arXiv:2506.01325v3 Announce Type: replace Abstract: Single sign-on (SSO) enables a user to log into multiple websites, called relying parties (RPs), by her username and credential set up in another trusted web system, called the identity provider (IdP). Identity transformations are proposed in UppreSSO to provide privacy-preserving SSO services, preventing both IdP-based login tracing and RP-based identity linkage. While the security and privacy guarantees of UppreSSO have been proved, several essential issues on the identity-transformation approach are not well studied. In this paper, we comprehensively investigate this approach as below. Firstly, several suggestions to efficiently integrate identity transformations into OpenID Connect (OIDC) are explained. Then, we uncover the relationship between identity transformations in SSO and oblivious pseudo-random functions (OPRFs), and present two variations of the properties required for SSO security as well as other requirements, to analyze existing OPRF protocols. Finally, new identity transformations different from those proposed in UppreSSO, are constructed based on some OPRFs. To the best of our knowledge, this is the first time to uncover the relationship between identity transformations in SSO services and OPRFs, and prove the SSO-related properties (i.e., output uniqueness, key-identifier freeness, and collision resistance on 1st/2nd-input) of typical OPRFs.