Cryptocurrencies without Proof of Work

We study cryptocurrency protocols that do not make use of {\em Proof of Work}. Such protocols commonly rely on {\em 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 {\em Proof of Stake} protocols, and argue that the they help in mitigating problems that the existing protocols suffer from.