# Multiple Encryption & Double DES

Again Multiple Encryption & Double DES is the important topic of the Subject Information and Network Security.

As we know that DES is venerable to the brute-force attack, we are interested to find an alternative.

One possible solution is to design completely new algorithm like AES.

The second solution is to use DES multiple times.

**Double DES: Multiple Encryption & Double DES**

The simplest form of multiple encryptions has two encryption stages and two keys and is known as Double DES.

- Given a plaintext P and two encryption keys K1 and K2, ciphertext C is generated as
**C = E(K2, E(K1, P))** - Decryption applies keys in reverse order:
**P = D(K1, D(K2, C))** - This scheme involves a key length of 56 * 2 = 112 bits, making Brute-Force attack impractical.
- However, other types of attacks are possible:

**Reduction to a Single Stage: Multiple Encryption & Double DES**

If it is possible to find a key such that: **E(K2, E(K1, P)) = E(K3, P) **then double encryption, or any number of stages of multiple encryptions with DES, would be useless.

Because the result would be equivalent to a single encryption with a single 56- bit key. o However, by the principle of reverse mapping, such a key is not possible.

**Meet-In-The-Middle Attack: Multiple Encryption & Double DES**

This attack based on the on the observation that if:

*C ***= E( K_{2}, E(K_{1}, P)), then **

*X***= E(**

*K*_{1},*P*) = D(*K*_{2},*C*)##### Given a known (P, C) pair, the attack proceeds as follows:

- First, encrypt P for all 256 possible values of K1.
- Store these results in a table and then sort the table by the values of X.
- Decrypt C using all 256 possible values of K2.
- Moreover, Check the result against the table for a match after every decryption.
- If a match occurs, then test the two resulting keys against a new known plaintext-ciphertext pair.
- If the two keys produce the correct ciphertext, accept them as the correct keys.
- For any given plaintext, 248 false alarms are possible since there are only 264 ciphertext values whereas 2112 key values.
- Thus, the order of attack can reduce to 248 instead of 2112.

**Related Terms**

Information and Network Security, Feistel Cipher, Details: Single Round, AES Transformation Function

## Leave a Reply