Contributions to Information Theoretically Secure Communication
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University of Calgary PRISM: University of Calgary's Digital Repository Graduate Studies The Vault: Electronic Theses and Dissertations 2020-05-15 Contributions to Information Theoretically Secure Communication Sharifian, Setareh Sharifian, S. (2020). Contributions to Information Theoretically Secure Communication (Unpublished doctoral thesis). University of Calgary, Calgary, AB. http://hdl.handle.net/1880/112107 doctoral thesis University of Calgary graduate students retain copyright ownership and moral rights for their thesis. You may use this material in any way that is permitted by the Copyright Act or through licensing that has been assigned to the document. For uses that are not allowable under copyright legislation or licensing, you are required to seek permission. Downloaded from PRISM: https://prism.ucalgary.ca UNIVERSITY OF CALGARY Contributions to Information Theoretically Secure Communication by Setareh Sharifian A THESIS SUBMITTED TO THE FACULTY OF GRADUATE STUDIES IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY GRADUATE PROGRAM IN COMPUTER SCIENCE CALGARY, ALBERTA MAY, 2020 c Setareh Sharifian 2020 Abstract Secure communication ensures the integrity and confidentiality of communication between connected devices. An information-theoretic approach to secure communication gives the strongest confidentiality guarantee by assuming that the attacker has unlimited computing power. The earliest formal model and definition of information-theoretic secure communication is by Shannon, who employed a secret key shared between communicating parties to provide confidentiality. An alternative elegant information-theoretic approach to secure communication views the natural characteristics of the environment (i.e., channel’s noise) as a resource to build security functionalities. This approach was first proposed by Wyner, and the corresponding secure communication model is called the wiretap channel model. These two approaches introduce two primary resources for providing information-theoretic secure communication: the shared secret key and physical properties of the communication medium. In this thesis, we study how to employ the above two resources for secure message transmission. We study this by using channel’s noise in the wiretap channel model. In this model, a sender is connected to the receiver and the adversary through two noisy channels. We propose a new wiretap encoding scheme with strong secrecy that provides perfect secrecy and reliability, asymptotically. The construction treats the noise in the adversary’s channel as a source of randomness that is extracted and used to hide the message from the adversary. We realize the wiretap channel model using cooperative jamming to evaluate the performance of wiretap codes in practice. We consider a model called keyed wiretap channel that unifies Wyner’s model with Shannon’s model of perfect secrecy for information systems, and propose a keyed encoding schemes with strong secrecy and other properties that are attractive in practice. We also study two-party information-theoretic secret key agreement when the two parties have access to samples of a common source of randomness and use a single message transmission to arrive at a shared random key. We propose a secret key agreement protocol in this setting, prove its security, and show its superior performance compared to other known protocols with the same properties. Finally, we propose an information-theoretic secret key agreement over a virtual wiretap channel created by cooperative jamming. ii Acknowledgements First of all, I would like to thank my supervisor, Dr. Reihaneh Safavi-Naini for her extensive support, patience and guidance during my studies, and for the opportunity to work in her exceptional research group. My sincere thanks goes to my supervisory committee, Dr. Michael J. Jacobson and Dr. Carey Williamson for providing valuable directions to improve my research outcome. I’m also thankful to Dr. Christoph Simon, G¨unther Ruhe and Dr. Prakash Narayan who provided me with constructive comments on this