Say we have a public key system where we have 2 users, Alice, and Bob each has a public and private key. We also have a publicly available server which stores a message.
I want to encrypt this message (M) for Alice and Bob only once. such that either Alice or Bob can decrypt the message with their private key.
The easy and well-studied way to do this is to generate a random symmetric key and encrypt the message with that key, then I can encrypt a small message (SM) For Alice and Bob with their public keys which gives them the symmetric key, with this they can now both decrypt the Message M available on the server.
However is there any known way that I can encrypt the message M, where both Alice and Bob can decrypt M without needing an additional symmetric key? I have looked briefly into double trapdoor encryption and Broadcast encryption but I don't think these schemes suit the purpose?
TL;DR One Ciphertext that can be decrypted by multiple Public, Private keypairs, without deriving an additional symmetric key