Abstract
This work shows how to improve the statistical distribution of signals produced by noise generators designed with one-dimensional chaotic maps. It also shows that in a electronic design the piecewise linear chaotic maps should be considered because they do not have stability islands in its chaotic behavior region, as it occurs with the logistic map commonly used to build noise generators. The design and implementation problems of the noise generators are analyzed and a solution is proposed. This solution relates the tent map output, defined in the real numbers’ domain, with a codebook of S elements. The proposed scheme produces digital noise signals using tent map without scaling and discretization process. Finally, this work shows that it is possible to have control over the statistical distribution of the noise signal by selecting the control parameter of the tent map and using, as a design criterion, the bifurcation diagram.
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
Puczko, M., Yarmolik, V.N.: Designing cryptographic key generators with low power consumption. In: Third IEEE International Workshop on Electronic Design, Test and Applications, DELTA 2006, p. 4 (2006)
Zeng, K., Yang, C.-H., Wei, D.-Y., Rao, T.R.N.: Pseudorandom bit generators in stream-cipher cryptography. IEEE Computer 24, 8–17 (1991)
Yu, C., Fang, Q., Jianbin, H., Zhong, C.: Density Adjustable Pseudorandom Sequence and its Applications in Information Hiding. In: International Conference on Multimedia Information Networking and Security, MINES 2009, vol. 2, pp. 91–94 (2009)
Ahmad, A., Al-Mashari, A., Al-Lawati, A.M.J.: On locking conditions in m-sequence generators for the use in digital watermarking. In: Proceeding of International Conference on Methods and Models in Computer Science, ICM2CS 2009, pp. 1–5 (2009)
Arnault, F., Berger, T., Minier, M., Pousse, B.: Revisiting LFSRs for Cryptographic Applications. IEEE Transactions on Information Theory 57, 8095–8113 (2011)
Katti, R.S., Kavasseri, R.G.: Secure pseudo-random bit sequence generation using coupled linear congruential generators. In: IEEE International Symposium on Circuits and Systems, SCAS 2008, pp. 2929–2932 (2008)
Karras, D.A., Zorkadis, V.: Improving pseudorandom bit sequence generation and evaluation for secure Internet communications using neural network techniques. In: Proceedings of the International Joint Conference on Neural Networks, vol. 2, pp. 1367–1372 (2003)
Cheng, L.M., Chan, C.: Pseudorandom generator based on clipped Hopfield neural network. In: Proc. of the IEEE International Symposium on Circuits and Systems, vol. 3, pp. 183–186 (1998)
Itoh, M.: Spread spectrum communication via chaos. Int. Journal Bifurcation Chaos 9, 155–213 (1999)
Mazzini, G., Setti, G., Rovatti, R.: Chaotic complex spreading sequences for asynchronous DS-CDMA–Part I: System modeling and results. IEEE Trans. Circ. Syst. 44, 937–947 (1997)
Kinzel, W., Kanter, I.: Secure Communication with Chaos Synchronization. In: Schoell, E., Schuster, H.G. (eds.) Contribution to Handbook of Chaos Control. Wiley-VCH (2007)
Tang, K.W., Tang, W.K.S., Man, K.F.: A chaos-based pseudo-random number generator and its application in voice communications. Int. J. Bifurcat Chaos 17, 923–933 (2007)
Rodrigo-Vazquez, A., Espejo-Meana, S.: Analog Building Blocks for Noise and Truly Random Generation in CMOS VLSI. In: Solid-State Circuits Conference, ESSCIRC, Grenoble France, pp. 225–228 (1990)
