [16,15,13,17,18] explored the rivalrous and excludable common good framework. Given a run r in the game tree, they introduce vector info(r) to be the n-tuple (t 1 , t 2 , .…”

Repeated Games for Generating Randomness in Encryption

“…There are many studies using game-theoretic analysis for cryptographic primitives, including secret sharing [10]- [19], two-party protocols [20]- [22], public-key encryption [9], leader election [23], [24], Byzantine agreement [25], delegation of computation [26]- [30], and protocol design [31], [32]. Among them, repeated games have been introduced only in rational secret sharing [33].…”

Perfectly Secure Message Transmission Against Rational Adversaries

“…Halpern and Teague [8] first studied the rational behavior of participants for secret sharing. Since then, rational secret sharing has been intensively studied [9], [10], [11], [12], [13], [14], [15]. Moreover, there have been many studies using game-theoretic analysis of cryptographic primitives/protocols, including two-party computation [16], [17], leader election [18], [19], Byzantine agreement [20], consensus [21], public-key encryption [22], [23], delegation of computation [24], [25], [26], [27], [28], [29], and protocol design [30], [31].…”