text: While the birthday attack attempts to find two values in the domain of a function that map to the same value in its range , the meet-in-the-middle attack attempts to find a value in each of the range and domain of the composition of two functions such that the forward mapping of one through the first function is the same as the inverse image of the other through the second function -- quite literally meeting in the middle of the composed function .
simplified: While the birthday attack attempts to find two values in the domain of a function that map to the same value in its range , the meet-in-the-middle attack attempts to find a value in each of the ranges and domains of the composition of two functions such that the forward mapping of one through the first function is the same as the inverse image of the other through the second function -- quite literally meeting in the middle of the composed function .