Cryptocurrency Tutorial

Posted 7/5/17

I was recently asked to give a talk on bitcoin and other related cryptocurrencies. My audience was to be a group of scientists and mathematicians, so people with significant STEM backgrounds, but not expertise in computer science. In preparation for giving my talk, I wrote this breakdown on the ins and outs of cryptocurrencies.

UPDATE 7/11/17

I gave the talk, it went great! Slides here [PDF].


What is Bitcoin?

Bitcoin is a decentralized currency. There is no governing body controlling minting or circulation, making it appealing to those who do not trust governments or financial institutions like Wall Street.

Where as most currencies have a physical paper representation, bitcoin is exchanged by adding on to a “blockchain”, or a global ledger of who owns what pieces of currency, and what transactions were made when.

Where does the value of Bitcoin come from?

Bitcoin is a fiat currency - Its value comes exclusively from what people are willing to exchange it for. This seems ephemeral, but is not uncommon, and is the same principle behind the value of the US dollar, at least since the United States left the gold standard.

Is Bitcoin anonymous?

Yes and no. All bitcoin transactions are public, and anyone can view the exact amount of money in a bitcoin wallet at any given time. However, bitcoin wallets are not tied to human identities, so as long as you keep the two distinct (which can be challenging), it is effectively “anonymous”.

How is Bitcoin handled legally?

Some countries consider bitcoin to be a currency (with a wildly fluctuating exchange rate), while others regard it as a commodity with an unstable value. Most countries will tax bitcoins in some way or another, but due to the aforementioned anonymity it is easy to avoid paying taxes on bitcoins.

What is the blockchain?

The blockchain is a technology solving two problems:

  1. How do we know who has what currency?
  2. How do we prevent someone from spending currency that isn’t theirs?

The second problem includes preventing someone from “double-spending” a bitcoin they legitimately own.

A blockchain is a sequence of “blocks”, where each block holds “facts”. These facts describe every transaction of bitcoins from one person to another. To make a transaction, you must create a block describing the transaction, and convince the majority of the nodes in the bitcoin blockchain to accept your transaction.

What does a block consist of?

A block has four fields:

  1. A string describing all contained facts
  2. The identifier of the previous block in the blockchain (maintains an explicit order for all transactions)
  3. A random string
  4. The SHA256 hash of all of the above

A block is accepted in to the blockchain if and only if the SHA256 hash starts with at least n leading zeroes. This makes generating a block equivalent to hash cracking (keep changing the random string until you get the hash you want), and the larger n is, the more challenging the problem is to solve.

For example, if n=5:

A losing block hash (will be rejected):
A winning block hash (will be accepted):

The number of leading zeroes n is increased periodically by group consensus so that even as more people begin to work on generating blocks, the rate of new blocks remains approximately constant (~one every ten minutes). This makes it extremely unlikely that two new and valid blocks will be generated near the same time, and therefore creates a continual chain of events making double-spending impossible.

Looking for a new valid block is colloquially referred to as “bitcoin mining”.

Note: The hashing algorithm (sha256) is specific to bitcoin. Other cryptocurrencies may use different hashing algorithms to discourage the use of GPUs in mining.

Can I spend someone else’s coins by mining a block?

Bitcoins are tied to a “bitcoin wallet”, which is a public/private keypair. To send coins to a new wallet you must make a blockchain fact describing a transfer of X bitcoins from one wallet’s public key to another, signed with the private key of the originating wallet. Therefore unless you have access to the private key, you’ll be unable to control the bitcoins associated with it.

Why would anyone mine blocks?

Each successfully mined block yields the miner some currency. They include their own wallet address as one of the facts in the block, and receive a fixed amount of currency (25BTC for bitcoin) at that address. This is also why you must pay a small transaction fee to send anyone a bitcoin - you are asking someone to include your transaction in their massive mining effort.

Doesn’t this mean there are a fixed number of bitcoins in the world?

