  We study decentralized cryptocurrency protocols in which the participants do
not deplete physical scarce resources. Such protocols commonly rely on Proof of
Stake, i.e., on mechanisms that extend voting power to the stakeholders of the
system. We offer analysis of existing protocols that have a substantial amount
of popularity. We then present our novel pure Proof of Stake protocols, and
argue that they help in mitigating problems that the existing protocols
exhibit.
