Glossary · Crypto
Private key
A private key is the secret number that lets you spend crypto coins: whoever knows it controls the coins, and if it is lost, nobody can recover them.
Also called: secret key, seed phrase, recovery phrase
In plain words
Think of a glass mailbox in a town square. Everyone can see what is inside and drop more in, but only one key opens the slot to take things out. On a blockchain, your address is the mailbox and the private key is that key.
It is simply a huge random number, 256 bits long, up to 78 digits. From it, math produces a public key, and from that, your address. The steps work one way only: going from key to address takes a split second, but working back from an address to its key is, as far as anyone knows, impossible in practice.
When you send coins, your wallet uses the private key to sign the payment. The network checks the signature against your public key, so it knows the payment is genuine without ever seeing the secret.
Example
How big is 2256?
- A bitcoin private key is a number from 1 up to almost 2256: about 1.16 × 1077 possible keys. Physicists estimate that the visible universe holds about 1080 atoms.
- Suppose every mining machine in the bitcoin network guessed keys instead of hashes: about 1.0 sextillion guesses a second (deriving a key is in fact much slower than a hash).
- Trying every key at that speed would take more than 1048 years. The universe is about 1.4 × 1010 years old.
- Finding the key of one particular address by luck would take, on average, half as long.
Nobody steals bitcoin by guessing keys. Coins are stolen by getting people to reveal them: phishing, malware, fake support agents.
One level deeper
Bitcoin and Ethereum use elliptic-curve cryptography, on a curve called secp256k1. The public key is the private key “multiplied” by a fixed point on that curve: easy to compute forwards and, as far as anyone knows, infeasible to reverse. Addresses are shortened hashes of public keys.
Most wallets never show you raw keys. They create one master secret and display it as a seed phrase of 12 or 24 words from a standard list of 2,048. Twelve words carry 128 bits of randomness, still far beyond any brute force, and every key in the wallet is derived from them.
Large quantum computers could one day break today’s elliptic-curve signatures, which is why researchers are preparing quantum-resistant replacements. Coins whose public keys are already visible on the blockchain would be the most exposed.
Why it matters
In crypto, owning means knowing the key. There is no other proof of ownership, and no ID check or court order can move coins without it.
It explains both the freedom (nobody can freeze a key you alone hold) and the danger (nobody can help if you lose it).
The same idea secures much of the internet: private keys sit behind every HTTPS connection to a website.
A common mistake
Myth: Someone could guess my private key if they tried hard enough.
In fact: Not by guessing: there are about 1077 possible keys. Keys are stolen when people reveal them, by typing a seed phrase into a fake site or keeping it in a cloud photo, or when a faulty wallet made a key that was not truly random.
Questions people ask
What is the difference between a private key and a public key?
The private key is your secret and signs payments; the public key is made from it and lets anyone check those signatures. Your address is a short form of the public key, safe to share.
What happens if someone gets my private key?
They can move every coin it controls, at once and for good. Payments cannot be reversed, so the usual advice is to move any remaining coins to a new wallet as soon as a key or seed phrase may have been seen.
Can a lost private key be recovered?
Only from a backup, such as your seed phrase. No company, network or government can regenerate it.
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About the numbers
- The numbers on this page are recalculated from the data every night; the sources are listed at the end of the page.
- Bitcoin hash rate: Coin Metrics Community Network Data, metric HashRate. License: CC BY-NC 4.0.
- Crypto data: Coin Metrics Community Network Data, used under the CC BY-NC 4.0 license.
- This page explains a term. It is not investment advice.