Cryptanalysis of Merkle-Hellman Cipher Using Parallel Genetic Algorithm

In 1976, Whitfield Diffie and Martin Hellman introduced the public key cryptography or asymmetric cryptography standards. Two years later, an asymmetric cryptosystem was published by Ralph Merkle and Martin Hellman called \( \mathcal {M} \mathcal {H} \), based on a variant of knapsack problem known as the subset-sum problem which is proven to be NP -hard. Furthermore, over the last four decades, Metaheuristics have achieved remarkable progress in solving NP-hard optimization problems. However, the conception of these methods raises several challenges, mainly the adaptation and the parameters setting. In this paper, we propose a Parallel Genetic Algorithm (PGA) adapted to explore effectively the search space of considerable size in order to break the \( \mathcal {M} \mathcal {H} \) cipher. Experimental study is included, showing the performance of the proposed attacking scheme, and finally a concluding comparison with lattice reduction attacks.