Mobile Networks and Applications

, Volume 23, Issue 4, pp 723–733 | Cite as

A Novel Whale Optimization Algorithm for Cryptanalysis in Merkle-Hellman Cryptosystem

  • Mohamed Abdel-Basset
  • Doaa El-Shahat
  • Ibrahim El-henawy
  • Arun Kumar SangaiahEmail author
  • Syed Hassan Ahmed


With the advance of the communication technology and the massive flow of information across the internet, it is becoming urgent to keep the confidentiality of the transmitted information. Using the internet has been extended to several fields such as e-mail, e-commerce, e-learning, health and medicine, shopping, and so on. Cryptography is the study of different techniques for securing the communication between the sender and the receiver. One of the most known cryptosystems is Merkle–Hellman Knapsack Cryptosystem (MHKC). It is one of the earliest Public Key Cryptosystem (PKC) that is used to secure the messages between the sender and the receiver. Developing a powerful cryptosystem comes after studying the fragility points of the current cryptosystems. The Whale Optimization Algorithm (WOA) is one of the most recent nature-inspired meta-heuristic optimization algorithms, which simulates the social behavior of humpback whales. WOA has validated excellent performance in solving the continuous problems and the engineering optimization problems. This paper introduces a novel Modified version of WOA (MWOA) for cryptanalysis of MHKC. The sigmoid function is used to map the continuous values into discrete one. A penalty function is added to the evaluation function to deal with the infeasible solutions. The mutation operation is employed for improving the solutions. The results show that MWOA is more effective and robust than other algorithms in the literature.


Whale optimization algorithm Knapsack cipher Subset sum problem Public key cryptosystem Merkle-Hellman Cryptosystem Cryptanalysis 


Compliance with ethical standards

This article does not contain any studies with human participants or animals performed by any of the authors.

Conflict of interest

The authors declare that there is no conflict of interests regarding the publication of this article.


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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  • Mohamed Abdel-Basset
    • 1
  • Doaa El-Shahat
    • 2
  • Ibrahim El-henawy
    • 2
  • Arun Kumar Sangaiah
    • 3
    Email author
  • Syed Hassan Ahmed
    • 4
  1. 1.Faculty of Computers and Informatics, Department of Operations ResearchZagazig UniversityZagazigEgypt
  2. 2.Computer Science Department, Faculty of Computers and InformaticsZagazig UniversityZagazigEgypt
  3. 3.School of Computing Science and Engineering, Vellore Institute of TechnologyVelloreIndia
  4. 4.Department of Electrical and Computer EngineeringUniversity of Central FloridaOrlandoUSA

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