Crypto glossary
Public-key cryptography (asymmetric)
Public-key cryptography uses a pair of linked keys, one private and one public, so anyone can verify your signatures without being able to forge them.
In asymmetric cryptography each user has a private key, kept secret, and a public key derived from it that can be shared freely. Anything signed with the private key can be verified with the public key, and data encrypted to the public key can only be decrypted with the private key. Deriving the private key from the public one is computationally infeasible with today's computers.
The idea, introduced publicly by Whitfield Diffie and Martin Hellman in 1976 and followed by RSA in 1977, underpins secure websites, messaging and banking. In crypto it is the basis of ownership: a wallet's private key signs transactions, the network checks the signature against the public key or the address derived from it, and no central authority needs to vouch for anyone.
Most blockchains use public-key cryptography for signatures, not for encrypting data, since transactions are public. The whole system is only as safe as the private key: if it is stolen, the thief has full control, and if it is lost, nobody can recover it. Large quantum computers could break today's widely used schemes, which is why post-quantum alternatives are being prepared.
Example
When you send ETH, your wallet signs the transaction with your private key; every Ethereum node verifies the signature using math tied to your public key and accepts it without ever seeing the private key.