Public key

On elliptic curves the public key is computed as Pub = priv · G, multiplying the private key by the generator point; reversing it amounts to solving the elliptic-curve discrete logarithm, currently infeasible. On secp256k1 the private key is a 256-bit integer and the public key is a point (x, y): 65 bytes uncompressed (prefix 0x04) or 33 bytes compressed (prefix 0x02 or 0x03 by the parity of Y). Addresses derive from it: Ethereum applies Keccak-256 and takes the last 20 bytes; Bitcoin applies SHA-256 then RIPEMD-160.

It is the receivable cryptographic identity: the addresses that receive assets are born from it, and signatures are verified against it without exposing the secret. In Ethereum, a transaction signature also lets you recover the signer's public key via ecrecover, so the address need not be published separately.

The standards base mirrors ECDSA: SEC 2 from SECG defines the secp256k1 parameters and FIPS 186-5 (2023) frames the signature. secp256k1 is not among the NIST-recommended curves in SP 800-186, yet NIST itself permits its use in blockchain and DLT applications. Real cases: Bitcoin and Ethereum addresses and the EVM ecrecover precompile at 0x01.