Computation, cryptography, and network security

free ebooks ==> www.ebook777.com Nicholas J Daras Michael Th Rassias Editors Computation, Cryptography, and Network Security www.ebook777.com free ebooks ==> www.ebook777.com Computation, Cryptography, and Network Security free ebooks ==> www.ebook777.com www.ebook777.com free ebooks ==> www.ebook777.com Nicholas J Daras • Michael Th Rassias Editors Computation, Cryptography, and Network Security 123 free ebooks ==> www.ebook777.com Editors Nicholas J Daras Department of Mathematics and Engineering Hellenic Military Academy Vari Attikis, Greece ISBN 978-3-319-18274-2 DOI 10.1007/978-3-319-18275-9 Michael Th Rassias Department of Mathematics ETH Zürich Zürich, Switzerland ISBN 978-3-319-18275-9 (eBook) Library of Congress Control Number: 2015945103 Mathematics Subject Classification (2010): 03D25, 11U05, 26D15, 31A10, 45P05, 47G10, 47A07, 44A10, 46E30, 68R10, 94C30 Springer Cham Heidelberg New York Dordrecht London © Springer International Publishing Switzerland 2015 This work is subject to copyright All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed The use of general descriptive names, registered names, trademarks, service marks, etc in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication Neither the publisher nor the authors or the editors give a warranty, express or implied, with respect to the material contained herein or for any errors or omissions that may have been made Printed on acid-free paper Springer International Publishing AG Switzerland is part of Springer Science+Business Media (www springer.com) www.ebook777.com free ebooks ==> www.ebook777.com Preface This book entitled Computation, Cryptography, and Network Security brings together a broad variety of mathematical methods and theories with several applications from a number of disciplines It discusses new directions for further inventions in computation, cryptography, and network security It is hoped to provide some good understanding of the subject of security in the broadest sense It consists of papers written by eminent scientists from the international mathematical community, who present important research works in several theories and problems These contributions focus on both old and new developments of pure and applied mathematics with emphasis to the geometry of the zeros of a polynomial, multivariate Birkhoff interpolation, variational principles in vector spaces, parameterized Yang-Hilbert-type integral inequalities and their operator expressions, operators preserving linear functions, integral estimates for the composition of Green’s and bounded operators, asymptotic behavior of orthogonal polynomials on the unit circle, generalized Laplace transform inequalities in multiple weighted Orlicz spaces, and functional equations Furthermore, some survey papers are published in this volume, which are particularly useful for a broader audience of readers, particularly in credential technologies, cryptographic schemes, current challenges for IT security with focus on biometry, flaws in the initialization process of stream ciphers, entropy and information measures, information theory, quantum analogues of HermiteHadamard type inequalities for generalized convexity, producing fuzzy inclusion and entropy measures, as well as applications on the unstable equilibrium points and system separations in electric power systems, and a supply chain game theory for cybersecurity investments subject to network vulnerability We would like to express our deepest thanks to all the contributors of papers who, through their works, participated in this book We would also wish to acknowledge the superb assistance that the staff of Springer has provided for the publication of this book Athens, Greece Princeton, NJ, USA Nicholas J Daras Michael Th Rassias v free ebooks ==> www.ebook777.com www.ebook777.com free ebooks ==> www.ebook777.com Contents Transformations of Cryptographic Schemes Through Interpolation Techniques Stamatios-Aggelos N Alexandropoulos, Gerasimos C Meletiou, Dimitrios S Triantafyllou, and Michael N Vrahatis Flaws in the Initialisation Process of Stream Ciphers Ali Alhamdan, Harry Bartlett, Ed Dawson, Leonie Simpson, and Kenneth Koon-Ho Wong 19 Producing Fuzzy Inclusion and Entropy Measures Athanasios C Bogiatzis and Basil K Papadopoulos 51 On Some Recent Results on Asymptotic