Abstract
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.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
References
Wang, X.Y., Qin, X.: A new pseudo-random number generator based on CML and chaotic iteration. Nonlinear Dyn. 70(2), 1589–1592 (2012)
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)
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)
Menezes, A.J., Oorschot, P.C.V., Vanstone, S.A.: Handbook of Applied Cryptography. CRC Press, Boca Raton (1997)
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)
Murillo-Escobar, M.A., Cruz-Hernández, C., Cardoza-Avendaño, L., Méndez-RamÃrez, R.: A novel pseudorandom number generator based on pseudorandomly enhanced logistic map. Nonlinear Dyn. 87(1), 407–425 (2017)
Lambić, D., Nikolić, M.: Pseudo-random number generator based on discrete-space chaotic map. Nonlinear Dyn. 90(1), 223–232 (2017)
Alvarez, G., Li, S.: Some basic cryptographic requirements for chaos based cryptosystems. Int. J. Bifur. Chaos 16, 2129–2151 (2006)
Kocarev, L., Lian, S. (eds.): Chaos-Based Cryptography: Theory, Algorithms and Applications, vol. 354. Springer, Heidelberg (2011). https://doi.org/10.1007/978-3-642-20542-2
Oishi, S.I., Inoue, H.: Pseudo-random number generators and chaos. IEICE Trans. 1976–1990 65(9), 534–541 (1982)
Hamza, R.: A novel pseudo random sequence generator for image-cryptographic applications. J. Inf. Secur. Appl. 35, 119–127 (2017)
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)
GarcÃa-MartÃnez, M., Campos-Cantón, E.: Pseudo-random bit generator based on multi-modal maps. Nonlinear Dyn. 82(4), 2119–2131 (2015)
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 2014
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)
Özkaynak, F.: Cryptographically secure random number generator with chaotic additional input. Nonlinear Dyn. 78(3), 2015–2020 (2014)
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 2011
May, R.M.: Simple mathematical models with very complicated dynamics. Nature 261(5560), 459 (1976)
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 2009
Pincus, S.: Approximate entropy (ApEn) as a complexity measure. Chaos Interdisc. J. Nonlinear Sci. 5(1), 110–117 (1995)
Rukhin, A., et al.: A statistical test suite for random and pseudorandom number generators for cryptographic applications. NIST Special Publication 800-22 (2001)
L’Ecuyer, P., Simard, R.: TestU01: AC library for empirical testing of random number generators. ACM Trans. Math. Softw. (TOMS) 33(4), 22 (2007)
Golomb, S.W.: Shift Register Sequences. Aegean Park Press, Laguna Hills (1982)
Pareek, N.K., Patidar, V., Sud, K.K.: A random bit generator using chaotic maps. IJ Netw. Secur. 10(1), 32–38 (2010)
Lambert, H.S.: International Business Machines Corporation, Method and apparatus for encryption of data. U.S. Patent 7,133, 522 (2006)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2019 Springer Nature Singapore Pte Ltd.
About this paper
Cite this paper
Ahmad, M., Doja, M.N., Beg, M.M.S. (2019). A New Chaotic Map Based Secure and Efficient Pseudo-Random Bit Sequence Generation. In: Thampi, S., Madria, S., Wang, G., Rawat, D., Alcaraz Calero, J. (eds) Security in Computing and Communications. SSCC 2018. Communications in Computer and Information Science, vol 969. Springer, Singapore. https://doi.org/10.1007/978-981-13-5826-5_42
Download citation
DOI: https://doi.org/10.1007/978-981-13-5826-5_42
Published:
Publisher Name: Springer, Singapore
Print ISBN: 978-981-13-5825-8
Online ISBN: 978-981-13-5826-5
eBook Packages: Computer ScienceComputer Science (R0)