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Breaking the Unbreakable: Exploiting Loopholes in Bell's Theorem To Linköping Studies in Science and Technology Dissertation No. 1875 Breaking the Unbreakable: Jonathan Jogenfors Breaking Unbreakable the Exploiting Loopholes in Bell’s Theorem to Hack Quantum Cryptography Jonathan Jogenfors 2017 Linköping Studies in Science and Technology Dissertations, No. 1875 Breaking the Unbreakable Exploiting Loopholes in Bell’s Theorem to Hack Quantum Cryptography Jonathan Jogenfors Akademisk avhandling som för avläggande av doktorsexamen vid Linköpings Universitet kommer att offentligt försvaras i sal Ada Lovelace, hus B, universitetsområde Valla, freda- gen den 17 november 2017 kl. 13:00. Fakultetsopponent är Professor Marek Zukowski,˙ Instytut Fizyki Teoretycznej i Astrofizyki, Uniwersytet Gdanski.´ Abstract In this thesis we study device-independent quantum key distribution based on energy-time entanglement. This is a method for cryptography that promises not only perfect secrecy, but also to be a practical method for quantum key dis- tribution thanks to the reduced complexity when compared to other quantum key distribution protocols. However, there still exist a number of loopholes that must be understood and eliminated in order to rule out eavesdroppers. We study several relevant loopholes and show how they can be used to break the se- curity of energy-time entangled systems. Attack strategies are reviewed as well as their countermeasures, and we show how full security can be re-established. Quantum key distribution is in part based on the profound no-cloning theorem, which prevents physical states to be copied at a microscopic level. This important property of quantum mechanics can be seen as Nature’s own copy-protection, and can also be used to create a currency based on quantum mechanics, i.e., quantum money. Here, the traditional copy-protection mech- anisms of traditional coins and banknotes can be abandoned in favor of the laws of quantum physics. Previously, quantum money assumes a traditional hierarchy where a central, trusted bank controls the economy. We show how quantum money together with a blockchain allows for Quantum Bitcoin, a novel hybrid currency that promises fast transactions, extensive scalability, and full anonymity. URL: http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-140912 ISBN 978-91-7685-460-0 ISSN 0345-7524 Linköping Studies in Science and Technology Dissertations, No. 1875 Breaking the Unbreakable Exploiting Loopholes in Bell’s Theorem to Hack Quantum Cryptography Jonathan Jogenfors Information Coding Group Department of Electrical Engineering Linköping University SE-581 83 Linköping, Sweden Linköping 2017 Breaking the Unbreakable: Exploiting Loopholes in Bell’s Theorem to Hack Quantum Cryptography Jonathan Jogenfors Author e-mail: [email protected] Cover image Layout of the Franson interferometer, a scheme used for testing the Bell inequality using energy-time entanglement. Edition 1:1 Copyright © 2017 Jonathan Jogenfors unless otherwise stated. All product names, logos, and brands are property of their respective owners. ISBN 978-91-7685-460-0 ISSN 0345-7524 URL http://urn.kb.se/resolve?urn=urn:nbn:se:liu:diva-140912 Typeset using LuaLATEX Printed by LiU-Tryck, Linköping, Sweden 2017 iii <3To Anna<3 Abstract In this thesis we study device-independent quantum key distri- bution based on energy-time entanglement. This is a method for cryptography that promises not only perfect secrecy, but also to be a practical method for quantum key distribution thanks to the reduced complexity when compared to other quantum key distri- bution protocols. However, there still exist a number of loopholes that must be understood and eliminated in order to rule out eaves- droppers. We study several relevant loopholes and show how they can be used to break the security of energy-time entangled systems. Attack strategies are reviewed as well as their countermeasures, and we show how full security can be re-established. Quantum key distribution is in part based on the profound no-cloning theorem, which prevents physical states to be copied at a microscopic level. This important property of quantum me- chanics can be seen as Nature’s own copy-protection, and can also be used to create a currency based on quantum mechanics, i.e., quantum money. Here, the traditional copy-protection mecha- nisms of traditional coins and banknotes can be abandoned in favor of the laws of quantum physics. Previously, quantum money assumes a traditional hierarchy where a central, trusted bank controls the economy. We show how quantum money together with a blockchain allows for Quantum Bitcoin, a novel hybrid currency that promises fast transactions, extensive scalability, and full anonymity. vii Populärvetenskaplig sammanfattning En viktig konsekvens av kvantmekaniken är att okända kvanttill- stånd inte kan klonas. Denna insikt har gett upphov till kvant- kryptering, en metod för två parter att med perfekt säkerhet kom- municera hemligheter. Ett komplett bevis för denna säkerhet har dock låtit vänta på sig eftersom en attackerare i hemlighet kan manipulera