Chaotic Encryption Based Data Transmission Using Delta and Delta-Sigma Modulators

Yıl 2016, , 368 - 373, 01.12.2016

Günyaz Ablay

https://doi.org/10.18100/ijamec.280466

Cited By: 1

Öz

Delta and Delta-Sigma modulation methods have been getting a great
interest recently due to the great progress in analog-digital very large scale
integration technology. Since the outputs of these methods are digital, the
data can be securely encrypted using very simple standard hardware. In this
work, a chaotic random bit generator based approach for encrypting digital data
of the delta and delta-sigma modulators is studied. The chaotic bit generation
can easily be implemented in the digital hardware of the modulators due to simplicity
of the chaotic dynamics.  The randomness
of the generated chaotic bits are proved with visual and statistical tests. The
security of the proposed approach is evaluated via key space estimation based
attacks. The efficiency of the methods is validated with simulations.

Anahtar Kelimeler

Chaos, delta modulation, delta-sigma modulation, random bits, cryptography, communication

Kaynakça

• Zrilic D. G. Circuits and Systems Based on Delta Modulation: Linear, Nonlinear and Mixed Mode Processing. Springer, 2006.
• Liberti J. and Rappaport T. S. Smart Antennas for Wireless Communications: IS-95 and Third Generation CDMA Applications, 1 edition. Upper Saddle River, NJ: Prentice Hall, 1999.
• Intersil Corporation, Delta Modulation For Voice Transmission. Intersil Corporation, Application Note, AN607.1, 2000.
• Rodenbeck C. T., Tracey K. J., Barkley K. R., and DuVerneay B.B. Delta Modulation Technique for Improving the Sensitivity of Monobit Subsamplers in Radar and Coherent Receiver Applications, IEEE Trans. Microw. Theory Tech., vol. 62, no. 8, pp. 1811–1822, Aug. 2014.
• Comaniciu C. and Mandayam N. B. Delta modulation based prediction for access control in integrated voice/data CDMA systems, IEEE J. Sel. Areas Commun., vol. 18, no. 1, pp. 112–122, Jan. 2000.
• Sira-Ramírez H. Sliding Mode Control: The Delta-Sigma Modulation Approach, 1st ed. Basel: Birkhäuser, 2015.
• Hu T., Lin Z., and Qiu L. Stabilization of exponentially unstable linear systems with saturating actuators, IEEE Trans. Autom. Control, vol. 46, no. 6, pp. 973–979, Jun. 2001.
• Elia N. and Mitter S. K. Stabilization of linear systems with limited information, IEEE Trans. Autom. Control, vol. 46, no. 9, pp. 1384–1400, Sep. 2001.
• Brockett R. W. and Liberzon D. Quantized feedback stabilization of linear systems, IEEE Trans. Autom. Control, vol. 45, no. 7, pp. 1279–1289, Jul. 2000.
• Liberzon D., Switching in Systems and Control. Springer Science & Business Media, 2012.
• Chong K. S., Zahedi E., Gan K. B., and Ali M. A. M. Evaluation of the Effect of Step Size on Delta Modulation for Photoplethysmogram Compression, Procedia Technol., vol. 11, pp. 815–822, 2013.
• Feely O. Nonlinear dynamics of discrete-time circuits: A survey, Int. J. Circuit Theory Appl., vol. 35, no. 5–6, pp. 515–531, Sep. 2007.
• Johnson T., Sobot R., and Stapleton S. CMOS RF class-D power amplifier with bandpass sigma–delta modulation, Microelectron. J., vol. 38, no. 3, pp. 439–446, Mar. 2007.
• Kuang W. V. and Wight J. 1-bit digital tuning of continuous-time filter by the use of unstable sigma-delta modulation, in IEEE International Symposium on Circuits and Systems, 2009. ISCAS 2009, 2009, pp. 41–44.
• Liang X., Zhang J., and Xia X. Improving the Security of Chaotic Synchronization With a -Modulated Cryptographic Technique, IEEE Trans. Circuits Syst. II Express Briefs, vol. 55, no. 7, pp. 680–684, Jul. 2008.
• Xia X. and Chen G. On delta-modulated control: A simple system with complex dynamics, Chaos Solitons Fractals, vol. 33, no. 4, pp. 1314–1328, Aug. 2007.