Behavior of Orthogonal Polynomials on the Unit Circle and Inserting Point Masses Kenier Castillo and Francisco Marcellán 75 On the Unstable Equilibrium Points and System Separations in Electric Power Systems: A Numerical Study 103 Jinda Cui, Hsiao-Dong Chiang, and Tao Wang Security and Formation of Network-Centric Operations 123 Nicholas J Daras A Bio-Inspired Hybrid Artificial Intelligence Framework for Cyber Security 161 Konstantinos Demertzis and Lazaros Iliadis Integral Estimates for the Composition of Green’s and Bounded Operators 195 Shusen Ding and Yuming Xing A Survey of Reverse Inequalities for f -Divergence Measure in Information Theory 209 S.S Dragomir vii free ebooks ==> www.ebook777.com viii Contents On Geometry of the Zeros of a Polynomial 253 N.K Govil and Eze R Nwaeze Approximation by Durrmeyer Type Operators Preserving Linear Functions 289 Vijay Gupta Revisiting the Complex Multiplication Method for the Construction of Elliptic Curves 299 Elisavet Konstantinou and Aristides Kontogeorgis Generalized Laplace Transform Inequalities in Multiple Weighted Orlicz Spaces 319 Jichang Kuang Threshold Secret Sharing Through Multivariate Birkhoff Interpolation 331 Vasileios E Markoutis, Gerasimos C Meletiou, Aphrodite N Veneti, and Michael N Vrahatis Advanced Truncated Differential Attacks Against GOST Block Cipher and Its Variants 351 Theodosis Mourouzis and Nicolas Courtois A Supply Chain Game Theory Framework for Cybersecurity Investments Under Network Vulnerability 381 Anna Nagurney, Ladimer S Nagurney, and Shivani Shukla A Method for Creating Private and Anonymous Digital Territories Using Attribute-Based Credential Technologies 399 Panayotis E Nastou, Dimitra Nastouli, Panos M Pardalos, and Yannis C Stamatiou Quantum Analogues of Hermite–Hadamard Type Inequalities for Generalized Convexity 413 Muhammad Aslam Noor, Khalida Inayat Noor, and Muhammad Uzair Awan A Digital Signature Scheme Based on Two Hard Problems 441 Dimitrios Poulakis and Robert Rolland Randomness in Cryptography 451 Robert Rolland Current Challenges for IT Security with Focus on Biometry 461 Benjamin Tams, Michael Th Rassias, and Preda Mih˘ailescu Generalizations of Entropy and Information Measures 493 Thomas L Toulias and Christos P Kitsos www.ebook777.com free ebooks ==> www.ebook777.com Contents ix Maximal and Variational Principles in Vector Spaces 525 Mihai Turinici All Functions g:N ! N Which have a Single-Fold Diophantine Representation are Dominated by a Limit-Computable Function f :N n f0g ! N Which is Implemented in MuPAD and Whose Computability is an Open Problem 577 Apoloniusz Tyszka Image Encryption Scheme Based on Non-autonomous Chaotic Systems 591 Christos K Volos, Ioannis M Kyprianidis, Ioannis Stouboulos, and Viet-Thanh Pham Multiple Parameterize Yang-Hilbert-Type Integral Inequalities 613 Bicheng Yang Parameterized Yang–Hilbert-Type Integral Inequalities and Their Operator Expressions 635 Bicheng Yang and Michael Th Rassias A Secure Communication Design Based on the Chaotic Logistic Map: An Experimental Realization Using Arduino Microcontrollers 737 Mauricio Zapateiro De la Hoz, Leonardo Acho, and Yolanda Vidal free ebooks ==> www.ebook777.com 742 M Zapateiro D et al Academy entitled Deuxième memoire sur la loi d’acroissement de la population (Second memory about the law of population growth) It was published in 1847 [30] and it was a critical revision of his previous work After Verhulst’s dead in 1849, the logistic curve lost interest until 1920 when it was rediscovered [9] In that year, a paper entitled On the rate of Growth of the Population of the United States since 1790 and its Mathematical Representation [23], Pearl and Reed studied the mathematical models that were used at the time to determine how the population size evolved along the time in the United States They concluded that the existing models did not reflect too much accuracy and came up with an equation that better fitted the real data That equation was exactly the same Verhulst’s logistic curve though they initially ignored it The logistic model then resurged to be widely used in natural sciences to represent the population dynamics of different species In 1972 the meteorologist Lorenz presented one of the pioneering works on chaotic dynamics His work entitled Does the flap of butterfly’s wings in Brazil set off a tornado in Texas? [15] was a research