A Novel Whale Optimization Algorithm for Cryptanalysis in Merkle-Hellman Cryptosystem
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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.
KeywordsWhale 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.
- 2.Li X, Niu J, Kumari S, Wu F, Sangaiah AK, Choo KKR (2017) A Three-factor anonymous authentication scheme for wireless sensor networks in internet of things environments. J Netw Comput Appl. https://doi.org/10.1016/j.jnca.2017.07.001
- 3.Mahmood K, Chaudhry SA, Naqvi H, Kumari S, Li X, Sangaiah AK (2017) An elliptic curve cryptography based lightweight authentication scheme for smart grid communication. Futur Gener Comput Syst. https://doi.org/10.1016/j.future.2017.05.002
- 4.Li X, Ibrahim MH, Kumari S, Sangaiah AK, Gupta V, Choo KKR (2017) Anonymous mutual authentication and key agreement scheme for wearable sensors in wireless body area networks. Comput Netw. https://doi.org/10.1016/j.comnet.2017.03.013
- 8.Srikanth K, Panwar LK, Panigrahi BK, Herrera-Viedma E, Sangaiah AK, Wang GG (2017) Meta-heuristic framework: quantum inspired binary grey wolf optimizer for unit commitment problem. Comput Electr Eng. https://doi.org/10.1016/j.compeleceng.2017.07.023
- 11.Garg P, Shastri A, Agarwal DC (2006) An enhanced cryptanalytic attackknetic algorithm. Trans Eng Comput Technol 12:829–832Google Scholar
- 12.Palit S, Sinha SN, Molla MA, Khanra A, Kule M (2011, September) A cryptanalytic attack on the knapsack cryptosystem using binary firefly algorithm. In: 2011 2nd International conference on computer and communication technology (ICCCT), IEEE, pp 428–432Google Scholar
- 13.Singh H (2016) Contravening esotery: cryptanalysis of knapsack cipher using genetic algorithms. arXiv preprint arXiv:1606.06047Google Scholar
- 14.Kochladze Z, Beselia L (2016) Cracking of the Merkle–Hellman cryptosystem using genetic algorithm. Int J Sci Technol 3(1–2):291–296Google Scholar
- 15.Agarwal A (2011) Encrypting messages using the Merkle-Hellman knapsack cryptosystem. IJCSNS 11(5):12Google Scholar
- 16.Padhmavathi B, Ray A, Anjum A, Bhat S (2013, January) Improvement of CBC encryption technique by using the Merkle-Hellman knapsack cryptosystem. In: 2013 7th international conference on intelligent systems and control (ISCO), IEEE, pp 340–344Google Scholar
- 17.Ray A, Bhat S (2013) Enhancement of Merkle-Hellman knapsack cryptosystem by use of discrete logarithmics. Int J Sci Res Publ 3(4):230Google Scholar
- 18.Jain A, Chaudhari NS (2014) Cryptanalytic results on knapsack cryptosystem using binary particle swarm optimization. In: International joint conference SOCO’14-CISIS’14-ICEUTE’14, Springer International Publishing, pp 375–384Google Scholar
- 19.Kennedy J, Eberhart RC (1997, October) A discrete binary version of the particle swarm algorithm. In: Computational cybernetics and simulation, 1997 I.E. international conference on systems, man, and cybernetics, vol. 5, IEEE, pp 4104–4108Google Scholar
- 21.Sinha SN, Palit S, Molla MA, Khanra A, Kule M (2011, September) A cryptanalytic attack on Knapsack cipher using differential evolution algorithm. In: 2011 I.E. recent advances in intelligent computational systems (RAICS), IEEE, pp 317–320Google Scholar
- 22.Beselia L (2016) Using genetic algorithm for cryptanalysis cryptoalgorithm Merkle-Hellman. Comput Sci Telecommun 48(2):49–53Google Scholar
- 25.Thangavel M, Varalakshmi P (2017, January) A novel public key cryptosystem based on Merkle-Hellman knapsack cryptosystem. In: 2016 eighth international conference on advanced computing (ICoAC), IEEE, pp 117–122Google Scholar