Esteban Tlelo-Cuautle José de Jesús Rangel-Magdaleno Luis Gerardo de la Fraga Engineering Applications of FPGAs Chaotic Systems, Artificial Neural Networks, Random Number Generators, and Secure Communication Systems Engineering Applications of FPGAs Esteban Tlelo-Cuautle é ú Jos de Jes s Rangel-Magdaleno Luis Gerardo de la Fraga Engineering Applications of FPGAs fi Chaotic Systems, Arti cial Neural Networks, Random Number Generators, and Secure Communication Systems 123 Esteban Tlelo-Cuautle LuisGerardo dela Fraga INAOE Computer Science Department Tonantzintla, Puebla CINVESTAV-IPN Mexico Mexico City Mexico JosédeJesús Rangel-Magdaleno Department ofElectronics INAOE Tonantzintla, Puebla Mexico ISBN978-3-319-34113-2 ISBN978-3-319-34115-6 (eBook) DOI 10.1007/978-3-319-34115-6 LibraryofCongressControlNumber:2016939064 ©SpringerInternationalPublishingSwitzerland2016 Thisworkissubjecttocopyright.AllrightsarereservedbythePublisher,whetherthewholeorpart 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 orinformationstorageandretrieval,electronicadaptation,computersoftware,orbysimilarordissimilar methodologynowknownorhereafterdeveloped. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publicationdoesnotimply,evenintheabsenceofaspecificstatement,thatsuchnamesareexemptfrom therelevantprotectivelawsandregulationsandthereforefreeforgeneraluse. 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 authorsortheeditorsgiveawarranty,expressorimplied,withrespecttothematerialcontainedhereinor foranyerrorsoromissionsthatmayhavebeenmade. Printedonacid-freepaper ThisSpringerimprintispublishedbySpringerNature TheregisteredcompanyisSpringerInternationalPublishingAGSwitzerland The authors want to dedicate this book to their families for the support provided during the preparation of this material. Preface Field-programmablegatearrays(FPGAs)wereinventedin1984byRossFreeman. Basically,itisasemiconductorconsistingofprogrammablelogicblocksthatcanbe usedtoreproducesimplefunctionsuptoacomplexsystemonachip(SoC).Themain advantagesoftheFPGAsare:theycanbereprogrammed,havelowdevelopmentand acquisitioncosts,andtheirapplicationisagoodoptioniftheproductisnotinhigh numbers.Thatway,FPGAsaregainingtheattentionofresearchesforthedevelop- ment of applications in a wide variety offields, for example, medicine, communi- cations, signal processing, avionics, space, finance, military, electronics, and other areasthatexploittheirflexibilityandcapabilityofbeingreprogrammed/configured. Configurability for engineering applications makes FPGA very crucial in initial stagesforanyembeddedproject.Someanalogcircuitsandanydigitalcircuitcanbe implemented using FPGA, so the possibilities are endless. However, applications foundonrecentarticlesandbooksdidnotdetailtherealizationsfromthemodelto the physical synthesis. That way, this book details engineering applications of FPGAsfrom mathematical modelsdescriptions toVHDLprogramming issues and hardware implementation of applications involving chaos theory. The reader can find insights on FPGA-based implementations for chaos gener- ators, artificial neural networks (ANNs), random number generators (RNGs), and master–slave synchronization of chaotic oscillators to implement a secure com- munication system for image transmission. The plus of this book is focused on providing VHDL programming guidelines and issues, along with co-simulation examples with Active-HDL and Simulink. In addition, we list some challenges on applying different kinds of numerical methods, problems on optimizing chaotic systems, selection of an ANN topology, its training, improvements on designing activation functions, data supply using serial communication with a computer, generation of random number generators from chaos theory, realization of chaotic secure communication systems, and other open problems for future research. vii viii Preface In summary, this book details FPGA realizations for: (cid:129) Chaos generators, which are described from their mathematical models, are characterized by their maximum Lyapunov exponent, and are implemented using minimal FPGA resources. (cid:129) Artificial neural networks (ANNs), discussing some topologies, different learning techniques, kinds of activation functions, and issues on choosing the length of the digital words being processed. One ANN topology is applied to chaotic time series prediction. (cid:129) Random number generators (RNGs), which are designed using different chaos generators, in the continuous-time and discrete-time domains. The RNGs are characterized by their maximum Lyapunov exponent and entropy, and are evaluated through NIST tests. (cid:129) Optimized chaotic oscillators are synchronized in a master–slave topology that is used to implement a secure communication system to process black and white, and grayscale images. Some chapters discuss computer arithmetic issues to minimize hardware resources and to reduce errors, before synthesizing the FPGA realization. At the end,thereadercaninferopenlinesforfutureresearchnotonlyinareaswherechaos generators, ANNs, random number generators, and secure communications are required,butalsotoextendthepresentedmaterialtootherproblemsinengineering. Acknowledgments The authors acknowledge the pretty good help of the graduate students at INAOE forpreparingsimulationsandexperiments.Theyare:AnaDaliaPano-Azucenaand Antonio de Jesus Quintas-Valles. Special acknowledgments to CONACyT-Mexico for funding support under projects 168357 and 237991. ix Contents 1 Introduction to Field-Programmable Gate Arrays. . . . . . . . . . . . . . 