On "the Power of Verification Queries" in Unconditionally Secure Message Authentication

In this paper, we consider authentication codes where the adversary has access to a verification oracle. We formally study two attack games: offline attack and online attack. In an offline impersonation attack with verification query of order i, the adversary launches its attack through two stages. In the first stage — the query stage — the adversary can adaptively choose i distinct messages to query the verification oracle. The verification oracle will answer whether these queried messages are valid or invalid under the secret encoding rule agreed by the transmitter and the receiver. In the later stage — the spoofing stage — the adversary creates a fraudulent message which is different from all its queried messages and sends this message to the receiver. The adversary wins if the receiver accepts the fraudulent message as a valid message. In an online impersonation attack with verification query of order i, the adversary has i + 1 chances to query the verification oracle and wins as soon as one of the qu...