Some readers may have noticed that SHA256 has a fixed length (256-bits, or 32 characters). If we periodically increase n, then eventually we will require that all 32 characters of the hash be “0”, which will make adding to the end of the blockchain impossible. Since you receive 25 bitcoins for each mined block, this puts the maximum number of bitcoins at about 21 million.

This upper limit poses a number of problems. There are a finite number of transaction blocks, after which all bitcoins will be unmovable, and therefore worthless. There are a finite number of bitcoins, so if you send some to a non-existent address, or forget your private key, those coins are effectively destroyed forever. This, along with commodity speculation, is responsible for the incredible fluctuation in the value of bitcoin.

Trust Issues

One problem with a decentralized currency like bitcoin is that there is no revocation of money transfers. With a bank, you can make a purchase with a credit card, and later dispute that purchase, claiming you did not receive what you paid for, and the bank can reverse the charge. You can also use banks and lawyers to create contracts, agreeing to pay a certain amount before a service is rendered and a certain amount after, with other complications like security deposits.

None of this infrastructure exists with bitcoin, making it an extremely scam-prone transaction system. Some people use escrow services, but these are all very ad-hoc. This is also one of the reasons bitcoin is commonly used in ransomware attacks, or for purchases of drugs or stolen property on the “deep web”.

What about alt-coins?

There are several variations on bitcoin, called “alternative-coins” or “alt-coins”. Some of the most interesting are:


Namecoin treats the blockchain as an extremely distributed database of information tied to specific identities. It’s effectively the same as bitcoin, except in addition to storing “coins” with particular wallets, you can store domain names, email addresses, public encryption keys, and more.

In theory, this removes the need for centralized DNS servers, or domain-registrars for the Internet. Everyone can perform DNS lookups by looking for the domain name in question in the blockchain, and can transfer domains to each-other in exchange for namecoins.


Ethereum tries to solve the trust issues of bitcoin by allowing you to write programmatically-enforceable contracts and embedding them in to the blockchain.

Consider the following blockchain:

ABC Blockchain

Block A contains a program with psuedocode like the following:

if( security_deposit_received and date == December 5th and house_not_destroyed )
    send(security_deposit, from=Bob, to=Alice)
else if( date > December 5th )

When block A is added to the chain the code inside is evaluated by every node in the chain. The code is re-evaluated as each subsequent block is added, until after December 5th when the code can be safely ignored.

Block B contains a transfer of $1000 from Alice to Bob, as a security deposit.

On December 5th, if the house is not destroyed, the security deposit is automatically returned to Alice by Bob.

Ethereum therefore allows you to create contracts which are enforceable without lawyers or banks, and cannot be violated by either party once issued.

Other uses for Ethereum contracts include provably-fair gambling, and generic distributed computation, where you pay each participating node for running your application.

Ethereum suffers from a few issues:

  • The complexity makes it less approachable than Bitcoin
  • Without widespread cryptographically verifiable Internet-of-Things devices the types of contracts you can express are limited
  • All code is publicly viewable, but not changeable, so if someone finds a security hole in your code, it cannot be easily patched

Despite these limitations, Ethereum has much more functionality than other cryptocurrencies and is gaining in popularity.


The best cryptocurrency. It uses a logarithmic reward function, so the first few blocks yield many dogecoins, while later blocks yield fewer. This guarantees that lots of coins enter circulation very quickly, making it a viable currency immediately after launch. It also uses scrypt instead of sha256, and so doesn’t suffer from the same GPU and ASIC-mining problems plaguing bitcoin.

Dogecoin was started as a meme in 2013, but is collectively valued at over $340 million as of June 2017, which its user-base finds hilarious. However, because of the massive number of coins in circulation, a single dogecoin is only worth about $0.00095.

The Dogecoin community is particularly noteworthy for donating more than $30,000 to ensure the Jamaican bobsledding team could travel to the 2014 Winter Olympics.