To give some foreground information: I acknowledge that I am a cryptography newb and not by any means an expert (and probably never will be).
In a recent CS class we had several assignments writing and implementing RSA and Diffie-Hellman. It was fun but it was exclusively two party encryption. I want to implement multi-party encryption. For example, a chatroom or IRC scenario where all parties involved send cyphertext to each other simultaneously. Looking around, I've seen that there are several libraries that accomplish this in other questions. But not just algorithms in general.
I can imagine something like this implemented in RSA and sending out public keys to everyone and simultaneously encrypting and decrypting messages multiple for every other member. For example, 3 people are in a chat room. Person A sends out "Hello guys" two unique cyphertext message that Person B and Person C receive and individually decrypt with their own private keys. This would work, but this seems inefficient and somewhat haphazard.
Is there a generally accepted algorithm that allows multiple parties to use public key encryption at once?
(Once again, this won't go to any production level system. This is just for my own academic curiosity.)