1 1.1 FPGA Architectures. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 Blocks Description . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.2.1 Logic Blocks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.2.2 Lookup Tables (LUTs) . . . . . . . . . . . . . . . . . . . . . . . . . 5 1.2.3 I/O Blocks. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 1.3 Programming Environments . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 1.3.1 Vivado. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 1.3.2 Quartus II . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 1.3.3 Aldec Active-HDL . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21 1.4 Computer Arithmetic. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 1.4.1 Fixed Point Numbers. . . . . . . . . . . . . . . . . . . . . . . . . . . 29 1.4.2 Operations with 2’ Complement Numbers . . . . . . . . . . . . 30 1.4.3 Floating-Point Numbers. . . . . . . . . . . . . . . . . . . . . . . . . 31 2 VHDL. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 2.1 A Brief History of VHDL . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 2.2 VHDL Structure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 2.3 Levels of Abstraction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 2.3.1 Behavioral Description. . . . . . . . . . . . . . . . . . . . . . . . . . 36 2.3.2 Data Flow Description. . . . . . . . . . . . . . . . . . . . . . . . . . 39 2.3.3 Structural Description . . . . . . . . . . . . . . . . . . . . . . . . . . 42 2.4 Modules Description Examples. . . . . . . . . . . . . . . . . . . . . . . . . 46 2.4.1 Combinational Circuits . . . . . . . . . . . . . . . . . . . . . . . . . 46 2.4.2 Sequential Circuits . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51 3 Matlab-Simulink Co-Simulation. . . . . . . . . . . . . . . . . . . . . . . . . . . 61 3.1 Co-Simulation Active-HDL/Matlab-Simulink . . . . . . . . . . . . . . . 61 3.2 Co-Simulation Xilinx System Generator/Matlab-Simulink. . . . . . . 67 3.3 Co-Simulation Altera DSP Builder/Matlab-Simulink . . . . . . . . . . 72 xi xii Contents 4 Chaos Generators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77 4.1 On Piecewise-Linear (PWL) Functions. . . . . . . . . . . . . . . . . . . . 77 4.1.1 Saturated Function Series as PWL Function . . . . . . . . . . . 77 4.1.2 Chua’s Diode as PWL Function . . . . . . . . . . . . . . . . . . . 78 4.1.3 Sawtooth as PWL Function . . . . . . . . . . . . . . . . . . . . . . 79 4.2 On the Simulation of Chaos Generators for FPGA Implementation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80 4.2.1 One-Step Methods for Simulating the Generation of 2-Scrolls . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82 4.3 Symmetric and Nonsymmetric PWL Functions . . . . . . . . . . . . . . 84 4.3.1 Symmetric PWL Function . . . . . . . . . . . . . . . . . . . . . . . 85 4.3.2 Nonsymmetric PWL Function. . . . . . . . . . . . . . . . . . . . . 87 4.3.3 VHDL Simulation and Computer Arithmetic Issues. . . . . . 87 4.4 VHDL Code Generation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92 4.5 Bifurcation Diagrams. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94 4.6 Multi-scroll Chaotic Attractors with High MLE and Entropy. . . . . 94 4.6.1 Lyapunov Exponents. . . . . . . . . . . . . . . . . . . . . . . . . . . 103 4.6.2 Evaluation of Entropy . . . . . . . . . . . . . . . . . . . . . . . . . . 109 4.7 Generating a 50-Scrolls Chaotic Attractor at 66 MHz. . . . . . . . . . 111 5 Artificial Neural Networks for Time Series Prediction. . . . . . . . . . . 117 5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117 5.2 Generating Chaotic Time Series Using FPGAs . . . . . . . . . . . . . . 118 5.3 ANN Design Issues. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121 5.3.1 ANN Topology Selection. . . . . . . . . . . . . . . . . . . . . . . . 124 5.3.2 ANN Training . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126 5.3.3 Weights Updating by Batches and Incremental Methods. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129 5.3.4 On the Activation Function in the Last Layer of the ANN . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 131 5.3.5 Time Series Prediction of Chaotic Signals with Different MLE. . . . . . . . . . . . . . . . . . . . . . . . . . . . 132 5.4 FPGA-Based ANN for Time-Series Prediction of Chaotic Signals. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133 5.4.1 FPGA Realization of the Hyperbolic Tangent Activation Function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 133 5.5 Serial Communication Protocol: PC-FPGA. . . . . . . . . . . . . . . . . 144 6 Random Number Generators. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151 6.1 Generating Pseudorandom Binary Sequences . . . . . . . . . . . . . . . 151 6.2 Numerical Method for Solving a Chaotic Dynamical System . . . . 151 6.3 Double-Scroll and Multi-scroll Chaos Generators. . . . . . . . . . . . . 152 6.3.1 Chua’s Chaotic Oscillator. . . . . . . . . . . . . . . . . . . . . . . . 152 6.3.2 Saturated Function Series-Based Chaotic Oscillator. . . . . . 153