on how some meteorological phenomena could be modeled with a chaotic dynamic system Then a series of works on chaotic systems began to be developed and the logistic model would soon come along with them In 1976 May presented an article entitled Simple mathematical models with very complicated dynamics [16] in which he described how the simple logistic map, i.e., the discrete-time version of Verhulst’s logistic curve, would lead to chaos The importance of the logistic map as a simple chaotic system then begun The equation of the logistic model as it appears in Verhulst’s works is: M dp Dm p dt np (1) where p is the population, m D l C nb, b is the population corresponding at the moment that the study begins, l=M is a coefficient relative to the weakening of the population, and n is a constant This is a first order differential equation It is well known that chaotic systems must be at least of third order, however this is not true for discrete time systems The logistic map, the discrete-time version of Verhulst’s logistic model is indeed chaotic under certain conditions Its equation is: xnC1 D rxn xn /; Ä x Ä (2) where r is a constant parameter Figure is the bifurcation diagram of the logistic map created by varying the parameter r from 2.5 to 4.0 As can be seen in the bifurcation diagram, there are different regions that depend on the value of r It is of particular interest when r D because there it begins the period doubling that leads to the chaotic dynamics when r 3:5699 : : : until r D 4:0 Figure shows the Lyapunov exponent of the logistic map as r is varied from 2.5 to 4.0 It can be seen that the Lyapunov exponent becomes positive for values of or greater than 3.56 approximately which is a strong indicator of chaos [33] free ebooks ==> www.ebook777.com A Secure Communication Design Based on the Chaotic Logistic Map 743 0.8 xn 0.6 0.4 0.2 2.5 3.5 r Fig Logistic map bifurcation diagram λ −1 −2 −3 −4 2.5 3.5 r Fig Logistic map Lyapunov exponent As was discussed earlier in Sect 1, digital communication systems based on chaotic maps are being widely studied and the logistic map is no exception Several works can be found in the literature in which the chaotic properties of the logistic maps are exploited in the design of cryptography techniques for improving secure communications For example, Murillo-Escobar et al [17] presented a symmetric text cipher in which they used a 128-bit secret key, two logistic maps with optimized pseudorandom sequences, plain text characteristics, and only one permutation diffusions round Security analysis was performed to demonstrate its feasibility Ursulean [28] studied the properties of the logistic map as a pseudo-random bit generator and carried out statistical tests to analyze its performance Lawrence and Wolff [12] explored the generation of one or more binary-valued sequences from a standard logistic map, according to the continuous values being in one of two subintervals of the map’s domain defined by cut-points, one applying to each binary www.ebook777.com free ebooks ==> www.ebook777.com 744 M Zapateiro D et al process and presented an application to secure communications Zhang and Cao [37] proposed a technique for encrypting images in which a new modification of the logistic map is proposed The modified logistic map is, according to the authors, a better choice for encryption due to the improved chaotic properties as a result of a much larger Lyapunov exponent Singh and Sinha [26] proposed an opto-electronic communication system that uses a logistic map and pulse position modulation In this scheme, the input signal (message) is added to a chaotic signal generated by a logistic map Then it is modulated with a pulse position modulator (PPM) The modulated signal is then sent through the channel to the receiver in which the inverse operation is performed in order to retrieve the message The authors experimentally tested this scheme with optical fiber with satisfactory results He et al [7] proposed a scheme in which the message is processed using a logistic map and the chaotic parameter modulation (CPM) technique Then it is sent to the receiver where a nonlinear control factor is introduced in order to synchronize the transmitter and the receiver and thus retrieve the message Chang [4] presented a communication system based on the asymptotic synchronization of modified logistic