Cryptographic Rational Secret Sharing Schemes over General Networks

Abstract

We propose cryptographic rational secret sharing protocols over general networks. In a general network, the dealer may not have direct connections to each player, and players may not have direct connections to each of the other players. We present conditions on the network topology for which our proposed protocols are computational strict Nash equilibria and (k−1)-resilient, along with analysis on their round and communication complexity. We also present new notions of equilibria such as Φ-resilient computational Nash equilibria, whereby a protocol is resilient to coalitions that satisfy conditions in Φ, regardless of the coalition’s size. We also propose (n−1)-key leakage-tolerant equilibria applicable to cryptographic protocols involving secret keys, whereby the equilibrium holds even if some players acquire (n−1) tuples of secret keys.