  Byzantine Fault-Tolerant (BFT) protocols have been proposed to tolerate
malicious behaviors in state machine replications. With classic BFT protocols,
the total number of replicas is known and fixed a priori. The resilience of BFT
protocols, i.e., the number of tolerated Byzantine replicas (denoted f ), is
derived from the total number of replicas according to the quorum theory.
  To guarantee that an attacker cannot control more than f replicas, so to
guarantee safety, it is vital to ensure fault independence among all replicas.
This in practice is achieved by enforcing diverse configurations of replicas,
i.e., each replica has a unique configuration, avoiding f fault compromises
more than f replicas.
  While managing replica diversity in BFT protocols has been studied in
permissioned environments with a small number of replicas, no prior work has
discussed the fault independence in a permissionless environment (such as
public blockchains) where anyone can join and leave the system at any time.
This is particularly challenging due to the following two facts. First, with
permissionless environment, any one can join as a replica at any time and no
global coordinator can be relied on to manage replica diversity. Second, while
great progress has been made to scale consensus algorithms to thousands of
replicas, the replica diversity cannot provide fault independence at this
scale, limiting practical and meaningful resilience.
  This paper provides the first discussion on the impact of fault independence
on permissionless blockchains, provides discussions on replica configuration
diversity, quantifies replica diversity by using entropy, and defines optimal
fault independence.
