Kaotik sistemler ve FPGA tabanlı kaotik osilatörlerin gerçek rasgele sayı üretimindeki (GRSÜ) önemi üzerine bir araştırma

Yıl 2018, , 473 - 492, 06.04.2018

Murat Tuna , Can Bülent Fidan

https://doi.org/10.17341/gazimmfd.416355

Cited By: 3

Öz

Rasgele sayı üreteçleri kriptografi, Monte-Carlo metodunun kullanıldığı uygulamalar, bilgisayar benzetimleri ve modellemeleri ile sayısal analiz uygulamaları gibi birçok alanda kullanılmaktadır. Hızlı, güvenli ve yoğun işlem gerektiren kriptografi ve güvenli haberleşme alanlarında kullanılan GRSÜ’ lerde entropi kaynağı olarak deterministik karaktere sahip olmayan fiziksel yöntemler kullanılmaktadır. Bu yöntemler doğrudan kuvvetlendirme, çift osilatör ve kaos tabanlı uygulamalardır. Kaotik osilatörlerin gürültü benzeri özellikler taşımaları ve bilgi işaretini gizleyebilme gibi özelliklerinden dolayı kaos tabanlı GRSÜ yapıların geliştirilmesi üzerine son yıllarda büyük çabalar sarf edilmektedir. Sayısal devre üzerinde (DSPs, ASIC, FPGA) kaos tabanlı GRSÜ’ leri geleneksel kaos tabanlı analog yapılarına göre etkili bir alternatiftir. Çünkü analog kaotik işaret üreteci kullanan GRSÜ sistemlerinde verici ile alıcının çok iyi şekilde senkronize edilmesi zordur. Bunların devre gerçeklemelerinde ısıl veya saçılma gürültüsü gibi fiziksel gürültü üreten zayıf kaynaklar kullanılmaktadır.
Sayısal tabanlı FPGA çipleri yüksek performans ve işlemci gücü gerektiren kriptoloji ve güvenli haberleşme gibi uygulamalarda bilgi güvenliği kapasitesini iyileştirmede önemli bir potansiyele sahiptir. Bu çalışmada son yıllarda tasarlanan kaotik sistemler ile FPGA üzerinde tasarlanan kaos tabanlı GRSÜ’ lerinin detaylı bir araştırılması ve geleneksel yöntemlerle performans karşılaştırılmaları yapılmıştır.

Anahtar Kelimeler

Kaos ve kaotik sistemler, RSÜ; GRSÜ; FPGA; VHDL.

Kaynakça

• Yılmaz D., Güler N.F., Kaotik zaman serisinin analizi üzerine bir araştırma, Journal of the Faculty of Engineering and Architecture of Gazi University, 21 (4), 759-779, 2006.
• Banerjee S., Kurths J., Chaos and Cryptography: A new dimension in secure communications, The European Physical Journal Special Topics, 223 (8), 1441-1445, 2014.
• Jin L., Mei J., Li L., Chaos control of parametric driven Duffing oscillators, Appl. Phys. Lett., 104 (13), 1011-1015, 2014.
• Hoang T.M., Tran D., Cryptanalysis and security improvement for selective image encryption, The European Physical Journal Special Topics, 223 (8), 1635-1646, 2014.
• Akgul A., Calgan H., Koyuncu İ., Pehlivan İ., Istanbullu A., Chaos-based engineering applications with a 3D chaotic system without equilibrium points, Nonlinear Dyn., 84, 841-495, 2016.
• Xiong A., Zhao X., Han J., Liu G., Application of the chaos theory in the analysis of EMG on patients with facial paralysis, Robot Intelligence Techlogy and Applications, 2 ( 274), 805-819, 2014.
• Zhengxing H., Wei D., Huilong D., Haomin L., Similarity measure between patient traces for clinical pathway analysis: problem, method, and applications, IEEE J. Biomed. Health. Inf., 18 (1), 4−14, 2014.
