According to The New York Times, libertarians and anarchists were attracted to the idea. Early bitcoin supporter Roger Ver said: "At first, almost everyone who got involved did so for philosophical reasons. We saw bitcoin as a great idea, as a way to separate money from the state."[131] The Economist describes bitcoin as "a techno-anarchist project to create an online version of cash, a way for people to transact without the possibility of interference from malicious governments or banks".[134] Economist Paul Krugman argues that cryptocurrencies like bitcoin are "something of a cult" based in "paranoid fantasies" of government power.[135]
The bitcoin blockchain is a public ledger that records bitcoin transactions.[79] It is implemented as a chain of blocks, each block containing a hash of the previous block up to the genesis block[d] of the chain. A network of communicating nodes running bitcoin software maintains the blockchain.[36]:215–219 Transactions of the form payer X sends Y bitcoins to payee Z are broadcast to this network using readily available software applications.

Cameron and Tyler Winklevoss, the founders of the Gemini Trust Co. exchange, reported that they had cut their paper wallets into pieces and stored them in envelopes distributed to safe deposit boxes across the United States.[106] Through this system, the theft of one envelope would neither allow the thief to steal any bitcoins nor deprive the rightful owners of their access to them.[105]

A lot of concerns have been raised regarding cryptocurrencies’ decentralized nature and their ability to be used almost completely anonymously. The authorities all over the world are worried about the cryptocurrencies’ appeal to the traders of illegal goods and services. Moreover, they are worried about their use in money laundering and tax evasion schemes.
According to the Library of Congress, an "absolute ban" on trading or using cryptocurrencies applies in eight countries: Algeria, Bolivia, Egypt, Iraq, Morocco, Nepal, Pakistan, and the United Arab Emirates. An "implicit ban" applies in another 15 countries, which include Bahrain, Bangladesh, China, Colombia, the Dominican Republic, Indonesia, Iran, Kuwait, Lesotho, Lithuania, Macau, Oman, Qatar, Saudi Arabia and Taiwan.[178]

According to the European Central Bank, the decentralization of money offered by bitcoin has its theoretical roots in the Austrian school of economics, especially with Friedrich von Hayek in his book Denationalisation of Money: The Argument Refined,[132] in which Hayek advocates a complete free market in the production, distribution and management of money to end the monopoly of central banks.[133]:22
As of November 2017, Bitcoin and other digital currencies are outlawed only in Bangladesh, Bolivia, Ecuador, Kyrgyzstan and Vietnam, with China and Russia being on the verge of banning them as well. Other jurisdictions, however, do not make the usage of cryptocurrencies illegal as of yet, but the laws and regulations can vary drastically depending on the country.
As of May 2018, over 1,800 cryptocurrency specifications existed.[24] Within a cryptocurrency system, the safety, integrity and balance of ledgers is maintained by a community of mutually distrustful parties referred to as miners: who use their computers to help validate and timestamp transactions, adding them to the ledger in accordance with a particular timestamping scheme.[14]

^ "Bitcoin: The Cryptoanarchists' Answer to Cash". IEEE Spectrum. Archived from the original on 4 June 2012. Around the same time, Nick Szabo, a computer scientist who now blogs about law and the history of money, was one of the first to imagine a new digital currency from the ground up. Although many consider his scheme, which he calls "bit gold", to be a precursor to Bitcoin

To understand the revolutionary impact of cryptocurrencies you need to consider both properties. Bitcoin as a permissionless, irreversible, and pseudonymous means of payment is an attack on the control of banks and governments over the monetary transactions of their citizens. You can‘t hinder someone to use Bitcoin, you can‘t prohibit someone to accept a payment, you can‘t undo a transaction.

In the blockchain, bitcoins are registered to bitcoin addresses. Creating a bitcoin address requires nothing more than picking a random valid private key and computing the corresponding bitcoin address. This computation can be done in a split second. But the reverse, computing the private key of a given bitcoin address, is mathematically unfeasible. Users can tell others or make public a bitcoin address without compromising its corresponding private key. Moreover, the number of valid private keys is so vast that it is extremely unlikely someone will compute a key-pair that is already in use and has funds. The vast number of valid private keys makes it unfeasible that brute force could be used to compromise a private key. To be able to spend their bitcoins, the owner must know the corresponding private key and digitally sign the transaction. The network verifies the signature using the public key; the private key is never revealed.[7]:ch. 5
Bitcoin (BTC) is a consensus network that enables a new payment system and a completely digital currency. Powered by its users, it is a peer to peer payment network that requires no central authority to operate. On October 31st, 2008, an individual or group of individuals operating under the pseudonym "Satoshi Nakamoto" published the Bitcoin Whitepaper and described it as: "a purely peer-to-peer version of electronic cash, which would allow online payments to be sent directly from one party to another without going through a financial institution."
Transactions are defined using a Forth-like scripting language.[7]:ch. 5 Transactions consist of one or more inputs and one or more outputs. When a user sends bitcoins, the user designates each address and the amount of bitcoin being sent to that address in an output. To prevent double spending, each input must refer to a previous unspent output in the blockchain.[81] The use of multiple inputs corresponds to the use of multiple coins in a cash transaction. Since transactions can have multiple outputs, users can send bitcoins to multiple recipients in one transaction. As in a cash transaction, the sum of inputs (coins used to pay) can exceed the intended sum of payments. In such a case, an additional output is used, returning the change back to the payer.[81] Any input satoshis not accounted for in the transaction outputs become the transaction fee.[81]