hyper-chaotic system For that purpose, they proposed a modification of the logistic map in which is uniformly distributed in [0,1] The difference with respect to the original logistic map is that the modified version does not exhibit windows This has the advantage of a greater key space for communications Volos [32] presented a chaotic random bit generator and implemented it in an Arduino board The microcontroller runs sideby-side two logistic maps working in different chaotic regimes due to the different initial conditions and system parameters Statistical tests were carried out to prove security against intruders Pande and Zambreno [18] presented another experimental realization of a chaotic encryption scheme, this time using a Xilin Virtex FPGA They implemented a modified logistic map that improves the performance of the logistic map in terms of Lyapunov exponent and uniformity of the bifurcation diagram In the next sections, we will use a logistic map as part of an encryption/decryption scheme for transmitting information In the next sections we will explain the details of the prototype of this communication system which is implemented in two Arduino Uno boards Experimental Implementation 4.1 Description of the Communication System The communication system implemented in this work consists of a transmitter and a receiver whose cores are the Arduino Uno R3 microcontroller boards, shown in Fig These are low cost, simple but powerful microcontrollers based on the ATmega328 chip They have 14 digital input/output pins (six of them can be used free ebooks ==> www.ebook777.com A Secure Communication Design Based on the Chaotic Logistic Map 745 Fig Picture of an Arduino Uno R3 microcontroller Picture taken from the Arduino website [3] as PWM outputs), six analog inputs, a 16 MHz crystal oscillator, a USB connection, and a reset button They can be programmed using a language similar to CCC called Wiring [3] The flow diagram of the programs executed by each Arduino is shown in Fig in order to facilitate the description of the communication system algorithms The communication starts when a message m.t/ is produced by a function generator and sent to the analog input A0 of the Arduino transmitter Arduino analog inputs only accepts unipolar signals in the range form to V An embedded 10-bit ADC converts the input signal from analog to digital at a maximum rate of 10,000 samples per second However, as can be seen in the flow diagram, the loop is repeated every 0.5 ms and thus, the message input is sampled at a rate of 2000 samples per second In order to guarantee the timing, we made use of the SimpleTimer library [25] Since the output of the ADC is a value between and 1023 (the ADC resolution), an internal operation to bring it back to the range from to V is executed The result is a sampled message signal m.k/ The next step is the 1-bit ADC conversion The ADC conversion scheme, also known as simple Delta modulation, shown in Fig 6, consists of a comparator in the forward path and an integrator in the feedback path of a simple control loop The modulated output mb.k/ is either true or false at any given time The signal m.k/ is compared to another signal xn.k/ which is generated internally by the algorithm xn.k/ is a digital implementation of an integrator, which is the base of the 1-bit ADC conversion [27] This value is updated every loop of the Arduino program After one bit from the ADC is obtained, the logistic map is called to generate a value x.k/ and then proceed to the encryption The encryption algorithm is then: www.ebook777.com free ebooks ==> www.ebook777.com 746 M Zapateiro D et al Fig Flow diagram of the Arduino codes Left: transmitter Right: receiver free ebooks ==> www.ebook777.com A Secure Communication Design Based on the Chaotic Logistic Map Fig Diagram of the 1-bit ADC/DAC converter also known as Delta modulator 747 clock m(k) + - mb(k) mb(k) m(k) xn(k) modulator (ADC) demodulator (DAC) if x(k) > 0.5 then me(k) = mb(k) s(k) = true else me(k) = !mb(k) //Symbol ! means boolean negation s(k) = false end where me.k/ is the encrypted message and s.k/ is the key These signals are sent to the receiver through digital outputs D2 and D7 The key signal s.k/ can also be encrypted using, for example, Karnaugh maps, however this was not done in this work In the receiver, the signals me.k/ and s.k/ go directly to the