The ANSI X9.52 standard defines a variant of DES encryption with keys
k1, k2, and k3 as:
C = Ek3 [Dk2 [Ek1 [M]]]
What is this DES variant?

A.
Double DES with an encryption and decryption with different keys

B.
Triple DES in the EEE mode

C.
Triple DES in theEDE mode

D.
DESX

Explanation:
This version of triple DES performs an encryption (E) of plaintext
message M with key k1, a decryption (D) with key k2 (essentially,
another encryption), and a third encryption with key k3. Another
implementation of DES EDE is accomplished with keys k1 and k2
being independent, but with keys k1 and k3 being identical. This
implementation of triple DES is written as:
C = Ek1 [Dk2 [Ek1 [M]]]
Answer a is incorrect since, in DESX, input plaintext is bitwise
XORed with 64 bits of additional key material before encryption
with DES, and the output of DES is also bitwise XORed with
another 64 bits of key material. Answer b, DES in the EEE, mode is
written as:
C = Ek3 [Ek2 [Ek1 [M]]]
where three consecutive encryptions are performed on plaintext
message, M, with three independent keys, k1, k2, k3.
Answer c is incorrect since the question contains three encryptions.

Implementing two DES encryptions does not provide the
additional security anticipated over a single DES encryption because
of the meet-in-the-middle attack. Consider a DES cipher with a key
size of p. A double encryption will result in an effective key size of
2p and yield the final result R. Thus, one would anticipate that one
would have to search a key space of 22p in an exhaustive search of
the keys. However, it can be shown that a search of the key space on
the order of 2p is all that is necessary. This search is the same size as
required for a single DES encryption. This situation is illustrated as
follows:
The sequences shown illustrate the first DES encryption of a
plaintext message M with all keys k1 through k2p yielding the
intermediate encrypted results C1 through C2p.
Ek1 [M] C1
Ek2 [M] C2
Ek2p [M] C2p
If we have available ciphertext R where R = Ek2 [Ek1 [M]] for a pair of
secret keys k1 and k2, for each key m there is only one key k such that
Dm[R] = Ek[M] where D is the decipherment of R back from the second
DES encipherment. In other words, there are 2p possible keys that will
result in the pair [M,R] and, thus, can be found in a search of order 2p.