Yıl 2019,
Cilt: 1 Sayı: 1, 1 - 18, 30.11.2019
Akif Akgül
,
Coşkun Arslan
,
Burak Arıcıoğlu
Kaynakça
- [1] Pehlivan, I., (2007). New Chaotic Systems: Electronic Circuit Realizations, Synchronization and Secure Communication Applications. (Ph.D. Thesis), Sakarya University, Sakarya,Turkey.
- [2] Kahyaolu, M. B., and S. (2015). The Analysis Of Individual Investor Behaviour within the Frame of Chaos Theory. The Journal of Business Science, 3(1), 38-51.
- [3] Arslan, C., Pehlivan, ., Varan, M., and Akgl, A. (2017, September). Simulation and Analog Circuit Implementation FitzHugh-Nagumo (FHN). In 5th International Symposium on Innovative Technologies in Engineering and Science 29-30 September 2017 (ISITES2017 Baku- Azerbaijan).
- [4] Yardm, F. E., and Afacan, E. (2010). Simulation of a Communication System Using Lorenz- Based Differential Chaos Shift Keying (DCSK) Model. Journal of the Faculty of Engineering and Architecture of Gazi University, 25(1).
- [5] Wang, Y., Liu, Z., Ma, J., and He, H. (2016). A pseudorandom number generator based on piecewise logistic map. Nonlinear Dynamics, 83(4), 2373-2391.
- [6] Cicek, I., Pusane, A. E., and Dundar, G. (2014). A novel design method for discrete time chaos based true random number generators. INTEGRATION, the VLSI journal, 47(1), 38-47.
- [7] Patidar, V., Sud, K. K., and Pareek, N. K. (2009). A pseudo random bit generator based on chaotic logistic map and its statistical testing. Informatica, 33(4).
- [8] avuolu, ., Kaar, S., Pehlivan, I., and Zengin, A. (2017). Secure image encryption algorithm design using a novel chaos based S-Box. Chaos, Solitons and Fractals, 95, 92-101.
- [9] Kaar, S. (2016). Analog circuit and microcontroller based RNG application of a new easy realizable 4D chaotic system. Optik, 127(20), 9551-9561.
- [10] Akgul, A., Calgan, H., Koyuncu, I., Pehlivan, I., and Istanbullu, A. (2016). Chaos-based engineering applications with a 3D chaotic system without equilibrium points. Nonlinear dynamics, 84(2), 481-495.
- [11] Rajagopal, K., Akgul, A., Jafari, S., Karthikeyan, A., avuolu, ., and Kacar, S. (2019). An Exponential Jerk System: Circuit Realization, Fractional Order and Time Delayed Form with Dynamical Analysis and Its Engineering Application. Journal of Circuits, Systems and Computers, 28(05), 1950087.
- [12] Rajagopal, K., Jafari, S., Kacar, S., Karthikeyan, A., and Akgl, A. (2019). Fractional Order Simple Chaotic Oscillator with Saturable Reactors and Its Engineering Applications. Information Technology and Control, 48(1), 115-128.
- [13] Rajagopal, K., Akgul, A., Jafari, S., Karthikeyan, A., Cavusoglu, U., and Kacar, S. (2019). An exponential jerk system, its fractional-order form with dynamical analysis and engineering application. Soft Computing, 1-11.
- [14] Hu, Y., Liao, X., Wong, K. W., and Zhou, Q. (2009). A true random number generator based on mouse movement and chaotic cryptography. Chaos, Solitons and Fractals, 40(5), 2286-2293.
- [15] Karakaya, B., Glten, A., and Frasca, M. (2019). A true random bit generator based on a memristive chaotic circuit: Analysis, design and FPGA implementation. Chaos, Solitons and Fractals, 119, 143-149.
- [16] Pareschi, F., Setti, G., and Rovatti, R. (2006, September). A fast chaos-based true random number generator for cryptographic applications. In 2006 Proceedings of the 32nd European Solid-State Circuits Conference (pp. 130-133). IEEE.
- [17] Alcin, M., Koyuncu, I., Tuna, M., Varan, M., and Pehlivan, I. (2019). A novel high speed Artificial Neural Networkbased chaotic True Random Number Generator on Field Programmable Gate Array. International Journal of Circuit Theory and Applications, 47(3), 365-378.
- [18] Lorenz, E. N. (1963). Deterministic nonperiodic flow. Journal of the atmospheric sciences,20(2), 130-141.
- [19] Rossler, O. E. (1976). An equation for continuous chaos. Physics Letters A, 57(5), 397-398.
- [20] Cartwbight, M. L. (1960). Balthazar van der Pol. Journal of the London Mathematical Society, 1(3), 367-376.