Arduino inputs D7 and D2, respectively The flow diagram of the receiver program is shown in Fig as well The receiver decrypts the message by analyzing the key signal s.k/ by running the following algorithm: if s(k) = then md(k)=me(k) else md(k)=!me(k) end where md.k/ is the decrypted signal The receiver runs every loop in 0.5 ms The output md.k/ is sent to the output pin D3 and it goes directly to the 1-bit DAC realized with analog electronics using operational amplifiers As shown in Fig 6, the DAC or Delta demodulation consists of an integrator The signal is passed through different stages though as shown in the circuit diagram of Fig The circuit has three main blocks The first one, composed of the amplifiers U1 and U2 is a unipolar to bipolar converter Recall that the Arduino inputs must be unipolar so in the case that the original signals are bipolar they must recovered to its original form at the output of the Arduino Thus the signal m.k/ Œ0; 5 V is converted to a signal m.t/ Œ 2:5; 2:5 V The second block is composed of amplifiers U3 and U4 They are an integrator that performs the DAC and an amplifier to adjust the quality of its output This signal is finally sent through a low-pass filter, an amplifier, and an inverter (amplifiers U5–U7) to get the final mr.t/ which should be approximately equal to m.t/ The codes of the Arduino transmitter and receiver are shown in the Appendix www.ebook777.com free ebooks ==> www.ebook777.com 748 M Zapateiro D et al Fig Circuit diagram of the analog electronics in the receiver 4.2 Experimental Results The communication system was implemented for experimental purposes Figure is a picture of the experiment in which we observe the two Arduino boards and a protoboard with the analog electronics For the experiments, the logistic map was implemented with r D 3:9018 and an initial condition x.0/ D 0:5 The sequence of numbers generated under these conditions is shown in Fig free ebooks ==> www.ebook777.com A Secure Communication Design Based on the Chaotic Logistic Map 749 Fig Picture of the circuit x[n] 0.8 0.6 0.4 0.2 0 50 100 150 n Fig Numbers generated by the logistic map with r D 3:9018 and x.0/ D 0:5 Figures 10, 11, and 12 are screenshots of the oscilloscope corresponding to the first experiment In this case, a 160 Hz sine wave, V peak-to-peak amplitude, was used as a message signal In Fig 10 we see a comparison of the sent message m.t/ (in blue) and the retrieved message mr.t/ (in yellow) Figure 11 compares the sent message m.t/ (in blue) and the key signal s.k/ (in yellow) Figure 12 is a comparison on the sent message m.t/ (in blue) and the encrypted message me.k/ (in yellow) In a second experiment, a 150 Hz triangular wave was used as a message The screenshots of the oscilloscope are displayed in Figs 13, 14, and 15 Figure 13 compares the sent message m.t/ to the retrieved message mr.t/ Figures 14 and 15 www.ebook777.com free ebooks ==> www.ebook777.com 750 M Zapateiro D et al Fig 10 160 Hz sine wave message Blue: sent message Yellow: retrieved message Fig 11 160 Hz sine wave message Blue: sent message Yellow: key signal are the key signal s.k/ and the encrypted message me.k/ compared to the sent message m.t/, respectively Finally, in Fig 16 we can see a random-like message signal (in yellow) and its retrieved version (in blue) This signal was generated by making sounds through an electret microphone For this experiment, it was necessary to reduce the execution time of every loop of the Arduino microcontrollers to 0.1 ms in order to account for the wider frequency spectrum of the signal free ebooks ==> www.ebook777.com A Secure Communication Design Based on the Chaotic Logistic Map 751 Fig 12 160 Hz sine wave message Blue: sent message Yellow: encrypted message Fig 13 160 Hz triangular wave message Blue: sent message Yellow: retrieved message Conclusion In this chapter we have reviewed the digital secure communication systems using the logistic map and proposed a new scheme based on it The communication system proposed uses a 1-bit DAC (also known as Delta modulator) to modulate the message signal and a logistic map for encryption The whole system was www.ebook777.com free ebooks ==> www.ebook777.com 752 M Zapateiro D et al Fig 14 160 Hz triangular wave message Blue: sent message Yellow: key signal Fig 15 160 Hz triangular wave message Blue: sent message Yellow: encrypted