been proven in the famous FLP impossibility result that a deterministic algorithm for achieving consensus is impossible. This impossibility result derives from worst-case scheduling scenarios, which are unlikely to occur in practice except in adversarial situations such as an intelligent denial-of-service attacker in the network. In most normal situations, process scheduling has a degree of natural randomness. In an asynchronous model, some forms of failures can be handled by a synchronous consensus protocol. For instance, the loss of a communication link may be modeled as a process which has suffered a Byzantine failure. Randomized consensus algorithms can circumvent the FLP impossibility result by achieving both safety and liveness with overwhelming probability, even under worst-case scheduling scenarios such as an intelligent denial-of-service attacker in the network. Permissioned versus permissionless consensus Consensus algorithms traditionally assume that the set of participating nodes is fixed and given at the outset: that is, that some prior (manual or automatic) configuration process has permissioned a particular known group of participants who can authenticate each other as members of the group. In the absence of such a well-defined, closed group with authenticated members, a Sybil attack against an open consensus group can defeat even a Byzantine consensus algorithm, simply by creating enough virtual participants to overwhelm the fault tolerance threshold. A permissionless consensus protocol, in contrast, allows anyone in the network to join dynamically and participate without prior permission, but instead imposes a different form of artificial cost or barrier to entry to mitigate the Sybil attack threat. Bitcoin introduced the first permissionless consensus protocol using proof of work and a difficulty adjustment function, in which participants compete to solve cryptographic hash puzzles, and probabilistically earn the right to commit blocks and earn associated rewards in proportion to their invested computational effort. Motivated in part by the high energy cost of this approach, subsequent permissionless consensus protocols have proposed or adopted other alternative participation rules for Sybil attack protection, such as proof of stake, proof of space, and proof of authority. Equivalency of agreement problems Three agreement problems of interest are as follows. Terminating Reliable Broadcast A collection of processes, numbered from to communicate by sending messages to one another. Process must transmit a value to all processes such that: if process is correct, then every correct process receives for any two correct processes, each process receives the same value. It is also known as The General's