This algorithm has $O(n^2^)$ time and space complexity.

!<scratch-meet-in-the-middle?2des.png 70%! h2. Breaking 2DES

h2. Breaking 2DES
!<scratch-meet-in-the-middle?2des.png 70%!

DES is an encryption standard which uses 56 bit keys. Today computers can use a brute force approach to break the encryption. One simple approach to make the encryption more secure is to apply it twice, using two different keys. This approach is susceptible to the meet in the middle attack developed by Diffie Hellman. 3DES is less susceptible as it encrypts the message three times using 3 keys.
Let’s see why 2DES is vulnerable. Let $Ek$ be the encryption function using the secret key $k$ and $Dk$ the decryption function using the secret key $k$. 2DES uses $Ek1(Ek2(p)) = s$ to encrypt and $Dk2(Dk1(s)) = p$ to decrypt.