Cryptocurrency, or just crypto, is a digital, virtual (non-physical) currency used on the Internet which uses cryptographic methods (electronic signatures etc.) to implement a decentralized system in which there is no authority to control the currency (unlike e.g. with traditional currencies that are controlled by the state or systems of digital payments controlled by the banks that run these systems). Cryptocurrencies use so called blockchain as an underlying technology and are practically always implemented as free and open-source software. Example of cryptocurrencies are Bitcoin, Monero or Dogecoin.
The word crypto in crpytocurrency doesn't imply that the currency provides or protects privacy -- it rather refers to the cryptographic algorithms used to make the currency work -- even though thanks to the decentralization, anonymity and openness cryptocurrencies actually are mostly privacy friendly (up to the points of being considered the currency of criminals).
LRS sees cryptocurrencies more or less as unethical because in our view money itself is unethical, plus the currencies based on proof of work waste not only human effort but also enormous amount of electricity and computing power that could be spent in a better way. Crypto is just an immensely expensive game in which people try to fuck each other over money that have been stolen from the people.
Cryptocurrency is build on top of so called blockchain -- a kind structure that holds records of transactions (exchanges of money or "coins", as called in the crypto world). Blockchain is a data structure serving as a database of the system. As its name suggests, it consists of blocks. Each block contains various data, most important of which are performed transactions (e.g. "A sent 1 coin to B"), and each block points to a previous one (forming a linked list). As new transactions are made, new blocks are created and appended at the end of the blockchain.
But where is the blockchain stored? It is not on a single computer; many computers participating in the system have their own copy of the blockchain and they share it together (similarly to how people share files via torrents).
But how do we know which one is the "official" blockchain? Can't just people start forging information in the blockchain and then distribute the fake blockchains? Isn't there a chaos if there are so many copies? Well yes, it would be messy -- that's why we need a consensus of the participants on which blockchain is the real one. And there are a few algorithms to ensure the consensus. Basically people can't just spam add new blocks, a new block to be added needs to be validated via some process (which depends on the specific algorithm) in order to be accepted by others. Two main algorithms for this are:
Can't people just forge transactions, e.g. by sending out a record that says someone else sent them money? This can be easily prevented by digitally signing the transactions, i.e. if there is e.g. a transaction "A sends 1 coint to B", it has to be signed by A to confirm that A really intended to send the money. But can't someone just copy-paste someone else's already signed transactions and try to perform them multiple times? This can also be prevented by e.g. numbering the transactions, i.e. recording something like "A sent 1 coin to B as his 1st transaction".
But where are the coins of a person actually stored? They're not explicitly stored anywhere; the amount of coins any participant has is deduced from the list of transactions, i.e. if it is known someone joined the network with 0 coins and there is a record of someone else sending him 1 coin, it is clear he now has 1 coin. For end users there are so called wallets which to them appear to store their coins, but a wallet is in fact just the set of cryptographic keys needed to perform transactions.
But why is blockchain even needed? Can't we just have a list of signed transactions without any blocks? Well, blockchain is designed to ensure coherency and the above mentioned consensus.
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