• Zexin K., Jiang S., Lin M., Yanhui Q., Shuisheng J., Multimode synchronization of chaotic semiconductor ring laser and its potential in chaos communication, IEEE J. Quantum Electron., 50 (3), 148-157, 2014.
• Barakat M.L., Mansingka A.S., Radwan A.G., Salama K.N., Hardware stream cipher with controllable chaos generator for colour image encryption, IET Image Proc., 8 (1), 33-43, 2014.
• Anees A., Siddiqui A.M., Ahmed F., Chaotic substitution for highly auto correlated data in encryption algorithm, Commun. Nonlinear Sci. Numer. Simul., 19 (9), 3106-3118, 2014.
• Ji Y., Zhang M., Wang Y., Wu Y., Zhang Y., Microwave-photonic sensor for remote water-level monitoring based on chaotic laser, Int. J. Bifurcation Chaos, 24 (3), 321-327, 2014.
• Zheng G.W., Peng S., Hongye S., Jian C., Sampled-data fuzzy control of chaotic systems based on a T–S fuzzy model, IEEE Transaction on Fuzzy Systems, 22 (1), 153-163, 2014.
• Yu S.H., Kang H.S., Kim Y.T., Hyun C.H., Park M., Fuzzy adaptive modular design of uncertain chaotic duffing oscillators, International Journal of Control Automation and Systems, 12 (1), 188-194, 2014.
• Deivasundari P., Uma G., Ashita S., Chaotic dynamics of a zero average dynamics controlled DC-DC Cuk converter, IET Power Electron., 7 (2), 289-298, 2014.
• Wan L., Luo X.S., Zeng S.Y., Zhang B., Global exponential stabilization for chaotic brushless DC motors with a single input, Nonlinear Dyn., 77, 209-212, 2014.
• Pomares J., Perea I., Torres F., Dynamic visual servoing with chaos control for redundant robots, IEEE/ASME Trans. Mechatron., 19 (2), 423-431, 2014.
• Jakimoski G., Kocarev L., Chaos and Cryptography: Block Encryption Ciphers Based on Chaotic Maps, IEEE Trans. Circuits Syst. I: Fundamental Theory and Applications, 48 (2), 163-169, 2001.
• Çavuşoğlu Ü., Akgül A., Kaçar S., Pehlivan İ., Zengin A., A novel chaos-based encryption algorithm over TCP data packet for secure communication, Security Comm. Networks, 9 (22), 1285-1296, 2016.
• Keyman E., Yıldırım M., Kriptolojiye Giriş Ders notları, Uygulamalı Matematik Enstitüsü, Kriptorafi Bölümü-ODTÜ, Türkiye, 2004.
• Lawande Q.V., Ivan B.R., and Dhodapkar S.D., Chaos Based Cryptography: A New Approach To Secure Communications, Barc Newsletter, 258, 2005.
• Çavuşoğlu Ü., Zengin A., Pehlivan İ., Kaçar S., A novel approach for strong S-Box generation algorithm design based on chaotic scaled Zhongtang system, Nonlinear Dyn., 87, 1081-1094, 2017.
• Avaroğlu E., Pseudorandom number generator based on Arnold cat map and statistical analysis, Turkish Journal of Electrical Engineering & Computer Sciences, 25, 633-643, 2017.
• Çavuşoğlu Ü., Kaçar S., Pehlivan İ., Zengin A., Secure image encryption algorithm design using a novel chaos based S-Box, Chaos, Solitons Fractals, 95 (2017), 92-101, 2017.
• Ferguson N., Schneier B., Kohno T., Generating Randomness, Cryptography Engineering: Design Principles and Practical Applications, Wiley Publishing, Indianapolis, 137-141, 2010.
• Zhong Z., Guanrong C., Simin Y., Hyperchaotic signal generation via DSP for efficient perturbations to liquid mixing, Int. J. Circuit Theory Appl., 37, 31-41, 2009.
• Kharel R., Busawon K., Aggoune W., Ghassemloy Z., Implementation of a secure digital chaotic communication scheme on a DSP board, 7th International Symposium on Communication Systems Networks and Digital Signal Process, Newcastle-England, 212-216, 21-23 July, 2010.