- [21] Chen, G., and Ueta, T. (1999). Yet another chaotic attractor. International Journal of Bifur- cation and chaos, 9(07), 1465-1466.
- [22] Sprott, J. C., and Chlouverakis, K. E. (2007). Labyrinth chaos. International Journal of Bifurcation and Chaos, 17(06), 2097-2108.
- [23] Rucklidge, A. M. (1992). Chaos in models of double convection. Journal of Fluid Mechanics, 237, 209-229.
- [24] Rikitake, T. (1958, January). Oscillations of a system of disk dynamos. In Mathematical Proceedings of the Cambridge Philosophical Society (Vol. 54, No. 1, pp. 89-105). Cambridge University Press.
- [25] Ito, K. (1980). Chaos in the Rikitake two-disc dynamo system. Earth and Planetary Science Letters, 51(2), 451-456.
- [26] Pehlivan, I, and Uyaroglu, Y. (2007). Rikitake attractor and its synchronization application for secure communication systems. Journal of Applied Sciences, 7(2), 232-236.
- [27] Pehlivan, I, and Uyarolu, Y. (2012). A new 3D chaotic system with golden proportion equilibria: Analysis and electronic circuit realization. Computers and Electrical Engineering, 38(6),1777-1784.
- [28] Kilbas, A. A., Srivastava, H. M., and Trujillo, J. J. (2006). Theory and applications of fractional differential equations. North-Holland mathematics studies.
- [29] Mathai, A. M., Saxena, R. K., and Haubold, H. J. (2009). The H-function: theory and applications. Springer Science and Business Media.
- [30] Korkmaz, M. (2013). Fractional Order PID Controllers, Design, Application and Comparison(M.Sc. Thesis, Seluk University, Konya, Turkey).
- [31] Petr, I. (2011). Fractional-order nonlinear systems: modeling, analysis and simulation.Springer Science and Business Media.
- [32] Walker, J. (2008). ENT: a pseudorandom number sequence test program. Software and documentation available at/www. fourmilab. ch/random/S.
Design of an Interface for Random Number Generators based on Integer and Fractional Order Chaotic Systems
Yıl 2019,
Cilt: 1 Sayı: 1, 1 - 18, 30.11.2019
Akif Akgül
,
Coşkun Arslan
,
Burak Arıcıoğlu
Öz
Chaos is one of the most topical subjects in the literature and is applied to various number of different fields such as system identification, optimization, brain functions identification, secure communication, encryption and random number generation. In this work, a user interface is designed for generation of random numbers based on fractional and integer order chaotic systems. In order to evaluate the randomness of the generated numbers NIST- 800-22 and ENT statistical tests are performed. The design interface provides the users a wide range of options. Moreover, the interface is also implemented on a microcomputer that the generated random number can be used in mobile applications. In this way, random numbers that have great importance on applications such as cryptographic and secure communication systems, statistical samplings, computer simulations and designs based on randomness are generated with different ways.
Kaynakça
- [1] Pehlivan, I., (2007). New Chaotic Systems: Electronic Circuit Realizations, Synchronization and Secure Communication Applications. (Ph.D. Thesis), Sakarya University, Sakarya,Turkey.
- [2] Kahyaolu, M. B., and S. (2015). The Analysis Of Individual Investor Behaviour within the Frame of Chaos Theory. The Journal of Business Science, 3(1), 38-51.
- [3] Arslan, C., Pehlivan, ., Varan, M., and Akgl, A. (2017, September). Simulation and Analog Circuit Implementation FitzHugh-Nagumo (FHN). In 5th International Symposium on Innovative Technologies in Engineering and Science 29-30 September 2017 (ISITES2017 Baku- Azerbaijan).
- [4] Yardm, F. E., and Afacan, E. (2010). Simulation of a Communication System Using Lorenz- Based Differential Chaos Shift Keying (DCSK) Model. Journal of the Faculty of Engineering and Architecture of Gazi University, 25(1).
- [5] Wang, Y., Liu, Z., Ma, J., and He, H. (2016). A pseudorandom number generator based on piecewise logistic map. Nonlinear Dynamics, 83(4), 2373-2391.
- [6] Cicek, I., Pusane, A. E., and Dundar, G. (2014). A novel design method for discrete time chaos based true random number generators. INTEGRATION, the VLSI journal, 47(1), 38-47.
- [7] Patidar, V., Sud, K. K., and Pareek, N. K. (2009). A pseudo random bit generator based on chaotic logistic map and its statistical testing. Informatica, 33(4).
- [8] avuolu, ., Kaar, S., Pehlivan, I., and Zengin, A. (2017). Secure image encryption algorithm design using a novel chaos based S-Box. Chaos, Solitons and Fractals, 95, 92-101.
