Description
MITM is a generic attack, applicable on several cryptographic systems. The internal structure of a specific system is therefore negligible to this attack. It is possible though to combine it with other kinds of attack as has been done.
Naturally it requires the ability to encrypt and decrypt, and the possession of pairs of plaintexts and corresponding ciphertexts.
When trying to improve the security of a block cipher, a tempting idea is to simply use several independent keys to encrypt the data several times using a sequence of functions (encryptions). Then one might think that this doubles or even n-tuples the security of the multiple-encryption scheme, depending on the number of encryptions the data must go through.
The Meet-in-the-Middle attack attempts to find a value using both of the range (ciphertext) and domain (plaintext) of the composition of several functions (or block ciphers) such that the forward mapping through the first functions is the same as the backward mapping (inverse image) through the last functions, quite literally meeting in the middle of the composed function.
The Multidimensional MITM (MD-MITM) uses a combination of several simultaneous MITM-attacks like described above, where the meeting happens in multiple positions in the composed function.
Certainly, an exhaustive search on all possible combination of keys (simple bruteforce) would take 2k·j attempts if j encryptions has been used with different keys in each encryption, where each key is k bits long. Using MITM or MD-MITM, this can be done better.
Read more about this topic: Meet-in-the-middle Attack
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