• Delgado R.M., Acosta A.J., Rodriguez V.A., A mixed-signal integrated circuit for FM-DCSK modulation, IEEE J. Solid-State Circuits, 40 (7), 1460-1471, 2005.
• Te S., Guosheng R., Yang Z., Song Z., Design method for Duffing system based on DSP builder, IEEE International Conference on Industrial and Information Systems, Yantai-China, 121-124, 06-09 August, 2012.
• Güler U., Ergün S., A high speed fully digital IC random number generator, AEU Int. J. Electron. Commun., 66, 143-149 2012.
• Yiwei Z., Zexiang L., Xinjian Z., A chaos-based image encryption ASIC using reconfigurable logic, IEEE Asia Pacific Conference on Circuits and Systems, Macao-China, 1782-1785, 30-3 December, 2008.
• Kohlbrenner P., Gaj K., An Embedded True Random Number Generator for FPGAs, SIGDA 12th international symposium on Field programmable gate arrays, New York-USA, 71-78, 22-24 February, 2004.
• Koyuncu İ., Design and Implementation of High Speed Artificial Neural Network Based Sprott 94-S System on FPGA, International Journal of Intelligent Systems and Applications in Engineering, 4 (2), 33-39, 2016.
• Xiang F., Chen X., A Method to Generate Chaotic Attractors Based on FPGA, Applied Mechanics and Materials, 66 (68), 1301-1304, 2011.
• Koyuncu İ., Özcerit A.T., Pehlivan İ., FPGA-Based A Chaotic Oscillator Design and Implementation, Nonlinear Dyn, 77 (2), 49-59, 2014.
• Alçın M., Pehlivan İ., Koyuncu İ., Hardware design and implementation of a novel ANN-based chaotic generator in FPGA, Optik, 127 (2016), 5500-5505, 2016.
• Tuna M., Koyuncu İ., Fidan C.B., Pehlivan İ., Real Time İmplementation of a novel Chaotic Generator on FPGA, IEEE Sinyal İşleme ve İletişim Uygulamaları Kurultayı, Malatya-Türkiye, 604-607, 16-19 Mayıs, 2015.
• Koyuncu I., Özcerit A.T., Pehlivan I., Implementation of FPGA-based real time novel chaotic oscillator, Nonlinear Dyn., 75 (2), 49-59, 2014.
• Azzaz M.S., Taugast C., Sadoudi S., Fellah R., Dandache A., A new auto-switched chaotic system and its FPGA implementation, Commun. Nonlinear Sci. Numer. Simul., 18 (7), 1792-1804, 2013.
• Merah L., Pascha A., Said A., Mamat N.H., Design and FPGA implementation of Lorenz chaotic system for information security issues, Application Mathematics Sciences, 7 (5), 237-246, 2013.
• Koyuncu İ., Özcerit A.T., Pehlivan İ., An analog circuit design and FPGA-based implementation of the Burke-Shaw chaotic system, Optoelectron. Adv. Mater. Rapid Commun., 7, 635-638, 2013.
• De micco L., Larrondo H.A., FPGA implementation of a chaotic oscillator using RK4 method, IEEE VII Southern Conferences on Programmable Logic, Cordoba-Spain, 185-190, 13-15 April, 2011.
• Sadoudi S., Mohamed S.A., Mustapha D., Mustapha B., An FPGA real-time implementation of the Chen’s chaotic system for securing chaotic communications, International Journal of nonlinear Science, 7 (4), 467-474, 2009.
• Eroğlu C., Implementation of synchronized chaotic systems by FPGA, Master Tezi, İzmir Yüksek Teknoloji Enstitüsü, İzmir, 2007.
• Tlelo-Cuautle E., Pa-Azucena A.D., Rangel-Magdale J.J., Carbajal-Gomez V.H., Rodriguez-Gomez G., Generating a 50-scroll chaotic attractor at 66MHz by using FPGAs, Nonlinear Dyn, 85 (4), 1-15, 2016.
