Public Key

A public key is the shareable half of a cryptographic key pair, derived from a private key and used to verify signatures made with it. In bitcoin, a public key is a point on the secp256k1 elliptic curve, most often encoded in compressed form as 33 bytes, and addresses are derived from it by hashing or tweaking.

Why it matters

Public key cryptography is what makes a purely digital bearer asset possible. Anyone can verify that a spend was authorized by the rightful owner without learning the private key, so ownership can be proven publicly while control stays secret. Before this invention, published in the 1970s, digital money required a trusted bookkeeper to know every account holder.

How it works

The public key equals the private key multiplied by the curve's generator point. That multiplication is quick to perform but computationally infeasible to reverse, which is the one-way property the whole system rests on. When coins are sent to a typical address, the network stores only a hash of the public key; the key itself is revealed when the owner spends, together with a signature that validates against it.

Taproot addresses, active since November 2021, instead place a tweaked public key directly on-chain, enabling signatures that make complex spends look identical to simple ones.