Chicago Fed Letter Bitcoin: A primer

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record of the transactions to an au- thority—as medieval merchants did when they paid each other by transferring sums on a bank’s books or as modern banks do when they settle their trans- actions on the books of the Fed. Bitcoin, however, does not rely on a single record- keeper. It solves the two challenges of controlling the creation of a unit of digi- tal currency and avoiding its duplication at once. Validation is difficult to do, and those who do it are rewarded for doing so by being allowed to create new bitcoins in a controlled way. Creation/validation details Now, to further explain how this process works, I have to be more technical and more precise. Consider the following scenario: Ann is the owner of a bitcoin— i.e., a string of zeros and ones whose pre- cise nature will become clear—stored in a “wallet” (essentially, an encrypted computer file), managed by an appli- cation that she has installed on a com- puting device. She wants to cede the bitcoin to Bob, who also has a wallet, managed by an application. The two applications carry out the transaction (ensuring its safety through the use of public and private keys—essentially, a way to send someone a padlock with which to lock the item before it’s sent while keeping the key to unlock the padlock). At this point, the application broadcasts a message to a large network of nodes on the Internet, announcing the proposed transaction between Ann and Bob (more precisely, between Ann’s wallet and Bob’s wallet, each identified by its public key). Every ten minutes, the nodes, called “miners,” gather up the proposed transactions that were recently broadcast and attempt to add them to the “block chain,” or the universal led- ger of bitcoin transactions. The key to preventing falsification of the block chain is to make the additions costly. Think of Ann and Bob exchang- ing a gold coin; the coin’s gold content, which is costly to extract from the earth, “proves” that Ann did not counterfeit the coin, but this will work only if it is reasonably easy for Bob to check the gold content. Bitcoin requires a similar “proof of work” from the miners, in the following way: A valid addition to the block chain must include the solution to a difficult mathematical problem, which is costly to find (in terms of computer hardware required, electricity consumed, and time expended). The problem is difficult to solve, but the solution is easy to verify, as it is difficult to factorize2 a very large number but easy to verify that a proposed factorization is correct. Moreover, the problem is not arbitrary or irrelevant, but tied to the verification of transactions. A final technical concept is needed. A hash function maps text or numbers of arbitrary length into a number of fixed length. For instance, taking the first letter of a word (or summing the digits of a number and summing the digits of the result until a single digit is obtained) maps any word (or number) to a hash of length one. The problem that miners solve is roughly the following: Let block chain be x, let the proposed added block be y, and let an additional number be n. The goal is to find n such that the resulting hash function, f (x, y, n), is less than a set value α. The hash function is deterministic but so complex that the output seems random. It is therefore nearly impossible to guess n, and the only reliable method is to try out many different values of n (using much com- puting power) until the condition is satisfied. Moreover, the lower the value of α, the harder it is to satisfy the con- dition. A proposed solution (x, y, n), how- ever, can easily be verified. Part of finding n involves verifying that no bitcoin trans- acted in the block y has already been spent in the block chain x. The code allows each miner to include in the block y a particular type of trans- action, one which creates N new bitcoins and attributes them to the miner. The first miner to find a solution broadcasts it to the other miners, who verify it. Once verified (i.e., accepted by the majority of other nodes), the new block is added to the chain. The fortunate miner now possesses N new bitcoins as a reward for the effort expended. Part of the bitcoin protocol regulates the values of N and α over time. The difficulty α is adjusted every two weeks so as to keep the rate at which blocks are added to six times per hour. Thus, if more miners join the network or if computing power improves, the diffi- culty increases. The size of the reward N was initially 50, and it is halved every 210,000 blocks (i.e., every four years at the rate of six blocks per hour). This implies that the total number of bitcoins in existence will approach but never exceed 2 × 50 × 210,000 = 21 million; moreover, this time path will be inde- pendent of the size or computing pow- er of the bitcoin network. With time, mining becomes unprofitable, but an additional incentive is provided to min- ers: Users can offer to pay a transaction fee to ensure inclusion of the transaction in the next block successfully added to the block chain; this fee will be allocated to the miner who adds that block. So, the bitcoin protocol provides an elegant solution to the problem of creating a digital currency—i.e., how to regulate its issue, defeat counterfeiting and double-spending, and ensure that it can be conveyed safely—without relying on a single authority. What, in the end, is this new currency? It is a list of autho- rized transactions, beginning with the creation of the unit by a miner and end- ing with the current owner. The currency can be exchanged because all potential recipients have the means to verify past transactions and validate new ones, and one’s ownership rests on the consensus of the nodes.3 Bitcoin is a fiduciary currency Fiduciary currencies—in contrast with commodity-based currencies (such as gold coins or bank notes redeemable in gold)—have no intrinsic value, and de- rive their value in exchange either from government fiat or from the belief that Bitcoin solves two challenges of digital money—controlling its creation and avoiding its duplication—at once.

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