• Xingyuan W., Xue Q., Lin T., A novel True Random Number Generator Based on Mouse Movement and a One-Dimensional Chaotic Map, Mathematical Problems in Engineering, 2012, 1-9, 2012.
• Stipčević M., Quantum random number generators and their use in cryptography, IEEE 34th International Convention of Proceedings, Opatija-Croatia, 1474-1479, 23-27 May, 2011.
• Danger J.L., Guilley S., Hoogvorst P., High speed true random number generator based on open loop structures in FPGAs, Microelectron. J., 40 (11), 1650-1656, 2009.
• Zidan M.A., Radwan A.G., Salama K.N., Random number generation based on digital differential chaos, IEEE 54th International Midwest Symposium on Circuits and Systems, Seoul-South Korea, 1-4, 7-10 August, 2011.
• Tavas V., Demirkol A.S., Ozoguz S., Kilinc S., Toker A., Zeki A., An IC Random Number Generator Based on Chaos, International Conference on Applied Electronics, Pilsen-Czech Republic, 1-4, 8-9 September, 2010.
• Jessa M., Jaworski M., Randomness of a Combined TRNG Based on the Ring Oscillator Sampling Method, The İnternational Conference on Signals and Electronic Systems, Poznan-Poland, 323-326, 7-10 September 2010.
• Wold K., Petrovic S., Optimizing Speed of a True Random Number Generator in FPGA by Spectral Analysis, IEEE Fourth International Conference on Computer Sciences and Convergence Information Techlogy, Seoul-South Korea, 1105-1110, 24-26 September, 2009.
• Istvan H., Suciu A., Cret O., FPGA based TRNG using automatic calibration, IEEE 5th Conferences on Intelligent Computer Communication and Processing, Cluj-Napoca, 373-376, 27-29 August, 2009.
• Stojavski T., Kocarev L., Chaos-Based Random Number Generators-Part I: Analysis, IEEE Trans. Circuits Syst. I Regul. Pap., 48 (3), 281-288, 2001.
• Stojavski T., Pihl J., Kocarev L., Chaos-Based Random Number Generators-Part II: Practical Realization, IEEE Trans. Circuits Syst. I Regul. Pap., 48 (3), 382-385, 2001.
• Ergun S., Özoğuz S., A Chaos-Modulated Dual Oscillator-Based Truly Random Number Generator, IEEE International Symposium on Circuits and Systems, New Orleans-USA, 2482-2485, 27-30 May, 2007.
• Alligood K.T., Sauer T.D., Yorke J.A., Crawford J.D., Chaos: An introduction to dynamical systems, Phys. Today, 50 (11), 67-68, 2008.
• Pehlivan İ., Uyaroğlu Y., Chaotic Circuit Design and Analyze of A New Chaotic Attractor, 6th International Advanced Techlogy Symposium, Elazığ-Turkey, 351-355, 16-18 Mayıs, 2011.
• Yardım F.E., Afacan E., Lorenz-Tabanlı Diferansiyel Kaos Kaydırmalı Anahtarlama (DCSK) Modeli Kullanılarak Kaotik Bir Haberleşme Sisteminin Simülasyonu, Journal of the Faculty of Engineering and Architecture of Gazi University, 25 (1), 101-110, 2010.
• Piper J.R., Sprott J.C., Simple Automous Chaotic Circuits, IEEE Trans. Circuits Syst. II Express Briefs, 57 (9), 730-734, 2010.
• Sprott J.C., Simple chaotic systems and circuits, American Journal Physics, 68 (8), 758-763, 2000.
• Çavuşoğlu Ü., Uyaroğlu Y., Pehlivan İ., Sürekli Zamanlı otonom Kaotik devre Tasarımı ve sinyal gizleme uygulaması, Journal of the Faculty of Engineering and Architecture of Gazi University, 29 (1), 79-87, 2014.
• Holmes P.J., Poincare celestial mechanics, dynamical-systems theory and chaos, Phys. Rep., 193 (3), 138-163, 1990.
• Lorenz E.N., Deterministic non-periodical flow, Journal Atmospheric Sciences, 20, 130-141, 1963.
