Diffie Hellman’s meet in the middle attack trades of 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 O(2^56) work to find a match.

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 $O(2^56^)$ work to find a match.

h2. Discrete logarithm

bq. Given n a prime number and p, q two integer numbers between 0 and n-1 find k such that  p^k = q modulo n.

bq. Given n a prime number and p, q two integer numbers between 0 and n-1 find k such that  $p^k^ = q modulo n$.

This problem can be solved using the baby step, giant step algorithm which uses the meet in the middle trick.
We can write k = i ([sqrt(n)] + 1) + j.