Consensus on Demand

Lower Bounds on Implementing Robust and Resilient Mediators

“…Because messages may take up to ∆ rounds to arrive, two honest miners can both extend a given block b, because neither has heard of the other's extension at the point when it is doing its own extension. To make our results as strong as possible, following the literature [10,13,21], we assume that a deviating miner is able to avoid forking with its own blocks. Thus, a deviator can extend paths in the blockdag faster than would be indicated by her relative power.…”

“…Since each miner i aims to maximize its relative revenue (i.e., the ratio between i's revenue and the total reward received by miners while i is active, just as is the case in, e.g., [8,19,17,11]), and (by assumption) deviators have less power than honest agents (i.e., agents that follow the prescribed protocol), a symmetric penalty to a deviator and an honest agent results in the deviator suffering more than the honest agents. Sliwinski and Wattenhofer [21] also use symmetric penalties in a blockdag for all blocks that are not connected by a directed path; each block in a set X of such blocks is penalized by |X|c (for some constant c). However, with their approach, an adversary can harm honest agents.…”