Meet-in-the-middle attack

An attack against a cryptosystem based on looking for a match between intermediate values which may be calculated from either end of the system.

The attack was first developed by Diffie and Hellman.

This why triple DES rather than just double DES is used. Suppose you use DES twice expecting to obtain the security of a 112-bit key by combining two 56-bit DES keys. You do indeed obtain that if the attacker tries a brute force attack searching all possible combinations of keys. However, attackers cannot be expected to co-operate.

Assuming the attacker can obtain or guess one block of plaintext for which he has the matching ciphertext, the meet-in-the-middle attack is a much better strategy for him. He runs a number of decryptions of the known ciphertext with possible 2nd-half keys, stores results in a table, then runs encryptions of the known plaintext using possible first-half keys and checking each output to see if it matches the table. On average, his total cost is 2⁵⁷ encrypt/decrypt operations. Against triple DES, a similar attack is possible but not practical; the cost is 2¹¹².

A naive version of this attack requires huge amounts of memory to store the intermediate values, but there has been considerable work on variants that reduce the memory requirement, often by trading off some speed. See for example