Normally somebody who signs a multisig transaction also needs the redeem script or all the public keys used for the creation of the redeem script, alongside their own private key.
No I was thinking, is this also required for a 2of2 multisig address. Let's say the 2 parties are Alice and Bob. Alice and Bob both generate a keypair. Bob sends his public key to Alice and she creates the redeem script. Now Alice knows both public keys but Bob does only know his public key. Alice now creates a transaction spending the funds and signs it with her private key. She sends this raw half signed transaction to Bob. So far so normal. But normally here Bob needs the redeem script or both public keys to generate the redeem script himself. I was wondering now: When signing the transaction Alice adds her signature to the transaction and also her public key so the signature can be verified. So Bob could extract Alice's public key from the raw transaction he just received and use that to generate the redeem script himself?
So my question is: Is this true? And if it is, does that mean that no matter if it is 2of2 or 4of4 the last signer can always recreate the redeem script from the received raw transaction?