The widespread use of distributed computer networks, it has become common to allow users to access various network services offered by distributed service providers. A crucial role in distributed computer networks to verify if a user is legal and can therefore be granted access to the services requested. To avoid bogus servers, users usually need to authenticate service providers. After mutual authentication, a session key may be negotiated to keep the confidentiality of the data exchanged between a user and a service provider. In many scenarios, the anonymity of legal users must be protected as well. A big challenge to design efficient and secure authentication protocols with these security properties in complex computer network environments. It is usually not practical by asking one user to maintain distinct pairs of identity and password for different service providers, since this could increase the workload of both users and service providers the communication overhead of networks. To tackle this problem, the single sign-on (SSO) mechanism has been introduced so that, after obtaining a credential from a trusted authority for a short period (say one day), each legal user’s authentication agent can use this single credential to complete authentication on behalf of the user and then access multiple service providers. Intuitively, an SSO scheme should meet at least three basic security requirements, unforgeability, credential privacy, and soundness. Unforgeability demands that, except the trusted authority, a collusion of users and service providers are not able to forge a valid credential for a new user. Credential privacy guarantees that colluded dishonest service providers should not be able to fully recover a user’s credential and then impersonate the user to log in to other service providers. Soundness means that an unregistered user without a credential should not be able to access the services offered by service providers.
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