To establish a secure communication channel, it is necessary to distribute between two users a key which allows safe encryption and decryption of messages. But because decryption is a simple task for any key holder, it is crucial that the key remains secret during distribution, Secrecy cannot be guaranteed if distribution occurs on the basis of classical physical mechanisms, as it is impossible to know whether the key has been intercepted during transmission. Quantum cryptography(1-3) provides a fundamental solution to this problem, When quantum-mechanical processes are used to establish the key, any eavesdropping during transmission leads to an unavoidable and detectable disturbance in the received key information, Quantum cryptography has been demonstrated using standard telecommunication fibres linking single pairs of users(4-8), but practical implementations will require communication networks with many users(9). Here I introduce a practical scheme for multi-user quantum cryptography, and demonstrate its operation on an optical fibre network The scheme enables a single controller on the network to establish, and regularly update, a distinct secret key with each network user, These keys can then be used to securely encrypt conventional data transmissions that are broadcast on the network.