Key generation for plain text in stream cipher via bi-objective evolutionary computing

Evolutionary algorithms are widely used to solve a wide variety of continuous, discrete and combinatorial optimization problems. Evolutionary multi-objective optimization problems seek Pareto front in order to negotiate the trade-off amongst various objective functions present in the problem. Much of the literature on cryptography focuses on making the inference problem harder, for securing the content. In this paper, we developed key generation algorithms using Non-Dominated Sorting Genetic Algorithm-II (NSGA-II) in the bi-objective optimization framework and Improved Modified Harmony Search + Differential Evolution (IMHS+DE), Differential Evolution (DE) and Improved Modified Harmony Search (IMHS), in the single objective optimization framework. For encoding the keystream thus generated as well as the plain text we employed the Mutated Huffman Tree Coding algorithm. In the next phase, we encrypted the encoded keystream as well as the encoded plain text in order to generate the cipher text. We then decrypted the cipher text using the encoded key stream followed by the decoding of the deciphered text using the code tables. Following the literature, we generated random texts of varying lengths and code table sizes in order to demonstrate the effectiveness of our proposed method. The proposed algorithms are compared with the extant methods. In the case of bi-objective optimization set up, we also plotted the empirical attainment function (EAF) surface to summarize the effectiveness of the NSGA-II based key generation algorithm. Of particular significance is the highest entropy value yielded by the NSGA-II based algorithm, which in turn indicates the strength of the key generated by the NSGA-II.