Monte carlo scheme: Cryptography application

It has been previously shown that the DES algorithm is strengthened when it begins with a variable permutation, following the JV Theorem. Said algorithm states that a positive integer number less than 64! ≈ 1089 may be associated to a 64 positions permutation in 63 steps, thus increasing the DES algorithm computational complexity by making each permutation a as a key. However, the effects of the variable initial permutation and the 56 bits key on the computational complexity of the algorithm are yet unexplored. The current work presents a robust evidence - that is, the error can be reduced as much as needed - for the efficiency of the algorithm. The latter is achieved using a Monte Carlo schemecoupled with a Birthday model for probabilities computation, and the numbers π and e for random strings generation. In this paper, the error has an upper bound of 1/2 ¹⁰⁰.