• Li T., Yorke J., Period three implies chaos, American Mathematical Monthly, 82, 985-992, 1975.
• Rössler O.E., An equation for continuous chaos, Physics Letters, 57 (5), 397−398, 1976.
• Matsumoto T., Chua L.O., Tanama S., Simplest chaotic automous circuit, Physical Review, 30, 1155−1157, 1984.
• Matsumoto T., A chaotic attractor from Chua’s circuit, IEEE Trans. Circuits Syst., 31 (12), 1055–1058, 1984.
• Merah L., Pacha A.A., Said N.H., Mamat M., A Pseudo Random Number Generator Based on the Chaotic System of Chua’s Circuit and its Real Time FPGA Implementation, Applied Mathematical Sciences, 7 (55), 2719-2734, 2013.
• Yamaçlı V., Abacı K., Köse E., Chua Devresinin Gerçeklenmesi ve Simülasyonu, 6th International Advanced Techlogies Symposium, Elazığ-Türkiye, 82-86, 16-18 Mayıs, 2011.
• Jesus M., Simulation of Chua‘s Circuit by Automatic Control of Step-Size, Appl. Math. Comput., 190, 1526-1533, 2007.
• Razminia A., Sadrnia M.A., Chua’s Circuit Regulation Using a nonlinear Adaptive Feedback Technique, International Journal of Electrical, Robotics, Electronics and Communications Engineering, l (10), 1508-1512, 2007.
• Kiliç R., Autonomous Chua’s Circuit: Classical and New Design Aspects, A Practical Guide For Studying Chua's Circuits, World Scientific Publishing Nonlinear Science, Singapore, USA, 1-6, 2010.
• MuraliI K., Lakshmanan M., Chua L.O., Controlling and Synchronization of Chaos in The Simplest Dissipative n-automous Circuit, Int. J. Bifurcation Chaos, 5, 563-571, 1995.
• Ameer L.F.A., Implementation of Digital Chaotic Signal Generator Based on Reconfigurable LFSRs for Multiple Access Communications, Aust. J. Basic Appl. Sci., 4 (7), 1691-1698, 2010.
• Milani M.M.R.A, Pehlivan H., Pour S.H., Kaos Tabanlı Bir Şifreleme Yöntemi ve Analizi, XIII. Akademik Bilişim Konferansı Bildirileri, Malatya-Türkiye, 487-493, 2-4 Şubat, 2011.
• Cicek I., Pusane A.E., Dundar G., Random number generation using field programmable analog array implementation of logistic map, 21st Signal Processing and Communications Applications Conference (SIU), Girne-Cyprus, 1-4, 24-26 April, 2013.
• Juncu V.D., Rafiei-Naeini M., Dudek P., Integrated Circuit Implementation of a Compact Discrete-Time Chaos Generator, Journal Analog Integrated Circuits and Signal Processing, 46 (3), 275-280, 2006.
• Özdemir, K., Sürekli-Zamanli Kaos ile Rastgele Sayi Üreteci Tasarımı, Yüksek Lisans Tezi, İstanbul Teknik Üniversitesi, Fen Bilimleri Enstitüsü, 2008.
• Lakshmanan M., MuraIi K., Chaos in nonlinear Oscillators, Control and Synchronization, World Scientific, 1996.
• Chua L., Wu W., Huang A., Zhong G., A Universal Circuit for Studying and Generating Chaos-Part I: Routes to Chaos, IEEE Trans. Circuits Syst. I Regul. Pap., 40, 732-744, 1993.
• Akgul A., Hussain S., Pehlivan İ., A new three-dimensional chaotic system, its dynamical analysis and electronic circuit applications, Optik, 127 (2016), 7062-7071, 2016.
• Li J., Liu F., Guan Z.H., Li T., A new chaotic Hopfield neural network and its synthesis via parameter switching’s, Elsevier Neurocomputing, 11, 33-39, 2013.
• Akgul A., Pehlivan İ., A new three-dimensional chaotic system without equilibrium points, its dynamical analyses and electronic circuit application, Technical Gazette, 23 (1), 209–214, 2016.
