Public Key Cryptography Using Harmony Search Algorithm

  • Suman Mitra
  • Gautam MahapatraEmail author
  • Valentina E. Balas
  • Ranjan Chattaraj
Conference paper
Part of the Advances in Intelligent Systems and Computing book series (AISC, volume 757)


Privacy is a very important requirement for viability of modern information sharing through cyberspace and the modern cryptology is ensuring success. Harmony Search Algorithm (HSA) is a new meta-heuristic computation technique inspired from musical improvisation techniques, where searching for a perfect harmony is the objective of this technique. Public Key Cryptography heavily relies on key pairs which are large prime numbers. Our adaptation of the HSA tries to provide a fast key generation mechanism with a feasible implementation. The keys are ranked based on their harmony and the best harmony is selected as the result of the search which in turn is used to generate the key pair of RSA, a Public Key Cryptography technique as a test of effectiveness and success.


Public Key Cryptography (PKC) Harmony Search Algorithm (HSA) Fast key generation Random Number Generator (RNG) RSA Keys management Prime numbers 



The authors wish to acknowledge the support of the Post Graduate Teaching and Research Council of Asutosh College.


  1. 1.
    Nechvatal, J.: Public-key cryptography. No. NIST-SP-800-2. NATIONAL COMPUTER SYSTEMS LAB GAITHERSBURG MD, (1991)Google Scholar
  2. 2.
    Rivest, R.L., Shamir, A., Adleman, L.: A method for ob-taining digital signatures and public-key cryptosystems. Commun. ACM 21(2), 120–126 (1978)CrossRefGoogle Scholar
  3. 3.
    Crow, J.: Prime Numbers in Public Key Cryptography. This is a paper from the SANS Institute Reading Room site (2003)Google Scholar
  4. 4.
    Hao, Chen, Clark, J.A., Jacob, J.L.: Automated design of security protocols. Comput. Intell. 20(3), 503–516 (2004)MathSciNetCrossRefGoogle Scholar
  5. 5.
    Mishra, M., et al.: A study on the limitations of evolutionary computation and other bio-inspired approaches for integer factorization. Procedia Comput. Sci. 62, 603–610 (2015)CrossRefGoogle Scholar
  6. 6.
    Spillman, R., Janssen, M., Nelson B., Kepner, M.: Use of a genetic algorithm in the cryptanalysis of simple substitution ciphers. Cryp-tologia 17(1):31–44 (1993)CrossRefGoogle Scholar
  7. 7.
    Geem, Z.W., Kim, J.H.: A new heuristic optimization algorithm: harmony search. Simulation 76(2), 60–68 (2001)CrossRefGoogle Scholar
  8. 8.
    Storn, R., Price, K.: Differential evolutiona simple and efficient heuristic for global optimization over continuous spaces. J. Global Optim. 11(4), 341–359 (1997)MathSciNetCrossRefGoogle Scholar
  9. 9.
    Kirkpatrick, S., Gelatt, C.D., Vecchi, M.P.: Optimization by simulated annealing. Science 220(4598), 671–680 (1983)MathSciNetCrossRefGoogle Scholar
  10. 10.
    Clark, J., Jacob, J.: A survey of authentication protocol literature: Version 1.0. (1997)Google Scholar
  11. 11.
    Bahadori, M., Mali, M.R., Sarbishei, O., Atarodi, M., Sharifkhani, M.: A novel approach for secure and fast generation of RSA public and private keys on SmartCard. In: NEWCAS Conference (NEWCAS), 2010 8th IEEE International, pp. 265–268. IEEE (2010)Google Scholar
  12. 12.
    Eberhart, R., Kennedy J.: A new optimizer using particle swarm theory. In: Micro Machine and Human Science, 1995. MHS’95. In: Proceedings of the Sixth International Symposium on, pp. 39–43. IEEE (1995)Google Scholar
  13. 13.
    Bishop, C.M.: Neural Networks for Pattern Recognition. Oxford University Press (1995)Google Scholar
  14. 14.
    Dorigo, M., Di Caro, G.: Ant colony optimization: a new meta-heuristic. In: Evolutionary Computation, 1999. CEC 99. Proceedings of the 1999 Congress on, vol. 2, pp. 1470–1477. IEEE (1999)Google Scholar
  15. 15.
    Karaboga, D., Basturk, B.: A powerful and efficient algorithm for numerical function optimization: artificial bee colony (ABC) algorithm. J. Global Optim. 39(3), 459–471 (2007)MathSciNetCrossRefGoogle Scholar
  16. 16.
    Yang, X.-S., Deb, S.: Cuckoo search via Lvy flights. In: Nature & Biologically Inspired Computing, 2009. NaBIC 2009. World Congress on, pp. 210–214. IEEE (2009)Google Scholar
  17. 17.
    Jhajharia, S., Mishra, S., Bali S.: Public key cryptography using neural networks and genetic algorithms. In: Contemporary Computing (IC3), 2013 Sixth International Conference on, pp. 137–142. IEEE (2013)Google Scholar
  18. 18.
    Patidar, V., Sud, K.K., Pareek, N.K.: A pseudo random bit generator based on chaotic logistic map and its statistical testing. Informatica, 33, 4 (2009)Google Scholar
  19. 19.
    Rukhin, A., Soto, J., Nechvatal, J., Smid, M., Barker, E.: A statistical test suite for random and pseudorandom number genera-tors for cryptographic applications. Booz-Allen and Hamilton Inc Mclean Va (2001)Google Scholar
  20. 20.
    Shannon, C.E.: Prediction and entropy of printed English. Bell Labs Technical J. 30(1), 50–64 (1951)CrossRefGoogle Scholar
  21. 21.
    Rabin, M.O.: Probabilistic algorithm for testing primality. J. Number Theory 12(1), 128–138 (1980)MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer Nature Singapore Pte Ltd. 2019

Authors and Affiliations

  • Suman Mitra
    • 1
  • Gautam Mahapatra
    • 2
    Email author
  • Valentina E. Balas
    • 3
  • Ranjan Chattaraj
    • 4
  1. 1.Department of Computer ScienceAsutosh College, University of CalcuttaKolkataIndia
  2. 2.Department of Computer Science and EngineeringBirla Institute of Technology MesraRanchiIndia
  3. 3.“Aurel Vlaicu” University of AradAradRomania
  4. 4.Department of MathematicsBirla Institute of Technology MesraRanchiIndia

Personalised recommendations