Say we have a system with strong shared keys (not passphrases), and we're trying to sign messages sent by the server that will be visible to an attacker. E.g. storing session state in a signed cookie. ...
I have a secret key k and message m. I send m || HMAC(m, k) to some other party, who can verify the integrity of m, assuming that they know k. Suppose I have multiple messages m1, m2, and so on. ...