Which attack targets hashing functions by finding two messages with the same hash value?

The correct answer is the Birthday Attack. This type of attack specifically targets collision-resistant properties of hashing functions. The name "Birthday Attack" comes from the probabilistic reasoning behind the likelihood of two different inputs resulting in the same hash value, akin to the birthday paradox in probability theory.

In the case of hashing functions, a collision occurs when two distinct messages yield the same hash output. The Birthday Attack exploits this by focusing on the probability of collisions occurring within a set number of hashes. In practice, it’s much easier to find two distinct inputs that hash to the same value than to directly guess one of the total possible values of the hash function, especially as the hash output size decreases. This makes it a potent strategy in compromising the integrity of systems relying on cryptographic hash functions.

While other attack types mentioned, such as the Collision Attack, do involve finding two messages with the same hash value, the specific probabilistic nature of the Birthday Attack makes it the more precise definition in this context. The Replay Attack involves intercepting and reusing data packets, and the Brute Force Attack focuses on systematically trying all possible combinations to crack passwords or keys, which don't directly involve the unique properties of hashing collisions. Hence, the Birthday Attack is the most accurate choice