message implemented with Arduino Uno microcontroller boards that run the encryption and decryption algorithms in the transmitter and receiver, respectively The results of experiments showed the feasibility of using the Arduino microprocessors for the task proposed In future works, the key signal used to decrypt the message is going to be encrypted as well in order to increase the security of the transmission free ebooks ==> www.ebook777.com A Secure Communication Design Based on the Chaotic Logistic Map 753 Fig 16 Random signal Blue: sent message Yellow: encrypted message Acknowledgements Mauricio Zapateiro is supported by the fellowship from CAPES/Programa Nacional de Pós-Doutorado from Brazil This work was funded by the European Union (European Regional Development Fund) and the Spanish Ministry of Economy and Competitiveness through the research projects DPI2012-32375/FEDER, DPI2011-28033-C03-01 and DPI2014-58427-C21-R and by the government of Catalonia (Spain) through 2014SGR859 Appendix Arduino Transmitter Code ///TX code #include SimpleTimer timer; double x=0.5; //Logistic map threshold for encryption double h=0.1; //Digital integrator parameter double xn=0; //Digital integrator signal xn(k) double r=3.9018;//Logistic map parameter r int mk; //k-th sample of message signal m(t) int aux; //Digital integrator parameter int me; //Encrypted message me(k) void setup(){ pinMode(2,OUTPUT); pinMode(7,OUTPUT); www.ebook777.com free ebooks ==> www.ebook777.com 754 M Zapateiro D et al timer.setInterval(0.5,repeatMe); } void repeatMe(){ mk=analogRead(A0)*5/1023; if(mk-xn>0){ me=HIGH; aux=5; } else{ me=LOW; aux=-5; } xn=xn+h*aux; x=r*x*(1-x); if(x>0.5){ digitalWrite(7,me); digitalWrite(2,HIGH); } else{ digitalWrite(7,!me); digitalWrite(2,LOW); } } void loop(){ timer.run(); } Arduino Receiver Code #include SimpleTimer timer; int me; //Encrypted signal from the transmitter me(k) void setup() { pinMode(2,INPUT); pinMode(7,INPUT); pinMode(3,OUTPUT); timer.setInterval(0.1,repeatMe); } void repeatMe(){ free ebooks ==> www.ebook777.com A Secure Communication Design Based on the Chaotic Logistic Map 755 me=digitalRead(7); if(digitalRead(2)==HIGH{ digitalWrite(3,me); } else{ digitalWrite(3,!me); } } void loop(){ timer.run(); } References Agiza, H.N., Yassen, M.T.: Synchronization of Rossler and Chen chaotic dynamical systems using active control Phys Lett A 278, 191–197 (2001) Alvarez, G., Li, S.: Some basic cryptographic requirements for chaos-based cryptosystems Int J Bifurcation Chaos 16(8), 2129–2151 (2006) Arduino: (2015) http://www.store.arduino.cc/product/A000066 Chang, S.-M.: Chaotic generator in digital secure communication In: Proceedings of the World Congress on Engineering 2009 (WCE2009), London, 1–3 July 2009 Chen, C.K., Lin, C.L.: Text encryption using ECG signals with chaotic logistic map In: The 5th IEEE Conference on Industrial Electronics and Applications (ICIEA 2010), Taichung, 15–17 June 2010 Fallalih, K., Leung, H.: A chaos secure communication scheme based on multiplication modulation Commun Nonlinear Sci Numer Simul 15, 368–383 (2010) He, L.-F., Zhang, G., Tian, Z.-S.: A chaotic secure communication scheme based on logistic map In: 2010 International Conference on Computer Application and System Modeling (ICCASM 2010), Taiyuan, 22–24 Oct 2010 Huang, J.: Adaptive synchronization between different hyper-chaotic systems with fully uncertain parameters Phys Lett A 372, 4799–4804 (2008) Kint, J., Constales, D., Vanderbauwhede, A.: Pierre-Frano¸ is Verhulst’s final triumph In: Ausloos, M., Dirickx, M (eds.) The Logistic Map and the Route to Chaos, p 13 Springer, Heidelberg (2006) 10 Kokarev, L., Jakimoski, G.: Logistic map as a block encryption algorithm Phys Lett A 289, 199–206 (2001) 11 Larger, L., Goedgebuer, J.-P.: Encryption using chaotic dynamics for otpimal telecommunications C R Phys 5, 609–611 (2004) 12 Lawrence, A.J., Wolff, R.C.: Binary time series generated by chaotic logistic maps Stochastics Dyn 3(4), 529–544 (2003) 13 Lee, P.-H., Pei, S.-C., Chen, Y.