birthday phenomenon

The phenomenon stating that, for a category size of 365 (the number of days in a year), after only 23 people are gathered, the probability is greater than 0.5 that at least two people have a common birthday (month and day). Note: The birthday phenomenon applied to DES encryption means that where category size is 264, this same probability of a repeat (match) occurs at approximately r=232. The theory behind this principle applies that for a 64-bit block encryption operation with a fixed key, if one has a text dictionary of 232 plaintext/ciphertext pairs and 232 blocks of ciphertext produced from random input, then it should be expected that one block of unknown ciphertext will be found in the dictionary.