A purely peer-to-peer version of electronic cash would allow online payments to be sent directly from one party to another without going through a financial institution. Digital signatures provide part of the solution, but the main benefits are lost if a trusted third party is still required to prevent double-spending. We propose a solution to the double-spending problem using a peer-to-peer network. The network timestamps transactions by hashing them into an ongoing chain of hash-based proof-of-work, forming a record that cannot be changed without redoing the proof-of-work. The longest chain not only serves as proof of the sequence of events witnessed, but proof that it came from the largest pool of CPU power. As long as a majority of CPU power is controlled by nodes that are not cooperating to attack the network, they'll generate the longest chain and outpace attackers.
A digital currency requires arbitrary tokens as a medium of exchange.
It does not require peer-to-peer creation and verification of tokens. It does not require mining, it does not require pseudo-anonymous transactions and a distributed public ledger of all past transactions. Those are all properties of Bitcoin but not of currencies in general.
Bitcoin has some interesting ideas, but it's hardly the only type of digital currency which can exist and mining is a concept particular to Bitcoin (and spin-offs) - it has the effect of enriching the devs and early adopters and transforming it into an appreciating asset rather than a currency.
Mining is not just for distribution of tokens. I would argue the more important use is for maintaining the proof-of-work blockchain. There have been some experimental attempts at maintaining a distributed ledger using a proof-of-stake/proof-of-work hybrid, but I don't know of any successful attempts to do it without a proof-of-work component.
If you have an idea of how it could be done, you may have a shot at dethroning Bitcoin.
Ripple achieves ledger consensus without proof-of-work. Absence of proof-of-work is how it gets a new ledger (analogous to the block) every few seconds. The XRP fee destruction deflationary scheme is effectively similar to a proof-of-stake inflationary scheme, because as the total supply of XRP decreases, it benefits all XRP holders in proportion to their holdings.