• Pehlivan İ., Yeni Kaotik Sistemler: Elektronik Devre Gerçeklemeleri, Senkronizasyon ve Güvenli Haberleşme Uygulamaları, Doktora Tezi, Sakarya Üniversitesi, Fen Bilimleri Enstitüsü, 2007.
• Liu C., A novel chaotic attractor, Chaos, Solitons Fractals, 39, 1037-1045, 2009.
• Zhou P., Huang K., A new 4-D n-equilibrium fractional-order chaotic system and its circuit implementation, Commun. Nonlinear Sci. Numer. Simul., 19 (2014), 2005-2011, 2014.
• Yu F., Wang C., A novel Three Dimension Automous Chaotic System with a Quadratic Exponential nonlinear Term, Engineering, Techlogy & Applied Science Research, 2 (2), 209-215, 2012.
• Ahmed I., Mu C., Zhang F., A New Chaotic Attractor with Quadratic Exponential nonlinear Term from Chen’s Attractor, International Journal of Analysis and Applications, 5 (1), 27-32, 2014.
• Kaçar S., Analog circuit and microcontroller based RNG application of a new easy realizable 4D chaotic system, Optik, 127 (2016), 9551-9561, 2016.
• Deng K., Li J., Yu S., Dynamics analysis and synchronization of a new chaotic attractor, Optics, 125 (13), 3071-3075, 2014.
• Leng J., Cao Y., Zhao K., Dynamics Analysis of Hyperchaotic Circuit, Applied Physics Frontier, 2 (2), 8-11, 2014.
• Akgul A., Moroz I., Pehlivan İ., Vaidyanathan S., A new four-scroll chaotic attractor and its engineering applications, Optik, 127 (2016), 5491-5499, 2016.
• Abooee A., Yaghini-Bonabi H.A., Jahed-Motlagh M.R., Analysis and circuitry realization of a novel three-dimensional chaotic system, Commun. Nonlinear Sci. Numer. Simul., 18, 1235-1245, 2013.
• Deng K., Yu S., Estimating ultimate bound and finding topological horseshoe for a new chaotic system, Optics, 125 (20), 1-5, 2014.
• Çiçek S., Ferikoğlu A., Pehlivan İ., A new 3D chaotic system: Dynamical analysis, electronic Circuit design, active control synchronization and chaotic masking communication application, Optik, 127 (2016), 4024-4030, 2016.
• Pehlivan İ., Uyaroğlu Y., A new 3D chaotic system with golden proportion equilibra: Analysis and electronic circuit realization, Comput. Electr. Eng., 38, 1777-1784, 2012.
• Ahadpour S., Sadra Y., Fard Z.A., A novel Chaotic Encryption Scheme based on Pseudorandom Bit Padding, International Journal of Computer Science Issues, 9 (1), 449-456, 2012.
• Kocarev L., Jakimoski G., Pseudorandom bits generated by chaotic maps, IEEE Circuits and Systems I: Fundamental Theory and Applications, 50 (1), 123-126, 2003.
• Cret O., Gyorfi T., Suciu A., Implementing True Random Number Generators Based on High Fault Nets, Romanian Journal Of Information Science And Techlogy, 15 (3), 277-298, 2012.
• Drutarovsky M., Simka M., A Simple PLL-Based True Random Number Generator for Embedded Digital Systems, Computing and Informatics, 23, 501-515, 2004.
• Yalcin M.E., Suykens J.A.K., Vandewalle J., True random bit generation from a double-scroll attractor, IEEE Trans. Circuits Syst. I Regul. Pap., 51 (7), 1395-1404, 2004.
• Cicek I., Pusane A.E., Dundar G., A novel design method for discrete time chaos based true random number generators, Integration the VLSI journal, 47 (1), 38–47, 2014.
• Avaroğlu E., Türk M., Son işlemin Gerçek Rasgele Sayı Üreteçleri Üzerindeki etkisinin İncelenmesi, 6. Uluslararası Bilgi Güvenliği ve Kriptoloji Konferansı, Ankara-Türkiye, 291-294, 20-21 Eylül, 2013.
