Diffie Hellman’s meet in the middle attack trades off space for time to find out the two secret keys.
For the pattern p it tries all the possible keys to obtain a set of numbers corresponding $Ek(p)$. Also for the pattern s it uses all the possible keys to decrypt s, $Dk(s)$.
If we find any match in the two sets it means that $Ek1(p) = Dk2(s)$ so the secret keys are k1 and k2.

The naive brute force algorithm would go through $2^56^ * 2^56^$ iterations by brute forcing through all possible values of k1 and k2 while this algorithm uses $2^56^ * 56$ memory to store $Ek(p)$ and does $2^56^$ work to find a match.

The naive brute force algorithm does $2^56^ * 2^56^$ iterations going through all possible values of k1 and k2 while this algorithm uses $2^56^ * 56$ memory to store $Ek(p)$ and does $2^56^$ work to find a match.

h2. Discrete logarithm