After an identity provider authenticates a principal, the identity provider sets a URL-encoded cookie defined in a predetermined domain common to all identity providers and service providers in the circle of trust. The common domain cookie is named _liberty_idp for Liberty ID-FF and _saml_idp for SAML v2. After successful authentication, a principal’s identity provider appends their particular encoded identifier to a list in the cookie. If their identifier is already present in the list, the identity provider may remove the initial appearance and append it again. The intent is that the service provider reads the last identifier on the cookie’s list to find the principal’s most recently established identity provider.
The identifiers in the common domain cookie are a list of SuccinctID elements encoded in the Base64 format. One element maps to each identity provider in the circle of trust. Service providers then use this SuccinctID element to find the user's preferred identity provider.