Cryptographic device that binds an additional authentication factor to multiple identities

Binding a security artifact to a service provider. A method includes generating a pseudonym for a security artifact. The pseudonym is an identifier of the security artifact to the service provider that is unique to the service provider in that the pseudonym is not used to identify the security artifact to other service providers. Further, the pseudonym uniquely identifies the particular security artifact to the service provider even when a user has available a number of different security artifacts to authenticate to the same service provider to access a user account for the user. The method further includes providing the pseudonym for the security artifact to the service provider. The pseudonym for the security artifact is bound with a user account at the service provider for a user associated with the security artifact.