Addabbo, T., Alioto, M., Fort, A., Rocchi, S., Vignoli, V.: Uniform-Distributed Noise Generator Based on a Chaotic Circuit. In: Proceedings of the IEEE Instrumentation and Measurement Technology Conference, IMTC 2006, Sorrento, Italy, pp. 1156–1160 (2006)
Peitgen, H.O., Jürgens, H., Dietmar, S.: Chaos and Fractals New Frontiers of Science, USA, p. 864 (2004)
Argyris, J., Faust, G., Haase, M.: An Exploration of Chaos: an Introduction for Natural Scientists and Engineers, p. 775. North-Holland, Netherlands (1994)
Peitgen, H.O., Jürgens, H., Saupe, D.: Fractals for the Classroom Part II: Complex Systems and Mandelbrot Set, pp. 593–594. Springer, New York (1991)
San Martín, J.: Intermittency cascade. Chaos Solitons Fractals 32, 816–831 (2007)
Jakimoski, G., Kocarev, L.: Chaos and Cryptography: Block Encryption Ciphers Based on Chaotic Maps. IEEE Transactions on Circuits and Systems I 48, 163–169 (2001)
Callegari, S., Setti, G., Langlois, P.J.: A CMOS tailed tent map for the generation of uniformly distributed chaotic sequences. In: IEEE International Symposium on Circuits and Systems, Hong Kong, pp. 781–784 (1997)
Nejati, H., Beirami, A., Massoud, Y.: A realizable modified tent map for true random number generation. In: MWSCAS 2008 Conference Proceedings, Knoxville, TN, USA, pp. 621–624 (2008)
Addabbo, T., Alioto, M., Bernardi, S., Fort, A., Rocchi, S., Vignoli, V.: The digital Tent map: performance analysis and optimized design as a source of pseudo-random bits. In: IMTC 2004 Conference Proceedings, Como, Italy, pp. 1301–1304 (2004)
Huawei, R., Yaz, E.E., Tongyan, Z., Yaz, Y.I.: A generalization of tent map and its use in EKF based chaotic parameter modulation/demodulation. In: 43rd IEEE Conference on Decision and Control, CDC 2004, vol. 2, pp. 2071–2075 (2004)
Montiel, O., Castillo, O., Melin, P., Sepúlveda, R.: Evolutionary Optimization of a Wiener Model. In: TI Hybrid Intelligent Systems. Studies in Fuzziness and Soft Computing, pp. 43–58. Springer, Heidelberg (2007)
EPC, Radio-Frequency Identity protocols, Class-1 Generation-2 UHF RFID, Protocol for Communicartions at 860 MHz-960MHz, EPC Global Inc., Ver 1.2.0, 46–48 (2008)
Pacheco, M.A.C., Vellasco, M.M.B.R.: Intelligent Systems in Oil Field Development under Uncertainty, 139–146 (2009)
Lassota, A., Mackey, M.C.: Chaos, Fractals and Noise, p. 64. Springer, New York (1994)
Luca, A., Ilyas, A., Vlad, A.: Generating random binary sequences using tent map. In: 10th International Symposium on Signals, Circuits and Systems (ISSCS), pp. 1–4 (2011)
Luca, A., Vlad, A., Badea, B., Frunzete, M.: A study on statistical independence in the tent map. In: International Symposium on Signals, Circuits and Systems, ISSCS 2009, pp. 1–4 (2009)
Jian-dong, L., Kai, Y., Shu-hong, W.: Coupled Chaotic Tent Map Lattices System with Uniform Distribution. In: 2010 2nd International Conference on e-Business and Information System Security (EBISS), pp. 1–5 (2010)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2012 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Vazquez-Medina, R., Del-Río-Correa, J.L., Rojas-López, C.E., Díaz-Méndez, J.A. (2012). Digital Chaotic Noise Using Tent Map without Scaling and Discretization Process. In: Corchado, E., Snášel, V., Abraham, A., Woźniak, M., Graña, M., Cho, SB. (eds) Hybrid Artificial Intelligent Systems. HAIS 2012. Lecture Notes in Computer Science(), vol 7209. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-28931-6_11
Download citation
DOI: https://doi.org/10.1007/978-3-642-28931-6_11
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-28930-9
Online ISBN: 978-3-642-28931-6
eBook Packages: Computer ScienceComputer Science (R0)