Ory is the largest open source community in the world for cloud software application security. We maintain advanced open source security software solving authentication, authorization, access control, application network security, and delegation. Ory implements a variety of industry and best-practice standards including OAuth 2.0 / OAuth 2.1, OpenID Connect, Zero Trust Networking, Google Zanzibar Policy Framework, FIDO2 U2F, WebAuthn, TOTP, and more.

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You either need two instances one that is publicly available to serve public endpoints and another to serve private/admin endpoints. (or one instance with an HTTP router in front of it that can apply permissions as necessary)

Just create a Dockerfile that inherits from hydra image

Pass to Cloud run an set one instance in port 4444 and another in 4445