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Analysis and Synthesis of Boolean Networks Analysis and Synthesis of Boolean Networks MING LIU Licentiate Thesis in Electronic and Computer Systems Stockholm, Sweden 2015 KTH School of Information and Communication Technology TRITA-ICT 2015:23 SE-164 40 Kista, Stockholm ISBN 978-91-7595-770-8 SWEDEN Akademisk avhandling som med tillstånd av Kungl Tekniska högskolan framlägges till offentlig granskning för avläggande av licentiatexamen i ämnet Elektronik och datorsystem fredag den 18 december 2015 klockan 09.00 i Sal B, Electrum, Kungl Tekniska högskolan, Kista 16440, Stockholm. © Ming Liu, November 2015 Tryck: Universitetsservice US AB iii Abstract In this thesis, we present techniques and algorithms for analysis and syn- thesis of synchronous Boolean and multiple-valued networks. Synchronous Boolean and multiple-valued networks are a discrete-space discrete-time model of gene regulatory networks. Their cycle of states, called attractors, are believed to give a good indication of the possible functional modes of the system. This motivates research on algorithms for finding at- tractors. Existing decision diagram-based approaches have limited capacity due to the excessive memory requirements of decision diagrams. Simulation- based approaches can be applied to large networks, however, their results are incomplete. In the first part of this thesis, we present an algorithm, which uses a SAT-based bounded model checking approach to find all attractors in a multiple-valued network. The efficiency of the presented algorithm is evaluated by analysing 30 network models of real biological processes as well as 35 000 randomly generated 4-valued networks. The results show that our algorithm has a potential to handle an order of magnitude larger models than currently possible. One of the characteristic features of genetic regulatory networks is their inherent robustness, that is, their ability to retain functionality in spite of the introduction of random faults. In the second part of this thesis, we focus on the robustness of a special kind of Boolean networks called Balanced Boolean Networks (BBNs). We formalize the notion of robustness and introduce a method to construct BBNs for 2-singleton attractors Boolean networks. The experiment results show that BBNs are capable of tolerating single stuck-at faults. Our method improves the robustness of random Boolean networks by at least 13% on average, and in some special case, up to 61%. In the third part of this thesis, we focus on a special type of synchronous Boolean networks, namely Feedback Shift Registers (FSRs). FSR-based filter generators are used as a basic building block in many cryptographic systems, e.g. stream ciphers. Filter generators are popular because their well-defined mathematical description enables a detailed formal security analysis. We show how to modify a filter generator into a nonlinear FSR, which is faster, but slightly larger, than the original filter generator. For example, the propagation delay can be reduced 1.54 times at the expense of 1.27% extra area. The presented method might be important for applications, which require very high data rates, e.g. 5G mobile communication technology. In the fourth part of this thesis, we present a new method for detect- ing and correcting transient faults in FSRs based on duplication and parity checking. Periodic fault detection of functional circuits is very important for cryptographic systems because a random hardware fault can compromise their security. The presented method is more reliable than Triple Modular Redundancy (TMR) for large FSRs, while the area overhead of the two ap- proaches are comparable. The presented approach might be important for cryptographic systems using large FSRs. iv Sammanfattning I denna avhandling presenterar vi metoder och algoritmer för analys och syntes av synkrona Booleska och flervärda nätverk. Synkrona Booleska och flervärda nätverk är rums-och tidsdiskret modell av regulatoriskt gennätverk. Deras fillständscykler, som kallas attractorer, tros ge en god indikation på möjliga funktionssätt i systemet. Detta motiverar forskning om algoritmer för att hitta attraktorer. Befintliga beslutsdiagram baserade metoder har begränsad kapacitet på grund av orimliga minneskrav. Simuleringsbaserade metoder kan tillämpas på stora nätverk, men ger ofull- ständiga resultat. I den första delen av denna avhandling presenterar vi en algoritm som använder en SAT-baserad modell för gränsvärdes kontroll för att hitta alla attraktorer i flervärda nätverk. Effektiviteten av den presenterade algoritmen utvärderas genom att analysera 30 nätverksmodeller av verkliga biologiska processer samt 35 000 slumpmässigt genererade 4-värda nätverk. Resultaten visar att vår algoritm har potential att hantera en storleksordning större modeller än vad som