Cryptocurrencies, Part 1 - How Digital Currencies Work

In 2009, there was a new currency (Bitcoin) invented. In recent years many variations have sprouted up, often called “altcoins”.1 They all operate similarly at a technical level.


Crypto wallets serve as your cryptocurrency identity, which is the private half of a public key pair. Other users send you money by sending coins to your public key, and you do the same to theirs. There isn’t an amount of money directly tied to this identity, but rather the sum of a long history of transactions.

The private keys are also used by the sender to sign transactions, to prove the transaction is authentic. Therefore, as usual, the entire system hinges on the users’ ability to keep private keys private–if a key is leaked all the money disappears as quickly as the next person can type. It’s also the only thing tying a user to his or her wallet, and if it’s lost so is the ability to spend the value of the wallet (by anyone, those coins are gone forever).


Every movement of coins is recorded as a transaction. A transaction is simply a record of some coins moving from one public address to another. These transactions are stored in blocks, and linked to one another in a sequential chain. As mentioned, this chain of transactions is precisely how the value of your wallet is determined.

Every user of the currency has his or her own complete copy of this transaction history, called the block chain, since the beginning of time. It’s a record of every transaction that ever happened. These block chains are asynchronously passed around and actively used by all users around the world. So, who’s to say my chain is more correct than your chain? After all, the value of a user’s wallet is determined simply by the sum of all transactions, so if I were to forge a block chain with an arbitrary number of transactions into my account I’d be a millionaire in no time.

This is a real concern, but building the block chain involves brute forcing hashes. The first solution to the presented problem adds that block to the chain, so making a transaction official is effectively a race among everyone in the world. No single entity has the processing power to consistently beat the rest of the network, so, theoretically, forging the transaction record is just not possible (in reality, pools of many users often form to solve blocks cooperatively, and some do arguably amass the power to cast doubt on the sanctity of this process2).

Because this entire process happens asynchronously, it’s completely possible that two different blocks are solved at the same time by different parties and cause the chain to diverge. When this happens, the chain used by the network is simply the longest one. Because these problems are so difficult, it’s very unlikely that two divergent transaction records stay in step for long, and as soon as one surpasses the other it becomes the accepted chain. This happens fairly quickly, as the first block that isn’t solved in a “tie” will determine the accepted chain (however, there have been times when a fork went unnoticed for longer than it should have3). The transactions in the chain not chosen are effectively thrown out; they never happened.

Solving Blocks

This is where the real cryptocurrency excitement comes in. Every block needs to be finalized to be accepted into the block chain. A block is finalized when a nonce is discovered that causes that transaction to hash to a particular range of values. For example, if an unconfirmed block is represented by \(01234ABCD\), and the accepted range of hashes is \([0,1000000]\), then the value that confirms the block is any value \(n\) such that \(0 < PRF( n, 01234ABCD ) < 1000000\). The value of 1000000 is chosen just for simplicity, in practice the Bitcoin family uses SHA256, so the range is actually enormous: \([0,2^{256})\).

Since these are meant to be real, usable currencies, and a transaction isn’t accepted until one of these outrageously difficult math problems is solved, it’s desirable that there’s some predictability regarding the length of time required to process a transaction. If I were a merchant and it took an arbitrarily long time to get paid, I wouldn’t be very interested in accepting these cryptocurrencies.

To keep the time to process transactions consistent and predictable, the block solution process implements a mutable level of difficulty. The difficulty effectively limits the field of acceptable answers. If the difficulty is 1, and the field again is \([0,1000000]\), then the acceptable range is \(1000000/1 = [0,1000000]\). Any value in that range is acceptable to finalize the block. To make it more difficult and slow the rate at which blocks are solved, the difficulty is increased. With a difficulty of 4 the range of acceptable answers becomes \(1000000/4 = [0,250000]\), and it will take the community 4 times longer to find a solution on average.

This process of solving blocks to finalize transactions is what’s referred to as “mining”. Currencies pay rewards for solutions, and so it’s lucrative to find these magic values. That’s why there’s a lot of buzz about building mining rigs to brute force the hash space as rapidly as possible.

The end result is a currency that pays its users to maintain the transaction record and determine the value of every wallet in the mix, and the process is proven authentic by its very nature (it’s too computationally difficult to forge). It’s really a brilliant solution.

Actually Mining

I found this all pretty fascinating on this slow weekend, and even started mining on a spare laptop myself to see what it’s like. More about that in Part 2…

  1. Wikipedia. Cryptocurrency. 

  2. Reddit. PSA : GHASH just mined the last 6 consecutive blocks and 42% of blocks in the past 24 hours. 

  3. Bitcoin Magazine. Bitcoin Network Shaken by Blockchain Fork. 

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