Is there a security problem in this system

Imagine if there is stream where every one posts a message using their public address. Once the message is posted every one can read it. Every user have a pair of public and privet keys, one of the public key is linked to the user and the other is used only for secret messages. Before posting on the stream the user encrypts the message which will contain his secret key, then encrypts it with N public keys and put it on the stream. Every user connected is constantly trying to decrypt messages using their privet key, If they succeed decrypting but the message is still crypted (because there is a multi layered encryption) they post the decrypted version on the stream. This way nor the sender or the receiver know where the message is coming from or where it is going.

I was thinking of this being on top of a tchat, this can also be used on top of twitter or any public social media.

P.S: I know this look a lot like tor, but this system is still centralised and all of it is still on the visible web