Which type of attack is based on the probability of two different messages using the same hash function producing a common message digest?

Birthday attack -a good hashing algorithm should not produce the same hash value for two different messages. if the algorithm does produce the same value for two distinctly different messages, it is referred to as a collision. if an attacker finds an instance of a collision, he has more information to use when trying to break the cryptographic methods used. a complex way of attacking a one-way hash function is called the birthday attack. if an attacker has one hash value and wants to find a message that hashes to the same hash value, this process could take him years. however, if he just wants to find any two messages with the same hashing value, it could take him only a couple hours.