What I have seen on brain wallet, they never asked for public key for verify signature. They just ask address, message and signature. Means you are able to verify signature with thses details. Public keys isn't necessary here. Even you don't need to provide address to verify signature, wallet automatically will show from which address it has been signed. If wallet themselves calculate public keys means it's not necessary for you. That's what my point.
That is incorrect.In ECDSA, to verify a signature, you MUST have the public key, the signature, and the message. However, there is a way that, given a signature and a message, you can compute a public key that would verify the trio. The caveat is that every signature and every message has a public key that makes the trio valid. Without knowing the public key or some representation of it, a signature and message combo is always valid for some public key. The point of a public key is that you are verifying the identify of the person who created the signature and message.
Bitcoin does not require you to have the public key for signed messages because you are required to have the address, which is a representation of the public key. Bitcoin signed messages are verified by recovering the pubkey from the signature and message. Then that public key is hashed and the address computed from that. That computed address is compared to the address given to the verifier. If it matches, then the signature is "valid". If not, it is "invalid".
So verifying a signed message absolutely requires the public key or some representation of it (aka the address).
