I'm looking for the ability to create a SINGLE CONSTANT shared secret amongst two or more users (a group) AND if a new user is added to such a secured group the new user should also be able to learn the already known and shared secret without the existing users needing to resend any new data or changing the common secret. The new user should only require ONE received piece of data such as with standard Diffie Hellman.
This can be a key exchange method or anything else that would not be compromised with a MiTM attack. The shared secret can result in an encryption key or can just be, a shared secret- if that's even possible.
What I'm trying to do is have a common group secret for a final layer of password-enabled AES that all group members can access. I already know of, and am implementing hybrid encryption/key exchanging. I want ANOTHER layer of security. Hybrid is great, however, eventually quantum will break asymmetric, that is why I want a final AES layer.
If you post an algorithm please make it as simple as your level of profession will allow, or even simpler.
Acknowledge, these resources come very close to what I need but as far as I know they don't satisfy what I'm trying to do & the reason they don't satisfy is my requirement above for new users added to the secured group.
Multi-party key agreement
Can one generalize the Diffie-Hellman key exchange to three or more parties?