- [9] Kaar, S. (2016). Analog circuit and microcontroller based RNG application of a new easy realizable 4D chaotic system. Optik, 127(20), 9551-9561.
- [10] Akgul, A., Calgan, H., Koyuncu, I., Pehlivan, I., and Istanbullu, A. (2016). Chaos-based engineering applications with a 3D chaotic system without equilibrium points. Nonlinear dynamics, 84(2), 481-495.
- [11] Rajagopal, K., Akgul, A., Jafari, S., Karthikeyan, A., avuolu, ., and Kacar, S. (2019). An Exponential Jerk System: Circuit Realization, Fractional Order and Time Delayed Form with Dynamical Analysis and Its Engineering Application. Journal of Circuits, Systems and Computers, 28(05), 1950087.
- [12] Rajagopal, K., Jafari, S., Kacar, S., Karthikeyan, A., and Akgl, A. (2019). Fractional Order Simple Chaotic Oscillator with Saturable Reactors and Its Engineering Applications. Information Technology and Control, 48(1), 115-128.
- [13] Rajagopal, K., Akgul, A., Jafari, S., Karthikeyan, A., Cavusoglu, U., and Kacar, S. (2019). An exponential jerk system, its fractional-order form with dynamical analysis and engineering application. Soft Computing, 1-11.
- [14] Hu, Y., Liao, X., Wong, K. W., and Zhou, Q. (2009). A true random number generator based on mouse movement and chaotic cryptography. Chaos, Solitons and Fractals, 40(5), 2286-2293.
- [15] Karakaya, B., Glten, A., and Frasca, M. (2019). A true random bit generator based on a memristive chaotic circuit: Analysis, design and FPGA implementation. Chaos, Solitons and Fractals, 119, 143-149.
- [16] Pareschi, F., Setti, G., and Rovatti, R. (2006, September). A fast chaos-based true random number generator for cryptographic applications. In 2006 Proceedings of the 32nd European Solid-State Circuits Conference (pp. 130-133). IEEE.
- [17] Alcin, M., Koyuncu, I., Tuna, M., Varan, M., and Pehlivan, I. (2019). A novel high speed Artificial Neural Networkbased chaotic True Random Number Generator on Field Programmable Gate Array. International Journal of Circuit Theory and Applications, 47(3), 365-378.
- [18] Lorenz, E. N. (1963). Deterministic nonperiodic flow. Journal of the atmospheric sciences,20(2), 130-141.
- [19] Rossler, O. E. (1976). An equation for continuous chaos. Physics Letters A, 57(5), 397-398.
- [20] Cartwbight, M. L. (1960). Balthazar van der Pol. Journal of the London Mathematical Society, 1(3), 367-376.
- [21] Chen, G., and Ueta, T. (1999). Yet another chaotic attractor. International Journal of Bifur- cation and chaos, 9(07), 1465-1466.
- [22] Sprott, J. C., and Chlouverakis, K. E. (2007). Labyrinth chaos. International Journal of Bifurcation and Chaos, 17(06), 2097-2108.
- [23] Rucklidge, A. M. (1992). Chaos in models of double convection. Journal of Fluid Mechanics, 237, 209-229.
- [24] Rikitake, T. (1958, January). Oscillations of a system of disk dynamos. In Mathematical Proceedings of the Cambridge Philosophical Society (Vol. 54, No. 1, pp. 89-105). Cambridge University Press.
- [25] Ito, K. (1980). Chaos in the Rikitake two-disc dynamo system. Earth and Planetary Science Letters, 51(2), 451-456.
- [26] Pehlivan, I, and Uyaroglu, Y. (2007). Rikitake attractor and its synchronization application for secure communication systems. Journal of Applied Sciences, 7(2), 232-236.
- [27] Pehlivan, I, and Uyarolu, Y. (2012). A new 3D chaotic system with golden proportion equilibria: Analysis and electronic circuit realization. Computers and Electrical Engineering, 38(6),1777-1784.
- [28] Kilbas, A. A., Srivastava, H. M., and Trujillo, J. J. (2006). Theory and applications of fractional differential equations. North-Holland mathematics studies.
- [29] Mathai, A. M., Saxena, R. K., and Haubold, H. J. (2009). The H-function: theory and applications. Springer Science and Business Media.
- [30] Korkmaz, M. (2013). Fractional Order PID Controllers, Design, Application and Comparison(M.Sc. Thesis, Seluk University, Konya, Turkey).
- [31] Petr, I. (2011). Fractional-order nonlinear systems: modeling, analysis and simulation.Springer Science and Business Media.
- [32] Walker, J. (2008). ENT: a pseudorandom number sequence test program. Software and documentation available at/www. fourmilab. ch/random/S.