Definition
Cryptography is the study and practice of sending secure, encrypted messages between two or more parties. Cryptography allows digital currency transactions to be anonymous, secure, and "trustless," without the need for banks or other intermediaries.

The "crypto" in the word "cryptocurrency" comes from the Greek word for "secret," which gives you a clue about the field of cryptography. Cryptography is the study and practice of sending secure, encrypted messages or data between two or more parties. The sender "encrypts" the message, making it unreadable to third parties, and the receiver "decrypts" it to make it visible again.

Cryptocurrencies use cryptography to make transactions anonymous, secure, and "trustless," meaning you can securely transact with anyone without needing to know them, and without intermediaries like banks, credit card companies, governments, or any other third party. Cryptography isn't just important for digital currencies—our computers and the networks they connect to are constantly encrypting and decrypting data, from every Google search you perform to every email you send.

Why is Cryptography Important?
Cryptocurrencies are entirely based on cryptographic ideas. Bitcoin was invented by a person (or group of people) using the pseudonym Satoshi Nakamoto, who introduced the idea in a whitepaper posted on a cryptography message board in 2009.

The toughest problem Satoshi solved was the so-called double-spending problem. Since Bitcoin is just code, what stops people from copying and spending their money repeatedly? Satoshi's solution was based on a well-known cryptographic scheme: public-private key encryption.

Bitcoin (as well as Ethereum and many other cryptocurrencies) uses a technique called public-private key cryptography. This technology makes cryptocurrencies "trustless" and enables secure transactions between strangers without the need for a "trusted intermediary" like a bank or PayPal.

How Does Public-Private Key Cryptography Work?
The Bitcoin network issues a private key (essentially a very strong password) to every user and generates an associated public key in encrypted form based on the private key. You are free to give your public key to others. In fact, it's the only information someone needs to send you Bitcoin. But to access those funds, the private key is required.

Part of Bitcoin's disruptive power lies in how it solves the double-spending problem: a peer-to-peer network that uses cryptographic methods to verify the authenticity of transactions.

The public key is generated from the private key using a method called "hashing," which takes a string of data and processes it through an algorithm. This process is entirely irreversible, so no one can guess the private key from the public key.

Because the public and private keys are linked, the network knows your Bitcoin belongs to you. As long as you hold the private key, it will always be yours.

Another consequence of having no intermediary is that Bitcoin transactions are irreversible (if you make a mistake, there's no credit card company to call). But this is a feature, not a bug: irreversible transactions are a key part of solving the double-spending problem.

The other half of the solution is the Bitcoin blockchain, a massive, decentralized ledger—like a bank's balance book—that records every transaction and is constantly verified and updated by all computers in the network.