In 2009, Satoshi Nakamoto introduced the Bitcoin cryptocurrency[Nak09], an online currency sys- tem which allowed peer-to-peer transfer of digital tokens. To ensure a consistent view of token ownership, Nakamoto used a public ledger which can be replicated and validated by all network participants. To avoid a single point of failure, this ledger is authenticated using a dynamic mem- bership multiparty signature (DMMS)[BCD+14] consisting of an expensive (but cheaply verifiable) computation done on the entire ledger history every “heartbeat”.