• Özdemir K., Kılınç S., Özoğuz S., Sürekli-Zamanlı Kaos ile Rastgele Sayı Üreteci Tasarımı, IEEE 16th Signal Processing Communication and Applications Conference, Aydın-Türkiye, 1-4, 20-22 April, 2008.
• Zhun H., Hongyi C., A Truly Number Generator Based on Thermal, IEEE Asicon, Shanghai-Chine, 862-864, 23-25 October, 2001.
• Bucci M., Luzzi R., A Fully-Digital Chaos-Based Random Bit Generator, Lect. Notes Comput. Sci., 9100, 396-414, 2016.
• Demirkol A.Ş., Kaotik Osilatör Girişli ADC Tabanlı Rastgele Sayı Üreteci, Master Tezi, İstanbul Teknik Üniversitesi, Fen Bilimleri Enstitüsü, 2007.
• Tavas V., Tümleştirmeye Uygun Rastgele Sayı Üreteçleri, Doktora Tezi, İstanbul Teknik Üniversitesi, Fen Bilimleri Enstitüsü, 2011.
• Tavas V., Demirkol A.S., Ozoguz S., Zeki A., Toker A., Integrated cross-coupled chaos oscillator applied to random number generation, IET Circuits Devices Syst, 3 (1), 1-11, 2009.
• Demirkol A.Ş., Tavas V., Özoğuz S., Toker A., High frequency chaos oscillators with applications, IEEE 18th European Conference on Circuit Theory and Design, Seville-Spain, 1026-1029, 27-30 August, 2007.
• Koyuncu İ., Kriptolojik Uygulamalar için FPGA tabanlı Yeni Kaotik Osilatörlerin ve Gerçek Rasgele Sayı Üreteçlerinin Tasarımı ve Gerçeklenmesi, Doktora Tezi, Sakarya Üniversitesi, Fen Bilimleri Enstitüsü, 2014.
• Güven P., Otonom Olmayan Kaotik Sistemlerde Rasgele Sayı Üretiminin İncelenmesi, Master Tezi, İstanbul Teknik Üniversitesi, Fen Bilimleri Enstitüsü, 2006.
• Ergün S., Özoguz S., Truly random number generators based on an n-automous chaotic oscillator, AEU Int. J. Electron. Commun., 61, 235-242, 2007.
• Cicek I., Pusane A.E., Dundar G., A new dual entropy core true random number generator, Analog Integration Circuit Signal Process, 81 (1), 61-70, 2014.
• Ning L., Ding J., Chuang B., Xuecheng Z., Design and validation of high speed true random number Generators based on prime-length ring oscillators, The Journal of China Universities of Posts and Telecommunications, 22 (4), 1-6, 2015.
• Pareschi F., Setti G., Rovatti R., Implementation and testing of high-speed CMOS TRNGs sased on chaotic systems, IEEE Trans. Circuits Syst. I Regul. Pap., 57 (12), 3124−3137, 2010.
• Dhanuskodi S.N., Vijayakumar A., Kundu S., A Chaotic Ring Oscillator based Random Number Generator, IEEE International Symposium on Hardware-Oriented Security and Trust, Arlington-USA, 160-165, 6-7 May, 2014.
• Aguilar Angulo J.A., Kussener E., Barthelemy H., Duval B., Discrete Chaos Based Random Number Generator, IEEE Faible Tension Consommation, Novotel Monte-Carlo-Monaco, 1-4, 4-6 May 2014.
• Park M., Rodgers J.C., Lathrop D.P., True random Number generation using CMOS Boolean chaotic Oscillator, Microelectron. J., 46 (2015), 1364-1370, 2015.
• Schellekens D., Preneel B., Verbauwhede I., FPGA Vendor Agstic True Random Number Generator, International Conference on Field Programmable Logic and Applications, Madrid-Spain, 1-6, 28-30 August, 2006.
• Dichtl, M., Golic, J., “High-speed TRNG with logic gates only”, Lect. Notes Comput. Sci., 4727, 45-62, 2007.
