A password authentication system includes an access control server configured to control access by a user computer to a resource dependent on authentication of user passwords associated with user IDs. The system further includes a plurality of authentication servers, storing respective secret values. For each user ID, the access control server stores a first ciphertext produced by encrypting the user password associated with that ID using a predetermined algorithm dependent on the secret values. In response to receipt of a user ID and an input password, the access control server communicates with the plurality of authentication servers to implement password authentication, requiring use of the secret values, in which a second ciphertext is produced by encrypting the input password using said predetermined algorithm. The access control server compares the first and second ciphertexts to determine whether the input password equals the user password to permit access to the resource.