-Y.: Generating chaotic stream ciphers using chaotic systems Chin J Phys 41(6), 559–581 (2003) 14 Liu, S.T., Sun, F.Y.: Spatial chaos-based image encryption design Sci China Ser G Phys Mech Astron 52(2), 177–183 (2009) 15 Lorenz, E.N.: Does the flap pf a butterfly’s wings in Brazil set off a tornado in Texas? In: 139th Meeting of the American Association for the Advancement of Science, 29 Dec 1972 www.ebook777.com free ebooks ==> www.ebook777.com 756 M Zapateiro D et al 16 May, R.M.: Simple mathematical models with very complicated dynamics Nature 261, 459–467 (1976) 17 Murillo-Escobar, M.A., Abundiz-Pérez, F., Cruz-Hernández, C., López-Gutiérrez, R.M.: A novel symmetric text encryption algorithm based on logistic map In: Proceedings of the 2014 International Conference on Communications, Signal Processing and Computers (ICNC 2014), Honolulu, 3–6 Feb 2014 18 Pande, A., Zambreno, J.: A chaotic encryption scheme for real-time embedded systems: design and implementation Telecommun Syst (2011) doi:10.1007/s11235-011-9460-1 19 Pareek, N.K., Patidar, V., Sud, K.K.: Image encryption using chaotic logistic map Image Vision Comput 24, 926–934 (2006) 20 Park, J.H.: Chaos synchronization between two different chaotic dynamical systems Chaos, Solitons Fractals 27, 549–554 (2006) 21 Pastijn, H.: Chaotic growth with the logistic model of P.-F Verhulstin In: Ausloos, M., Dirickx, M (eds.) The Logistic Map and the Route to Chaos, p Springer, Heidelberg (2006) 22 Patidar, V., Sud, K.K.: A pseudo random bit generator based on chaotic logistic map and its statistical testing Informatica 33, 441–452 (2009) 23 Pearl, R., Reed, L.J.: On the rate of growth of the population of the United States since 1790 and its mathematical representation Proc Natl Acad Sci 6, 275–288 (1920) 24 Pecora, L.M., Caroll, T.L.: Synchronization in chaotic systems Phys Rev Lett 64, 821–825 (1990) 25 Romani, M.: SimpleTimer library for Arduino (2010) http://www.playground.arduino.cc/ Code/SimpleTimer 26 Singh, N., Sinha, A.: Chaos-based secure communication system using logistic map Opt Lasers Eng 48, 398–404 (2010) 27 Taylor, D.S.: Design of continuously variable slope delta modulation communication systems Motorola Technical Document AN1544 (1996) 28 Ursulean, R.: Reconsidering the generalized logistic map as a pseudo random bit generator Elektronika ir Elektrotechnila 7(56), 100–113 (2004) 29 Verhulst, P.F.: Recherches mathématiques sur la loi d’acroissement de la population Mémoires de l’Académie Royale des Sciences, des Lettres et des Beaux-Arts de Belgique 18, 1–38 (1845) 30 Verhulst, P.F.: Deuxième mémoire sur la loi d’acroissement de la population Mémoires de l’Académie Royale des Sciences, des Lettres et des Beaux-Arts de Belgique 20, 1–32 (1847) 31 Volos, C.K.: Chaotic random bit generator realized with a mocrocontroller J Comput Model 3(4), 115–136 (2013) 32 Volos, C.K., Doukas, N., Kyprianidis, I.M., Stouboulos, I.N., Kostis, T.G.: Chaotic autonomous mobile robot for military missions In: The 17th International Conference on Communications, Rhodes Island, July 2013 33 Wolf, A., Swift, J.B., Swinney, H.L., Vastano, J.A.: Determining Lyapunov exponents form a time series Phys D 16, 285–317 (1985) 34 Yang, T., Chua, L.O.: Impulsive stabilization for control and synchronization of chaotic systems: theory and application to secure communication IEEE Trans Circuits Syst I Fundam Theory Appl 44(10), 976–988 (1997) 35 Zapateiro, M., Vidal, Y., Acho, L.: A secure communication scheme based on chaotic duffing oscillators and frequency estimation for the transmission of binary-coded messages Commun Nonlinear Sci Numer Simul 19(4), 991–1003 (2014) 36 Zapateiro De la Hoz, M., Acho, L., Vidal, Y.: A modified Chua chaotic oscillator and its application to secure communications Appl Math Comput 247, 712–722 (2014) 37 Zhang, X., Cao, Y.: A novel chaotic map and an improved chaos-based image encryption scheme Sci World J 2014 (2014) http://www.dx.doi.org/10.1155/2014/713541 38 Zhang, L., Liao, X., Wang, X.: An image encryption approach based on chaotic maps Chaos, Solitons Fractals 24, 759–765 (2005) ... Computation, Cryptography, and Network Security free ebooks ==> www.ebook777.com www.ebook777.com free ebooks ==> www.ebook777.com Nicholas J Daras • Michael Th Rassias Editors Computation, Cryptography,. .. Switzerland 2015 N.J Daras, M.Th Rassias (eds.), Computation, Cryptography, and Network Security, DOI 10.1007/978-3-319-18275-9_1 www.ebook777.com free ebooks ==> www.ebook777.com S.-A.N Alexandropoulos... mathematical methods and theories with several applications from a number of disciplines It discusses new directions for further inventions in computation, cryptography, and network security It is