# Symmetric Multi-Key Decryption

Is there an encryption decryption scheme in which a group of people are all given different keys, and of which each key can decrypt a file. (I’m not talking about a scenario where a file is encrypted with a single symmetric key, and then the symmetric key is separately encrypted with each individuals public key.)

I’ve read articles about broadcast encryption and multi-trapdoors but I'm unsure if any of these would match the correct scheme so I’m looking for.

• Why does each key have to be different? What would go wrong if every user had the same key? – Squeamish Ossifrage Jul 17 '18 at 14:12
• Pretend we had to revoke access to one user. Since we used the same key for $$n$$ users, we now have to change the keys for $$n - 1$$ users. That means each revoke operation is linear instead of constant. – SlackOverflow Jul 18 '18 at 18:36