nu är möjligt. En karakteristisk egenskap hos regulatoriskt gennätverk är dess innebo- ende robusthet, det vill säga dess förmåga att bibehålla funktionalitet trots införandet av slumpmässiga fel. I den andra delen av denna uppsats fokuserar vi på robustheten hos en speciell typ av Booleska nätverk som kallas Balanse- rade Booleska Nätverk (BBN). Vi formaliserar begreppet robusthet och inför en metod för att bygga BBN för 2 -singleton attraktorer Booleska nätverk. Experimentets resultat visar att BBN har förmåga att tolerera enstaka fel. Vår metod förbättrar robustheten läsnings slumpmässigt genererade Booleska nätverk med minst 13% i genomsnitt och i vissa specialfall upp till 61%. I den tredje delen av denna uppsats fokuserar vi på en speciell typ av synkrona Booleska nätverk, nämligen Feedback Shift Register (FSR). FSR- baserade filtergeneratorer används som en grundläggande byggsten i många kryptografiska system, t.ex. strömchiffer. Filtergeneratorer är populära ef- tersom deras väldefinierade matematiska beskrivning möjliggör en detalje- rad formell säkerhetsanalys. Vi visar hur blir en filter generator i modifierad icke-linjärt FSR, snabbare, men något större, än den ursprungliga filterge- neratorn. Exempelvis kan utbredningsfördröjningen minskas 1,54 gånger på bekostnad av 1,27 % extra yta. De presenterade metoderna kan vara viktiga för tillämpningar som kräver mycket höga datahastigheter, t.ex. 5G mobil kommunikationsteknik. I den fjärde delen av denna avhandling presenterar vi en ny metod för att detektera och korrigera transienta fel i FSRer med hjälp av duplicering och paritetskontroll. Periodiskt fel-detektering av funktionella kretsar är mycket viktigt för krypteringssystem eftersom slumpmässiga hårdvarufel kan äventy- ra dess säkerhet. Denna metod är mer pålitlig än Triple Modular Redundancy (TMR) för stora FSRer, men med jämförbar area. Det presenterade tillväga- gångssättet kan vara viktigt för kryptografiska system som använder stora FSRer. Acknowledgements First of all, I would like to thank my supervisor, Professor Elena Dubrova, for inspiring me with so many topics and ideas, and especially, for all the patience and encouragement she offered me when I was in trouble. I would like to thank Professor Zhonghai Lu for reviewing this thesis. I would like to thank Professor Fredrik Jonsson for his help on the Swedish abstract. I would like to thank Ms. Alina Munteanu for her help on everything in school. I would like to thank all the professors and scholars who teach me, encourage me and enlighten my own research. I would like to thank all my colleagues and friends, Shaoteng Liu, Li Xie, Jue Shen, Pei Liu, Shuo Li, Yuan Yao, Xueqian Zhao, Fan Pan, Shao Tao, Nan Li and Shohreh Sharif Mansouri, for the discussions as well as happiness we shared together. Finally, I would like to thank my parents for their love and support. Thank you! Ming Liu Stockholm, November, 2015 v Contents Contents vii List of Figures ix List of Tablesx List of Abbreviations xi 1 Introduction1 1.1 Previous Work.........................................................1 1.2 Overview and Contributions of the Author..........................3 2 Background7 2.1 Notation................................................................7 2.2 Boolean Networks.....................................................9 2.3 Feedback Shift Registers.............................................. 11 2.4 Relationship between Boolean Networks and FSRs................. 13 3 Multiple-valued Networks 15 3.1 Multiple-valued Networks............................................. 15 3.2 Computation of Attractors........................................... 16 3.3 Converting GINML Format to CNET Format...................... 18 3.4 Conclusion............................................................. 19 4 Balanced Boolean Networks 21 4.1 Computational Scheme Based on Boolean Networks............... 21 4.2 Single Stuck-at Fault Model.......................................... 23 4.3 Robustness Evaluation................................................ 24 4.4 Balanced Boolean Networks.......................................... 25 4.5 Conclusion............................................................. 26 5 Design of Secure FSRs 27 5.1 Filter Generators...................................................... 27 vii viii CONTENTS 5.2 Main Ideas of the Presented Approach.............................. 29 5.3 The Fibonacci to Galois Transformation............................ 30 5.4 Example................................................................ 31 5.5 Conclusion............................................................. 35 6 Design of Reliable FSRs 37 6.1 Stream Ciphers........................................................ 37 6.2 Transient Faults and Triple Modular Redundancy.................
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