thesis. I appreciate that despite their busy schedule, they accepted to be members of my examining committee. I would especially like to thank Fuchun Lin and Alireza Poustindouz for their significant collaborations. I would like to thank the fellows of the ISPIA lab and the vibrant academic community of the department of computer science at the University of Calgary whom I had the pleasure of working with during my research tenure. I am also thankful to my friends Sepideh Avizheh, Niloufar Dadkhah, Mahshid Marbouti, and all those who were my best friends and companions on this journey. Last but not the least, I am thankful to my wonderful family for their unlimited support during my studies. I owe a great debt to my brother, mother, and father without whom none of this would be possible. iii Dedicated to the memory of all the dear stolen lives of flight PS752. iv Table of Contents Abstract ii Acknowledgements iii Dedication iv Table of Contents viii List of Figures ix List of Tables x List of Abbreviations xi Epigraph xiii 1 Introduction 1 1.1 Objectives . .2 1.1.1 Problem 1: How to securely transmit a message using noisy channels? . .3 1.1.2 Problem 2: How to securely transmit a message using noisy channels and a secret key?6 1.1.3 Problem 3: How to establish an information-theoretic secret key? . .7 1.2 Contributions . .9 1.2.1 Modular semantically secure wiretap encoding . .9 1.2.2 Modular semantically secure keyed wiretap encoding . 12 1.2.3 Information-theoretic secret key agreement . 13 1.3 Background . 14 1.3.1 Inequalities . 14 1.3.2 Information measures . 14 1.3.3 Communication channels . 15 1.3.4 Randomness extraction . 17 1.4 Organization . 18 I Modular Semantically Secure Wiretap Encoding 19 2 Hash-then-Encode: A Modular Semantically Secure Wiretap Code 20 2.1 Introduction . 20 2.1.1 Our work . 22 2.1.2 Related works . 23 2.2 Preliminaries . 24 2.3 A modular construction of efficiently invertible UHFs (ei-UHF) . 26 2.4 The HtE (Hash-then-Encode) construction . 28 2.4.1 Hash-then-Encode (HtE).................................. 28 2.4.2 Achieving the capacity . 30 v 2.4.3 Effective rate for short messages . 33 2.5 Concluding remarks . 33 3 Post-Quantum Security using Channel Noise 34 3.1 Introduction . 34 3.2 Approach . 36 3.3 Results . 38 3.4 Conclusion . 40 4 A Virtual Wiretap Channel for Secure Message Transmission 41 4.1 Introduction . 42 4.1.1 Our work . 43 4.1.2 Related works . 44 4.2 Preliminaries and notations . 45 4.2.1 QAM and OFDM . 47 4.2.2 iJam and Basic iJam Transmission (BiT) protocol . 47 4.2.3 Eavesdropper’s strategies . 48 4.3 BiT as a virtual wiretap channel – An example . 48 4.4 Virtual wiretap channel model . 51 4.5 Secure message transmission using BiT . 54 4.5.1 A semantically secure wiretap code . 54 N 4.5.2 Using the wiretap construction with BiTη,q ........................ 55 4.6 BiT over noisy receiver’s channel . 55 4.7 Conclusion and future works . 58 II Modular Semantically Secure Keyed Wiretap Encoding 60 5 A Modular Semantically Secure Wiretap Code with Shared Key for Weakly Symmetric Channels 61 5.1 Introduction . 61 5.1.1 Our work . 62 5.2 Preliminaries . 63 5.2.1 Notations and background . 63 5.2.2 Channels . 63 5.3 Wiretap channel with shared key . 65 5.4 The capacity-achieving construction . 66 5.4.1 The KHtE construction . 67 6 72 6.1 Introduction . 73 6.2 Preliminaries . 75 6.2.1 Notations . 75 6.2.2 Communication channels . 76 6.2.3 Randomness extractors . 78 6.3 Wiretap channels and keyed wiretap channels . 79 6.3.1 Wiretap coding . 79 6.3.2 Constructions of wiretap codes . 82 6.3.3 Wiretap channel with a shared key. 84 6.3.4 Codes for keyed wiretap channel encryption . 86 6.3.5 Our work . 87 6.4 KHtE∗: A new keyed wiretap encryption scheme . 88 6.4.1 Overview . 89 6.4.2 KHtE∗ construction . 90 6.4.3 Amortizing the seed . 98 vi 6.5 Special cases . 98 6.5.1 Wiretap chanel construction: RK =0 ........................... 99 6.5.2 One-Time Pad: Cs(WT)=0 ................................ 100 6.6 Using the construction in practice . 101 6.6.1 Single block encryption . 101 6.6.2 Encryption of 2t blocks................................... 102 6.7 Related works . 106 6.8 Concluding remarks . ..