If we find any match in the two sets it means that Eki(p) = Dkj(s) so the secret keys are ki and kj.
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 all Eki(p) and does $2^56^$ work to find a match.

Breaking 2DES was basically the DOUBLE problem from the International Olympiad in Informatics 2001.
 

h2. Discrete logarithm
bq. Given n a prime number and p, q two integers between 0 and n-1, find k such that  p^k^ = q (mod n).