• Fischer V., Drutavosky M., Simka M., Bochard N., High performance TRNG in Altera stratix FPLDs, Field Programmable Logic and Application, 3203, 555–564, 2004.
• Wıeczorek P.Z., Golofıt K., Dual-metastability time-competitive TRNG, IEEE Trans. Circuits Syst. I Regul. Pap., 61 (1), 134−145, 2014.
• Lozach F., Ben R.M., Graba T., Danger J.L., FPGA design of an open-loop TRNG, Euromicro Conferances on Digital Systems Design, Santander-Spain, 615-622, 4-6 September, 2013.
• Wold K., Tan C.H., Analysis and Enhancement of Random Number Generator in FPGA Based on Oscillator Rings, International Journal of Reconfigurable Computing, 2009, 1-8, 2009.
• Sunar B., Martin W.J., Stinson D.R., A Provably Secure True Random Number Generator with Built-In Tolerance to Active Attacks, IEEE Trans. Comput., 56 (1), 109-119, 2007.
• Tuncer T., Avaroğlu E., Türk M., Ozer A.B., Implementation of non-periodic Sampling True Random Number Generator on FPGA, Journal of Microelectronics, Electronic Components and Materials, 44 (4), 296-302, 2014.
• Avaroğlu E., Tuncer T., Özer A.B., Ergen B., Türk M., A Novel chaos-based post-processing for TRNG, Nonlinear Dyn., 81, 189-199, 2015.
• Avaroğlu E., Donanım Tabanlı Rasgele Sayı Üretecinin Gerçekleştirilmesi, Doktora Tezi, Fırat Üniversitesi, Fen Bilimleri Enstitüsü, 2014.
• Özkaynak F., Cryptographically secure random number generator with chaotic additional input, Nonlinear Dyn., 78, 2015-2020, 2014.
• Avaroglu E., Tuncer T., Özer A.B., Türk, M., A new method for hybrid pseudo random number generator, J. Microelectron. Electron. Compon. Mater., 4 (4), 303-311, 2014.
• Merah L., Ali-Pacha A., Said N.H., Mamat M., Pseudo Random Number generator Based on the Chaotic System of Chua’s Circuit, and its Real Time FPGA Implementation, Applied Mathematical Sciences, 7 (55), 2719-2734, 2013.
• Avaroğlu E., Koyuncu İ., Özer A.B., Türk M., Hybrid pseudo-random number generator for cryptographic systems, Nonlinear Dyn, 82, 239-248, 2015.
• Zidan M.A., Radwan A.G., Salama K.N., Random number generation based on digital differential chaos, IEEE 54th International Midwest Symposium on Circuits and Systems, Seoul-South Korea, 1-4, 7-10 August, 2011.
• Koyuncu İ., Özcerit A.T., Pehlivan İ., Avaroğlu E., Design and implementation of chaos based true random number generator on FPGA, IEEE Signal Processing and Communications Applications Conference, Trabzon-Turkey, 236-239, 23-25 Nisan, 2014.
• Wang Q., Yu S., Li C., Lü J., Fang X., Guyeux C., Bahi J.M., Theoretical Design and FPGA-Based Implementation of Higher-Dimensional Digital Chaotic Systems, IEEE Trans. Circuits Syst. I Regul. Pap., 63 (3), 401-4012, 2016.
• Fatemi-Behbahani E., Ansari-Aslı K., Farshidi E., A New Approach to Analysis and Design of Chaos-Based Random Number Generators Using Algorithmic Converter, Circuits Systems and Signal Processing, 35 (11), 3830-3846, 2016.
• Wang Y., Li S., A High-Speed Digital True Random Number Generator Based on Cross Ring Oscillator, IEICE Trans. Fundam. Electron. Commun. Comput. Sci., E99-A (4), 806-818, 2016.
• Koyuncu İ., Özcerit A.T., The design and realization of a new high speed FPGA-based chaotic true random number generator, Comput. Electr. Eng., 2016, 1-12, 2016.