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Cryptanalysis of Merkle-Hellman Cipher Using Parallel Genetic Algorithm

  • Nedjmeddine KantourEmail author
  • Sadek Bouroubi
Article

Abstract

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.

Keywords

Cryptanalysis Merkle-Hellman Cryptosystem Knapsack problem Genetic algorithm Lattice reduction algorithms 

Notes

Acknowledgments

The authors thank the anonymous referees for their valuable time to review our manuscript. This work was supported by L’IFORCE Laboratory.

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.L’IFORCE Laboratory, Faculty of MathematicsUniversity of Sciences and Technology Houari Boumediene (USTHB)AlgiersAlgeria

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