Abstract
Pseudo-Random Bit Generation (PRBG) is required in many aspects of cryptography as well as in other applications of modern security engineering. In this work, PRBG based on 2D symmetrical chaotic mappings of logistic type is considered. The sequences generated with a chaotic PRBG of this type, are statistically tested and the computational effectiveness of the generator is estimated. Considering this PRBG valid for cryptography, the size of the available key space is also calculated. Different cryptographic applications can be suitable to this PRBG, being a stream cipher probably the most immediate of them.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Anderson, R.: Security Engineering, A Guide to Build Dependable Distributed Systems. John Wiley and Sons Inc., New York (2001), http://www.cl.cam.ac.uk/~rja14/book.html
Menezes, A., van Oorschot, P., Vanstone, S.: Handbook of Applied Cryptography. CRC Press, Florida (1997)
NIST Special Publication 800-22: A Statistical Test Suite for the Validation of Random Number Generators and Pseudo Random Number Generators for Cryptographic Applications (2001)
Marsaglia, G.: The diehard test suite (1995), http://stat.fsu.edu/geo/diehard.html
Knuth, D.E.: The Art of Computer Programming, 3rd edn. Seminumerical Algorithms, vol. 2. Addison-Wesley Longman Publishing Co., Massachusetts (1997)
Li, S.: Analyses and New Designs of Digital Chaotic Ciphers. PhD thesis, School of Electronic and Information Engineering, Xi’an Jiaotong University (2003)
Stojanovski, T., Kocarev, L.: Chaos based Random Number Generators. Part I: Analysis. IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications 43, 281–288 (2001)
Protopopescu, V.A., Santoro, R.T., Tollover, J.S.: Fast secure encryption-decryption method based on chaotic dynamics. US Patent No. 5479513 (1995)
Kocarev, L., Jakimoski, G.: Pseudorandom Bits Generated by Chaotic Maps. IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications 50(1), 123–126 (2003)
Madhekar, S.: Cryptographic Pseudo-Random Sequences from the Chaotic Hénon Map, http://arxiv.org/abs/cs/0604018
Hénon, M.: A two-dimensional mapping with a strange attractor. Communications in Mathematical Physics 50, 69–77 (1976)
Lopez-Ruiz, R., Pérez-Garcia, C.: Dynamics of Maps with a Global Multiplicative Coupling. Chaos, Solitons and Fractals 1, 511–528 (1991)
Alvarez, G., Li, S.: Some Basic Cryptographic Requirements for Chaos-Based Cryptosystems. International Journal of Bifurcation and Chaos 16, 2129–2151 (2006)
Po-Han, L., Soo-Chang, P., Yih-Yuh, C.: Generating chaotic stream ciphers using chaotic systems. Chinese Journal of Physics 41, 559–581 (2003)
Li, S., Mou, X., Cai, Y.: Pseudo-random bit generator based on couple chaotic systems and its application in stream-ciphers cryptography. In: Pandu Rangan, C., Ding, C. (eds.) INDOCRYPT 2001. LNCS, vol. 2247, pp. 316–329. Springer, Heidelberg (2001)
Bogdan, C., Chargé, P., Fournier-Purnaret, D.: Behaviour of chaotic sequences under a finite representation and its cryptographic applications. In: IEEE Workshop on Nonlinear Maps and Applications (NOMA), Toulouse (2007)
Guckenheimer, J.M., Holmes, P.: Nonlinear Oscillations, Dynamical Systems and Bifurcation of Vector Fields. Springer, Heidelberg (1983)
Li, S., Chen, G., Mou, X.: On the dynamical degradation of digital piecewise linear chaotic maps. International Journal of Bifurcation and Chaos 15, 3119–3151 (2005)
Falcioni, M., Palatella, L., Pigolotti, S., Vulpiani, A.: Properties making a chaotic system a good pseudo random number generator. Physical Review E 016220 (2005)
Kocarev, L.: Chaos-based Cryptography: a brief overview. IEEE Circuits and Systems Magazine 1, 6–21 (2001)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2008 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Pellicer-Lostao, C., López-Ruiz, R. (2008). Pseudo-Random Bit Generation Based on 2D Chaotic Maps of Logistic Type and Its Applications in Chaotic Cryptography. In: Gervasi, O., Murgante, B., Laganà, A., Taniar, D., Mun, Y., Gavrilova, M.L. (eds) Computational Science and Its Applications – ICCSA 2008. ICCSA 2008. Lecture Notes in Computer Science, vol 5073. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-69848-7_62
Download citation
DOI: https://doi.org/10.1007/978-3-540-69848-7_62
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-69840-1
Online ISBN: 978-3-540-69848-7
eBook Packages: Computer ScienceComputer Science (R0)