Authentication system, authentication server, service providing server, authentication method, and computer-readable recording medium

An authentication system 100 includes an authentication server 10 and a service providing server 20 for providing a service. When a user requests authentication, the authentication server lets the user input login information, transmits the login information to the service providing server 20, and calculates a first hash value from the login information using a hash function. The service providing server 20 calculates a second hash value from the login information using the same hash function if the login information transmitted from the authentication server 10 matches information that is registered in advance. The authentication server 10 establishes a session with a terminal 30 if the first hash value and the second hash value match each other.