Cryptocurrencies without Proof of Work.

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.