Public-Key Cryptography

Public-key, or asymmetric, cryptography solves the key-distribution problem inherent in symmetric encryption by using two mathematically related keys instead of one: a public key, which can be freely shared, and a private key, which must be kept secret. Data encrypted with a person's public key can only be decrypted with the corresponding private key, allowing anyone to send that person a confidential message without any prior shared secret, while data signed with a private key can be verified by anyone using the matching public key, enabling authentication. This approach relies on trapdoor functions: mathematical operations that are easy to compute in one direction but computationally infeasible to reverse without special knowledge, such as the private key. The concept was introduced publicly in 1976 by Whitfield Diffie and Martin Hellman in their paper "New Directions in Cryptography," which is widely regarded as the founding document of public-key cryptography. It later emerged that British intelligence had discovered the same underlying ideas earlier but in secret: James Ellis conceived the general concept of non-secret encryption around 1970, and his colleagues at the Government Communications Headquarters, Clifford Cocks and Malcolm Williamson, independently devised equivalents of RSA and Diffie-Hellman key exchange in 1973 and 1974, respectively, work that remained classified until 1997 and therefore had no influence on the field's public development.