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Overview
Decentralized cryptocurrency is produced by the entire cryptocurrency system collectively....resume
History
In 1998, Wei Dai published a description of "b-money", an anonymous, distributed electronic cash system. Shortly thereafter...
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Legality
The legal status of cryptocurrencies varies substantially from country to country and is still undefined or changing in many of them...resume

Timestamping
Cryptocurrencies use various timestamping schemes to avoid the need for a trusted third party to timestamp transactions added to the blockchain ledger
  -Proof-of-work schemes

The first timestamping scheme invented was the proof-of-work scheme. The most widely used proof-of-work schemes are based on SHA-256, which was introduced by bitcoin, and scrypt, which is used by currencies such as Litecoin. The latter now dominates over the world of cryptocurrencies, with at least 480 confirmed implementations.

Some other hashing algorithms that are used for proof-of-work include CryptoNight, Blake, SHA-3, and X11.

Modifications of the proof-of-work algorithm have been created to address the problem of scaling, such as the way the IOTA ledger works. IOTA uses a simplified Proof-of-work algorithm making use of directed acyclic graph. A new transaction becomes part of the ledger after its sender does a small amount of proof-of-work. Each network participant is therefore also a miner. This system scales automatically as it gets used more.

  -Proof-of-stake and combined schemes
Some cryptocurrencies use a combined proof-of-work/proof-of-stake scheme. The proof-of-stake is a method of securing a cryptocurrency network and achieving distributed consensus through requesting users to show ownership of a certain amount of currency. It is different from proof-of-work systems that run difficult hashing algorithms to validate electronic transactions. The scheme is largely dependent on the coin, and there's currently no standard form of it.