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.:ch. 5
Various journalists, economists, and the central bank of Estonia have voiced concerns that bitcoin is a Ponzi scheme. In April 2013, Eric Posner, a law professor at the University of Chicago, stated that "a real Ponzi scheme takes fraud; bitcoin, by contrast, seems more like a collective delusion." A July 2014 report by the World Bank concluded that bitcoin was not a deliberate Ponzi scheme.:7 In June 2014, the Swiss Federal Council:21 examined the concerns that bitcoin might be a pyramid scheme; it concluded that, "Since in the case of bitcoin the typical promises of profits are lacking, it cannot be assumed that bitcoin is a pyramid scheme." In July 2017, billionaire Howard Marks referred to bitcoin as a pyramid scheme.
In the end, the majority of the Ethereum community voted to perform a hard fork, and retrieve The DAO investors money. But not everyone agreed with this course of action. This resulted in a split where two parallel blockchains now exist. For those members who strongly disagree with any changes to the blockchain even when hacking occurs there is Ethereum classic. For the majority who agreed to rewrite a small part of the blockchain and return the stolen money to their owners, there is Ethereum.
Full clients verify transactions directly by downloading a full copy of the blockchain (over 150 GB As of January 2018). They are the most secure and reliable way of using the network, as trust in external parties is not required. Full clients check the validity of mined blocks, preventing them from transacting on a chain that breaks or alters network rules.:ch. 1 Because of its size and complexity, downloading and verifying the entire blockchain is not suitable for all computing devices.
Researchers have pointed out at a "trend towards centralization". Although bitcoin can be sent directly from user to user, in practice intermediaries are widely used.:220–222 Bitcoin miners join large mining pools to minimize the variance of their income.:215, 219–222:3 Because transactions on the network are confirmed by miners, decentralization of the network requires that no single miner or mining pool obtains 51% of the hashing power, which would allow them to double-spend coins, prevent certain transactions from being verified and prevent other miners from earning income. As of 2013 just six mining pools controlled 75% of overall bitcoin hashing power. In 2014 mining pool Ghash.io obtained 51% hashing power which raised significant controversies about the safety of the network. The pool has voluntarily capped their hashing power at 39.99% and requested other pools to act responsibly for the benefit of the whole network. Between 2017 and 2019 over 70% of the hashing power and 90% of transactions were operating from China.