Public-key cryptography

Public-key cryptography relies on one-way functions with a trapdoor: problems easy to compute in one direction yet infeasible to reverse, such as integer factorization (RSA), the discrete logarithm (DSA, Diffie-Hellman) or the elliptic-curve discrete logarithm (ECC, ECDSA). It has two main uses, asymmetric encryption and digital signatures. In blockchain the second dominates: the private key authorizes spending and the public key, or a hash of it, produces the address.

It authenticates the owner of funds without a trusted intermediary and without revealing the secret, replacing institutional trust with mathematical proof. It also solves the historic key-distribution problem that burdened symmetric cryptography. It is the conceptual foundation beneath the signatures that validate every transaction and the basis that makes self-custody of tokenized assets possible.

The public concept emerged with Whitfield Diffie and Martin Hellman in New Directions in Cryptography (1976), followed by RSA from Rivest, Shamir and Adleman in 1977. The current US signature standard is FIPS 186-5, issued on 3 February 2023. In practice, Bitcoin (2009) and Ethereum sign with ECDSA over the secp256k1 curve, while TLS and HTTPS combine RSA and ECC.