The learning path
A private key is a huge secret number that controls your funds. A public key is derived from it through one way math, and your address is a short form of that public key. Signing with the private key proves ownership without ever revealing it, which is why you can share an address safely but must never share a key or seed phrase.
One way math, in one paragraph
Some math is easy to do forward and effectively impossible to reverse. Multiplying two large prime numbers takes a moment. Factoring the result back into those primes takes longer than the universe has existed.
Crypto keys use a version of this with elliptic curves. Your private key is a random number. Multiply it by a fixed point on the curve and you get your public key. Going the other way, from public back to private, has no known shortcut.
The three things and how they relate
| Thing | What it is | Share it? | If it leaks |
|---|---|---|---|
| Private key | A 256 bit random number, usually shown as 64 hex characters | Never, to anyone, for any reason | Everything in that account is gone, immediately and permanently |
| Public key | Derived from the private key through curve multiplication | Safe | Nothing happens. It reveals no secret |
| Address | A hashed, shortened form of the public key with a checksum | Safe, it is how you receive funds | Nothing happens, though your full history becomes linkable to you |
How signing proves ownership
When you send a transaction, your wallet does not transmit your private key anywhere. That would be catastrophic. Instead it produces a signature, a number derived from both the transaction and the key.
Your wallet builds the transaction
Amount, destination, fee, and a sequence number so the same transaction cannot be replayed.
It signs with your private key
The math produces a signature unique to this exact transaction and this exact key. Change one character of the transaction and the signature no longer matches.
The network verifies against your public key
Anyone can check that the signature corresponds to the public key that owns those funds. Nobody learns the private key in the process.
It executes
The network accepts it because the math checks out. No identity, no account, no permission needed.
How large is a 256 bit number, really
There are roughly 10 to the power of 77 possible private keys. That is close to the estimated number of atoms in the observable universe.
If every computer on earth guessed keys continuously for the remaining lifetime of the sun, the chance of finding one in use would remain effectively zero. Nobody is brute forcing your key. They are trying to trick you into handing it over.
Where seed phrases fit in
Managing raw private keys is impractical, especially across many accounts and chains. So wallets use a seed phrase: twelve or twenty four words that encode one master secret, from which every key is derived deterministically.
The practical consequence is important. Your seed phrase is not a password to one account. It is the master key to every account that wallet has ever generated, on every chain. Protecting it is the whole game.
Why addresses look different on each chain
| Chain | Address format | Example shape |
|---|---|---|
| Ethereum and all EVM chains | 0x followed by 40 hex characters | 0x742d35Cc... |
| Bitcoin | Several formats, commonly bc1 for native segwit | bc1qxy2kgd... |
| Solana | Base58, no 0x prefix | 7Np41oeYq... |
| Cosmos chains | Bech32 with a chain prefix | cosmos1abc... |
Common questions
Can two people ever generate the same private key?
Theoretically possible, practically impossible. The number of keys so vastly exceeds the number of keys anyone will ever generate that collisions do not occur in practice.
Is my address the same as my public key?
Not quite. The address is derived from the public key by hashing it and adding a checksum. On Ethereum the address is the last 20 bytes of the hash of the public key.
What is a signature request in my wallet?
An app asking you to prove you control an address, or asking permission to do something. Read them. Some signatures just log you in. Others grant permission to move your tokens.
Can quantum computers break this?
A sufficiently large quantum computer could theoretically derive private keys from public keys. None exists, the timeline is contested, and post quantum signature schemes are already being researched and standardized. It is a real long term consideration and not a near term threat.
Where to go next
Stuck on this one?
Some things click faster with someone walking you through them live. Orca sessions are one to one, screen shared, and paced for wherever you actually are.