Which cryptographic attack exploits the mathematical probability that two different inputs produce the same hash output?

Correct answer: Birthday attack

Option B is correct because the birthday attack exploits the birthday paradox from probability theory, which shows that finding any two inputs that produce the same hash collision requires far fewer attempts than finding a preimage for a specific hash, making it the attack that directly targets collision resistance in hash functions. Option A is incorrect because a rainbow table attack precomputes hash-to-plaintext mappings to reverse a known hash value, targeting preimage resistance rather than exploiting collision probability. Option C is incorrect because a brute force attack exhaustively tries all possible inputs without leveraging any mathematical property of the hash function, making it far less efficient than a birthday attack for finding collisions. Option D is incorrect because a side-channel attack extracts cryptographic keys by observing physical or environmental characteristics such as timing, power consumption, or electromagnetic emissions, not by analyzing the mathematical properties of hash outputs.