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Data & cryptography · 2 min read

What is a public key?

By Oliver James Whitmore · Updated 20 October 2026

In one sentence

A public key is the shareable half of a key pair: a value calculated from a private key that lets anyone check signatures made with that private key, without being able to make them.

Private key to public key to address: easy in one direction, practically impossible in reverse.Private keysecretPublic keyshareableAddressshort formcurve mathshashingreverse direction: practically impossibleAnyone may know the public key and the address. Only the holder knows the private key.
Private key to public key to address: easy in one direction, practically impossible in reverse.

How it works

Public-key cryptography was introduced in the open literature by Whitfield Diffie and Martin Hellman in 1976. Its central trick is a pair of keys that are mathematically linked but play opposite roles.

In Bitcoin and Ethereum, the private key is a randomly chosen 256-bit number. The public key is calculated by elliptic-curve multiplication: a fixed starting point on a curve called secp256k1 is "multiplied" by the private key, which lands on another point of the curve. That point is the public key. Computing it is fast. Going the other way — finding the private key from the public key — is known as the elliptic-curve discrete logarithm problem, and for well-chosen curves there is no known practical method on ordinary computers.

Because of this one-way link, the public key can be handed to the whole world. Nodes use it to check that each transaction was signed by the matching private key. In many address formats, only a hash of the public key appears on the chain until the address is first used to send, at which point the public key itself is revealed in the transaction.

A simple example

Think of mixing paint. Starting from a shared base colour, you add your own secret shade and get a mixed colour that you show to everyone. Mixing is easy; separating the mixed colour back into the exact secret shade is practically impossible. The secret shade plays the part of the private key, and the colour on display plays the part of the public key.

Common misconception

Misconception: If someone learns my public key, they can take what it controls.

In fact: A public key only lets people check signatures. Creating a signature requires the private key. The real cost of a public key becoming known is privacy: anyone who links it to you can follow its activity on the public record.

Where you meet it

  • Inside every signed transaction, so nodes can verify it.
  • As the starting point for most addresses.
  • Outside crypto: HTTPS certificates, SSH logins and signed software updates.

Sources

This card explains a technical concept for general education. It is not a recommendation to acquire, sell or hold any crypto-asset, and it is not financial advice.