What is a public key in crypto? Keys, addresses, and signatures explained

A public key is the cryptographic counterpart to a private key. Together they let you prove ownership of cryptocurrency without revealing the secret that controls it. Summary A public key is a large number derived mathematically from a private key using elliptic curve multiplication, a one-way function that is fast to compute forward but practically impossible to reverse. Bitcoin and Ethereum both use the secp256k1 elliptic curve, which produces 256-bit private keys and 512-bit uncompressed public keys (or 257-bit compressed public keys). A wallet address is not the same as a public key; the address is a shorter, hashed version of the public key designed to be easier to share and more resistant to certain theoretical attacks. The private key signs transactions, the public key verifies those signatures, and the address receives funds. Losing the private key means permanent loss of access; sharing the public key or address carries no risk to fund security. The July 2026 Coldcard firmware vulnerability, which exposed weak private key generation affecting $116 million in bitcoin, underscores why proper key generation and storage remain the most critical aspects of self-custody. Public ...