This document proposes a system for secure cross-cloud single sign-on (SSO) using electronic IDs (eIDs). It discusses how most cloud services currently rely on weak username/password authentication and how eIDs can provide stronger authentication. The proposed system would extend an existing SSO architecture to allow a user to authenticate once using their national eID and then gain access to services from multiple cloud providers without re-authenticating. This provides stronger security while maintaining the convenience of single sign-on across different cloud service providers.