utrustningen så att den läcker information. Som ett svar på detta utvecklades apparatsoberoende kvantkryptering som i teorin är immun mot sådana attacker. Apparatsoberoende kvantkryptering har en mycket högre grad av säkerhet än vanlig kvantkryptering, men det finns fortfarande ett par luckor som en attackerare kan utnyttja. Dessa kryphål har tidigare inte tagits på allvar, men denna avhandling visar hur även små svagheter i säkerhetsmodellen läcker information till en attackerare. Vi demonstrerar en praktisk attack där attackeraren aldrig upptäcks trots att denne helt kontrollerar systemet. Vi visar också hur kryphålen kan förhindras med starkare säkerhetsbevis. En annan tillämpning av kvantmekanikens förbud mot klo- ning är pengar som använder detta naturens egna kopieringsskydd. Dessa kvantpengar har helt andra egenskaper än vanliga mynt, sedlar eller digitala banköverföringar. Vi visar hur man kan kombi- nera kvantpengar med en blockkedja, och man får då man en slags “kvant-Bitcoin”. Detta nya betalningsmedel har fördelar över alla andra betalsystem, men nackdelen är att det krävs en kvantdator. ix Acknowledgments I would like to express gratitude to my advisor, Jan-Åke Lars- son, for his support, patience and encouragement throughout my graduate studies. His guidance has helped me tremendously, and thanks to him I was able to overcome the many hurdles I encountered in the process of performing this research. My thanks also go to my co-supervisor, Associate Professor Fredrik Karlsson for his guidance. I could not have done this without my awesome wife Anna. Writing this thesis has required long days and late nights, and she has supported me all this time. Thank you, Anna, for your love and understanding. I am so fortunate to have you by my side. My colleagues at the Information Coding Group and the De- partment of Electrical Engineering made me feel welcome from the first day. Special thanks to Niklas Johansson and Vahid Kesh- miri, who have endured sharing an office with me all these years. I am indebted to all those who have supported me, including Monica, Jan-Erik, and Andreas. Last but not least I would thank my parents, Eva and Stefan, and my sisters, Susanna and Elisabeth, for their continued support and love. Jonathan Jönköping, October 2017 xi Contents Abstract vii Acknowledgments xi Contents xiii List of Figures xvii List of Tables xxi List of Theorems xxiii List of Acronyms xxvii List of Symbols xxxi Preface xxxix 1 Introduction 1 1.1 History of Cryptography ............... 1 1.2 Fundamental Principles of Cryptography . 3 1.3 Public-Key Cryptography ............... 6 1.4 Cryptography and the Quantum World . 8 1.5 Outline ......................... 11 1.6 Included Publications . 13 2 Basic Concepts 19 2.1 Linear Algebra ..................... 19 xiii 2.2 Probability Theory ................... 20 2.3 Fundamental Quantum Mechanics . 21 3 Quantum Key Distribution 29 3.1 The BB84 Protocol . 31 3.2 Security Analysis of BB84 . 34 4 Bell’s Theorem 37 4.1 EPR and Hidden Variables . 37 4.2 Intuitive Explanation . 41 4.3 The Black Box Model . 44 4.4 Ekert’s QKD Protocol . 49 4.5 Device-Independent QKD . 51 5 Loopholes in Bell Experiments 57 5.1 The Detection Loophole . 59 5.2 The Coincidence-Time Loophole . 63 5.3 Experimental Bell testing . 67 5.4 Conclusions ...................... 70 6 Energy-Time Entanglement 71 6.1 The Franson Interferometer . 72 6.2 The Postselection Loophole . 76 7 Quantum Hacking 81 7.1 The LHV Attack .................... 82 7.2 The Blinding Attack . 84 7.3 Optical Considerations . 86 7.4 Experimental Demonstration . 91 8 Countermeasures to Quantum Hacking 95 8.1 Chaining the Bell Inequality . 98 8.2 Interferometric Visibility . 105 8.3 Modified Franson Setups . 110 8.4 Conclusions . 115 9 Quantum Bitcoin 117 xiv 9.1 Hashcash . 118 9.2 Bitcoin . 121 9.3 Further Blockchain Developments . 124 9.4 Quantum Money . 125 10 Conclusions 131 10.1 Future Work . 134 Index 137 Bibliography 143 Publications 171 A Energy-Time Entanglement, Elements of Reality, and Local Realism 171 B Hacking the Bell Test Using Classical Light in Energy-Time Entanglement–Based Quantum Key Distribution 189 C Tight Bounds for the Pearle-Braunstein-Caves Chained Inequality Without the Fair-Coincidence Assumption 199 D High-Visibility Time-Bin Entanglement for Testing Chained Bell Inequalities 207 E Quantum Bitcoin: An Anonymous and Distributed Currency Secured by the No-Cloning Theorem of Quantum Mechanics 217 F Comment on “Franson Interference Generated by a Two-Level System” 237 xv List of Figures 1.1 Basic communication scheme for cryptography, adapted from Trappe and Washington [11, p. 3]. Alice and Bob use cryptography to communicate securely in the presence of an eavesdropper, Eve. The message is encrypted using an encryption key, turning the plaintext into a ciphertext before it is broadcast over a public channel. Bob then uses the decryption key to recover the message. ................ 5 3.1 The BB84 QKD protocol. This is a prepare-and- measure QKD protocol, where Alice encodes informa- tion using photons polarized in non-orthogonal bases.
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