• Reiss J. D. and Sandler M. B. The benefits of multibit chaotic sigma delta modulation, Chaos Interdiscip. J. Nonlinear Sci., vol. 11, no. 2, pp. 377–383, Jun. 2001.
• Hussain I. and Gondal M. A. An extended image encryption using chaotic coupled map and S-box transformation, Nonlinear Dyn., vol. 76, no. 2, pp. 1355–1363, Jan. 2014.
• Lynnyk V., Sakamoto N., and Čelikovský S. Pseudo random number generator based on the generalized Lorenz chaotic system, IFAC-Pap., vol. 48, no. 18, pp. 257–261, 2015.
• Park M., Rodgers J. C., and Lathrop D. P. True random number generation using CMOS Boolean chaotic oscillator, Microelectron. J., vol. 46, no. 12, Part A, pp. 1364–1370, Dec. 2015.
• Cicek I., Pusane A. E., and Dundar G. A novel design method for discrete time chaos based true random number generators, Integr. VLSI J., vol. 47, no. 1, pp. 38–47, Jan. 2014.
• Kocarev L. and Lian S. Chaos-based cryptography theory, algorithms and applications. Berlin: Springer, 2011.
• Martínez-González R. F., Díaz-Méndez J. A., Palacios-Luengas L., López-Hernández J., and Vázquez-Medina R. A steganographic method using Bernoulli’s chaotic maps, Comput. Electr. Eng., 2016.
• Ranasinghe D. C., Lim D., Devadas S., Abbott D., and Cole P. H. Random numbers from metastability and thermal noise, Electron. Lett., vol. 41, no. 16, pp. 13–14, Aug. 2005.
• Walker J. HotBits: Genuine Random Numbers, 2016. [Online]. Available: https://www.fourmilab.ch/hotbits/.
• Kroese D. P., Taimre T., and Botev Z. I. Handbook of Monte Carlo Methods, 1 edition. Hoboken, N.J: Wiley, 2011.
• Öztürk I. and Kılıç R. A novel method for producing pseudo random numbers from differential equation-based chaotic systems, Nonlinear Dyn., vol. 80, no. 3, pp. 1147–1157, Feb. 2015.
• Romero N., Silva J., and Vivas R. On a coupled logistic map with large strength, J. Math. Anal. Appl., vol. 415, no. 1, pp. 346–357, Jul. 2014.
• Wang X. and Bao X. A novel block cryptosystem based on the coupled chaotic map lattice, Nonlinear Dyn., vol. 72, no. 4, pp. 707–715, Jan. 2013.
• Alvarez G. and Li S. Some Basic Cryptographic Requirements for Chaos-Based Cryptosystems, Int J Bifurc Chaos Appl Sci Eng, vol. 16, no. 8, p. 2129, 2006.
• Strogatz S. H. Nonlinear Dynamics and Chaos: With Applications to Physics, Biology, Chemistry, and Engineering, Second Edition, Second Edition edition. Boulder, CO: Westview Press, 2014.
• Sprott J. C. Chaos and Time-Series Analysis, 1 edition. Oxford ; New York: Oxford University Press, 2001.
• Ablay G. Chaotic map construction from common nonlinearities and microcontroller implementations, Int. J. Bifurc. Chaos, vol. 26, no. 7, p. 1650121, 2016.
• Ablay G. Novel chaotic delay systems and electronic circuit solutions, Nonlinear Dyn., vol. 81, no. 4, pp. 1795–1804, May 2015.
• Ablay G. Chaos in PID Controlled Nonlinear Systems, J. Electr. Eng. Technol., vol. 10, no. 4, pp. 1843–1850, 2015.
• Simpson D. J. W. On the relative coexistence of fixed points and period-two solutions near border-collision bifurcations, Appl. Math. Lett., vol. 38, pp. 162–167, Dec. 2014.
• Mansingka A. S., Affan Zidan M., Barakat M. L., Radwan A. G., and Salama K. N. Fully digital jerk-based chaotic oscillators for high throughput pseudo-random number generators up to 8.77 Gbits/s, Microelectron. J., vol. 44, no. 9, pp. 744–752, Sep. 2013.
• Marsaglia G. Random Number Generators, J. Mod. Appl. Stat. Methods, vol. 2, no. 1, May 2003.
• Menezes A. J., van Oorschot P. C., and Vanstone S. A. Handbook of Applied Cryptography. CRC Press, 1996.
• Naccache D. Cryptography and Security: From Theory to Applications: Essays Dedicated to Jean-Jacques Quisquater on the Occasion of His 65th Birthday. Springer, 2012.