Can we prevent a man-in-the-middle attack with symmetric-key cryptography?

Question

Suppose that Alice signs the message M = "I love security" and then encrypts it with Bob's public key before sending it to Bob. As well known, Bob can decrypt this to obtain the signed message and then encrypt the signed message with, say, Charlie's public key and forward the resulting ciphertext to Charlie. Could Alice prevent this "attack" by using symmetric key cryptography?

Answer 1

Is your issue that Bob leaked the data to Charlie? There isn't anything you can really do about this. If Bob can read the data, he can always share it with someone else. If symmetric key cryptography was used, Bob could just send the key itself to Charlie as well as the encrypted message. Better yet, he can still just the decrypted message. There is no way to prevent Bob from doing things if he's the intended recipient of the data.

Answer 2

In addition to Oleksi's answer, depending on the type of data A can have B sign a non-disclosure agreement, secretly embed unique identifiers within the work (like a watermark in an image/video; a message hidden within the least significant bits like in steganography; or change the names of variables in source code) that identifies that this data was given to B. If the data is later publicly leaked, you can examine the leaked data to identify B as the source of the leak and sue for damages or at least cut B off from your stream of sensitive information in the future.

Granted if your method of putting in secret identifiers is known it can probably be scrambled before copying, but this could help ensure that B treats your data as a valuable secret.