On the application of symbolic regression and genetic programming for cryptanalysis of symmetric encryption algorithm

The aim of the paper is to show different point of view on the problem of cryptanalysis of symmetric encryption algorithms. Our dissimilar approach, compared to the existing methods, lies in the use of the power of evolutionary principles which are in our cryptanalytic system applied with leveraging of the genetic programming (GP) in order to perform known plaintext attack (KPA). Our expected result is to find a program (i.e. function) that models the behavior of a symmetric encryption algorithm DES instantiated by specific key. If such a program would exist, then it could be possible to decipher new messages that have been encrypted by unknown secret key. The GP is employed as the basis of this work. GP is an evolutionary algorithm-based methodology inspired by biological evolution which is capable of creating computer programs solving a corresponding problem. The symbolic regression (SR) method is employed as the application of GP in practical problem. The SR method builds functions from predefined set of terminal blocks in the process of the GP evolution; and these functions approximate a list of input value pairs. The evolution of GP is controlled by a fitness function which evaluates the goal of a corresponding problem. The Hamming distance, a difference between a current individual value and a reference one, is chosen as the fitness function for our cryptanalysis problem. The results of our experiments did not confirmed initial expectation. The number of encryption rounds did not influence the quality of the best individual, however, its quality was influenced by the cardinality of a training set. The elimination of the initial and final permutations had no influence on the quality of the results in the process of evolution. These results showed that our KPA GP solution is not capable of revealing internal structure of the DES algorithm's behavior.