Our result Sample Clauses

Our result. P The security of our protocol is measured as the probability that an adversary can get some (partial) information on the key. This probability is denoted Advake and depends on the number of messages sent on the network.

Our result. In this paper, we show that a baiting strategy, that one can implement with these undeniable proofs-of-fraud, is necessary and sufficient to devise a consensus protocol that is robust to a coalition of up to k rational players and t Byzantine players, a problem we call the rational agreement problem. This result holds under the assumption of partial synchrony, where there is an unknown bound on the delay of messages [14]. First, we introduce the notion of baiting strategy as a particular case of pun- ishment strategy and show that it is impossible to solve the rational agreement problem without a baiting strategy: A (k, f, m)-baiting strategy is a (k − m, f )- punishment strategy such that 0 < m ≤ k, and the m rational players that do not collude would lower their utility by not playing the baiting strategy and deviating with the rest of the players of the coalition. Second, we present a solution to the rational agreement problem that relies on a baiting strategy. To this end, we devise the Huntsman protocol for the partially synchronous model that extends an existing consensus protocol that is t-accountable for t < n/3 to become ǫ-(k, t)-robust when n > max( 3 k +3t, 2(k + t)). The key idea is to reward a single player if it exposes the coalition to which it belongs. If the reward is larger than the individual return that a rational gains from causing a disagreement, then rational players in a coalition can find that the strategy to form a coalition and cause a disagreement is strictly dominated by the strategy to betray the coalition in the sequential game. The solution thus finds relevance in the context of a distributed ledger where a disagreement can allow a player to steal digital assets but where requiring play- ers to deposit some of their assets can be used to threaten them. In particular, our protocol pre-decides decisions from a t-accountable consensus protocol that it extends with the Byzantine Fault Tolerant Commit-Reveal protocol (BFTCR) that consists of two reliable broadcasts and one additional broadcast. BFTCR ensures the existence of a baiting strategy (baiting-dominance) and that the protocol still solves agreement even after playing the baiting strategy (baiting- agreement). We also add an additional property outside the problem definition, lossfree-reward, which states that the increase in utility for baiting rational play- ers comes at no cost to non-deviating players. For this purpose, we introduce a deposit per player and reward to ...