Cryptanalytic Results on Knapsack Cryptosystem Using Binary Particle Swarm Optimization

Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 299)


The security of most Public Key Cryptosystem (PKC) proposed in literature relies on the difficulty of the integer factorization problem or discrete logarithm problem. However, using shor’s [19] algorithm the problems can be solved in acceptable amount of time via ‘quantum computers’. Therefore in this context knapsack (more accurately subset sum problem(SSP)) based PKC is reconsidered as a viable option by the cryptography community. However, before considering the practicability of this cryptosystem, there is a growing need to cryptanalyze it using all possible present techniques, in order to guarantee their security. We believe that modern Computation Intelligence (CI) techniques can provide efficient cryptanalytic results (because of the new aspects have been incorporated in CI techniques). In this paper, we use two different binary particle swarm optimization techniques to cryptanalyze knapsack PKC. The results obtained via extensive testing are promising and proficient. We present, discuss and compare the effectiveness of the proposed work in the result section.


Cryptanalysis of Knapsack Cryptosystem Binary Particle Swarm Optimization (BPSO) Modified Binary Particle Swarm Optimization (MBPSO) CI Merkle-Hellman (MH) 


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  1. 1.
    Bansal, J.C., Deep, K.: A modified binary particle swarm optimization for knapsack problems. Applied Mathematics and Computation 218(22), 11,042–11,061 (2012)Google Scholar
  2. 2.
    Coster, M.J., Joux, A., LaMacchia, B.A., Odlyzko, A.M., Schnorr, C.P., Stern, J.: Improved low-density subset sum algorithms. Computational Complexity 2(2), 111–128 (1992)CrossRefMATHMathSciNetGoogle Scholar
  3. 3.
    Danziger, M., Henriques, A.: Computational intelligence applied on cryptology: a brief review. IEEE Latin America Transactions (Revista IEEE America Latina) 10(3), 1798–1810 (2012)CrossRefGoogle Scholar
  4. 4.
    Engelbrecht, A.P.: Computational intelligence: an introduction. John Wiley & Sons (2007)Google Scholar
  5. 5.
    Garg, P., Shastri, A.: An improved cryptanalytic attack on knapsack cipher using genetic algorithm. International Journal of Information Technology 3(3) (2006)Google Scholar
  6. 6.
    Garg, P., Shastri, A., Agarwal, D.: An enhanced cryptanalytic attack on knapsack cipher using genetic algorithm. Transaction on Engineering, Computing and Technology 12 (2006)Google Scholar
  7. 7.
    Herrero, Á., Navarro, M., Corchado, E., Julián, V.: Rt-movicab-ids: Addressing real-time intrusion detection. Future Generation Computer Systems 29(1), 250–261 (2013)CrossRefGoogle Scholar
  8. 8.
    Herrero, A., Zurutuza, U., Corchado, E.: A neural-visualization ids for honeynet data. International Journal of Neural Systems 22(2) (2012)Google Scholar
  9. 9.
    Jen, S.M., Lai, T.L., Lu, C.Y., Yang, J.F.: Knapsack cryptosystems and unreliable reliance on density. In: 2012 IEEE 26th International Conference on Advanced Information Networking and Applications (AINA), pp. 748–754. IEEE (2012)Google Scholar
  10. 10.
    Kate, A., Goldberg, I.: Generalizing cryptosystems based on the subset sum problem. International Journal of Information Security 10(3), 189–199 (2011)CrossRefGoogle Scholar
  11. 11.
    Kennedy, J., Eberhart, R.C.: A discrete binary version of the particle swarm algorithm. In: 1997 IEEE International Conference on Systems, Man, and Cybernetics, 1997. Computational Cybernetics and Simulation, vol. 5, pp. 4104–4108. IEEE (1997)Google Scholar
  12. 12.
    Lagarias, J.C., Odlyzko, A.M.: Solving low-density subset sum problems. Journal of the ACM (JACM) 32(1), 229–246 (1985)CrossRefMATHMathSciNetGoogle Scholar
  13. 13.
    Lyubashevsky, V., Palacio, A., Segev, G.: Public-key cryptographic primitives provably as secure as subset sum. In: Micciancio, D. (ed.) TCC 2010. LNCS, vol. 5978, pp. 382–400. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  14. 14.
    Merkle, R., Hellman, M.: Hiding information and signatures in trapdoor knapsacks. IEEE Transactions on Information Theory 24(5), 525–530 (1978)CrossRefGoogle Scholar
  15. 15.
    Murakami, Y., Hamasho, S., Kasahara, M.: A public-key cryptosystem based on decision version of subset sum problem. In: 2012 International Symposium on Information Theory and its Applications (ISITA), pp. 735–739. IEEE (2012)Google Scholar
  16. 16.
    Murakami, Y., Katayanagi, K., Kasahara, M.: A new class of cryptosystems based on chinese remainder theorem. In: International Symposium on Information Theory and Its Applications, ISITA 2008, pp. 1–6. IEEE (2008)Google Scholar
  17. 17.
    Shamir, A.: A polynomial-time algorithm for breaking the basic merkle-hellman cryptosystem. IEEE Transactions on Information Theory 30(5), 699–704 (1984)CrossRefMATHMathSciNetGoogle Scholar
  18. 18.
    Shi, Y., Eberhart, R.: A modified particle swarm optimizer. In: The 1998 IEEE International Conference on Evolutionary Computation Proceedings, IEEE World Congress on Computational Intelligence, pp. 69–73. IEEE (1998)Google Scholar
  19. 19.
    Shor, P.W.: Polynomial-time algorithms for prime factorization and discrete logarithms on a quantum computer. SIAM Journal on Computing 26(5), 1484–1509 (1997)CrossRefMATHMathSciNetGoogle Scholar
  20. 20.
    Spillman, R.: Cryptanalysis of knapsack ciphers using genetic algorithms. Cryptologia 17(4), 367–377 (1993)CrossRefMATHGoogle Scholar
  21. 21.
    Wang, B., Hu, Y.: Quadratic compact knapsack public-key cryptosystem. Computers & Mathematics with Applications 59(1), 194–206 (2010)CrossRefMATHMathSciNetGoogle Scholar
  22. 22.
    Wang, B., Wu, Q., Hu, Y.: A knapsack-based probabilistic encryption scheme. Information Sciences 177(19), 3981–3994 (2007)CrossRefMATHMathSciNetGoogle Scholar

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© Springer International Publishing Switzerland 2014

Authors and Affiliations

  1. 1.Discipline of Computer Science and Engineering IndianInstitute of Technology IndoreIndoreIndia

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