A New Chaotic Map Based Secure and Efficient Pseudo-Random Bit Sequence Generation

  • Musheer AhmadEmail author
  • M. N. Doja
  • M. M. Sufyan Beg
Conference paper
Part of the Communications in Computer and Information Science book series (CCIS, volume 969)


The security strength of symmetric encryption schemes rely on its internal source responsible for generation of efficient random encryption keys. A cryptographically strong encryption scheme needs a perfect mechanism that can generate statistically profound and secure pseudo-random sequences. To fulfill the requirement, we propose to present a novel pseudo-random number generation (PRNG) algorithm based on dynamical behaviour of a new and improved one-dimensional chaotic map. The dynamical characteristics of proposed chaotic map are analyzed through lyapunov exponents and bifurcation diagrams. The upright features of improved chaotic map are explored for synthesis of an efficient PRNG algorithm. The performance of proposed PRNG algorithm is examined using NIST SP800-22 and TestU01 randomness test suites, linear complexity, 0-1 balancedness, key-sensitivity, key space, etc. The randomness and other relevant statistical performance results of proposed PRNG algorithm demonstrate that it is consistent and suitable for its usage in cryptographic applications.


Pseudo-random sequence Chaotic map NIST randomness test Encryption keys 


  1. 1.
    Wang, X.Y., Qin, X.: A new pseudo-random number generator based on CML and chaotic iteration. Nonlinear Dyn. 70(2), 1589–1592 (2012)MathSciNetCrossRefGoogle Scholar
  2. 2.
    Hwang, S.Y., Park, G.Y., Kim, D.H., Jhang, K.S.: Efficient implementation of a pseudorandom sequence generator for high-speed data communications. ETRI J. 32(2), 222–229 (2010)CrossRefGoogle Scholar
  3. 3.
    Niederreiter, H., Winterhof, A.: On a new class of inversive pseudorandom numbers for parallelized simulation methods. Periodica Mathematica Hungarica 42(1–2), 77–87 (2001)MathSciNetCrossRefGoogle Scholar
  4. 4.
    Menezes, A.J., Oorschot, P.C.V., Vanstone, S.A.: Handbook of Applied Cryptography. CRC Press, Boca Raton (1997)zbMATHGoogle Scholar
  5. 5.
    Petrie, C.S., Connelly, J.A.: A noise-based IC random number generator for applications in cryptography. IEEE Trans. Circuits Syst. I Fundam. Theory Appl. 47(5), 615–621 (2000)CrossRefGoogle Scholar
  6. 6.
    Murillo-Escobar, M.A., Cruz-Hernández, C., Cardoza-Avendaño, L., Méndez-Ramírez, R.: A novel pseudorandom number generator based on pseudorandomly enhanced logistic map. Nonlinear Dyn. 87(1), 407–425 (2017)MathSciNetCrossRefGoogle Scholar
  7. 7.
    Lambić, D., Nikolić, M.: Pseudo-random number generator based on discrete-space chaotic map. Nonlinear Dyn. 90(1), 223–232 (2017)MathSciNetCrossRefGoogle Scholar
  8. 8.
    Alvarez, G., Li, S.: Some basic cryptographic requirements for chaos based cryptosystems. Int. J. Bifur. Chaos 16, 2129–2151 (2006)MathSciNetCrossRefGoogle Scholar
  9. 9.
    Kocarev, L., Lian, S. (eds.): Chaos-Based Cryptography: Theory, Algorithms and Applications, vol. 354. Springer, Heidelberg (2011). Scholar
  10. 10.
    Oishi, S.I., Inoue, H.: Pseudo-random number generators and chaos. IEICE Trans. 1976–1990 65(9), 534–541 (1982)Google Scholar
  11. 11.
    Hamza, R.: A novel pseudo random sequence generator for image-cryptographic applications. J. Inf. Secur. Appl. 35, 119–127 (2017)Google Scholar
  12. 12.
    Akhshani, A., Akhavan, A., Mobaraki, A., Lim, S.C., Hassan, Z.: Pseudo random number generator based on quantum chaotic map. Commun. Nonlinear Sci. Numer. Simul. 19(1), 101–111 (2014)CrossRefGoogle Scholar
  13. 13.
    García-Martínez, M., Campos-Cantón, E.: Pseudo-random bit generator based on multi-modal maps. Nonlinear Dyn. 82(4), 2119–2131 (2015)MathSciNetCrossRefGoogle Scholar
  14. 14.
    Singla, P., Sachdeva, P., Ahmad, M.: A chaotic neural network based cryptographic pseudo-random sequence design. In: 2014 Fourth International Conference on Advanced Computing and Communication Technologies (ACCT), pp. 301–306. IEEE, February 2014Google Scholar
  15. 15.
    Stoyanov, B., Kordov, K.: Novel secure pseudo-random number generation scheme based on two tinkerbell maps. Adv. Stud. Theor. Phys. 9(9), 411–421 (2015)CrossRefGoogle Scholar
  16. 16.
    Özkaynak, F.: Cryptographically secure random number generator with chaotic additional input. Nonlinear Dyn. 78(3), 2015–2020 (2014)MathSciNetCrossRefGoogle Scholar
  17. 17.
    Ahmad, M., Farooq, O.: Chaos based PN sequence generator for cryptographic applications. In: 2011 International Conference on Multimedia, Signal Processing and Communication Technologies (IMPACT), pp. 83–86. IEEE, December 2011Google Scholar
  18. 18.
    May, R.M.: Simple mathematical models with very complicated dynamics. Nature 261(5560), 459 (1976)CrossRefGoogle Scholar
  19. 19.
    Xie, J., Yang, C., Xie, Q., Tian, L.: An encryption algorithm based on transformed logistic map. In: 2009 International Conference on Networks Security, Wireless Communications and Trusted Computing, NSWCTC 2009, vol. 2, pp. 111–114. IEEE, April 2009Google Scholar
  20. 20.
    Pincus, S.: Approximate entropy (ApEn) as a complexity measure. Chaos Interdisc. J. Nonlinear Sci. 5(1), 110–117 (1995)MathSciNetCrossRefGoogle Scholar
  21. 21.
    Rukhin, A., et al.: A statistical test suite for random and pseudorandom number generators for cryptographic applications. NIST Special Publication 800-22 (2001)Google Scholar
  22. 22.
    L’Ecuyer, P., Simard, R.: TestU01: AC library for empirical testing of random number generators. ACM Trans. Math. Softw. (TOMS) 33(4), 22 (2007)CrossRefGoogle Scholar
  23. 23.
    Golomb, S.W.: Shift Register Sequences. Aegean Park Press, Laguna Hills (1982)zbMATHGoogle Scholar
  24. 24.
    Pareek, N.K., Patidar, V., Sud, K.K.: A random bit generator using chaotic maps. IJ Netw. Secur. 10(1), 32–38 (2010)Google Scholar
  25. 25.
    Lambert, H.S.: International Business Machines Corporation, Method and apparatus for encryption of data. U.S. Patent 7,133, 522 (2006)Google Scholar

Copyright information

© Springer Nature Singapore Pte Ltd. 2019

Authors and Affiliations

  • Musheer Ahmad
    • 1
    Email author
  • M. N. Doja
    • 1
  • M. M. Sufyan Beg
    • 2
  1. 1.Department of Computer Engineering, Faculty of Engineering and TechnologyJamia Millia IslamiaNew DelhiIndia
  2. 2.Department of Computer EngineeringAligarh Muslim UniversityAligarhIndia

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