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A Study of Secrecy Codes and Their Real-World Performance Thesis Directed by Assistant Professor Willie K

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A Study of Secrecy Codes and Their Real-World Performance Thesis Directed by Assistant Professor Willie K ASTUDY OF SECRECY CODES AND THEIR REAL-WORLD PERFORMANCE BY JAYADEV VASANTH NAIR A THESIS SUBMITTED TO THE GRADUATE FACULTY OF THE UNIVERSITY OF COLORADO COLORADO SPRINGS IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE DEPARTMENT OF ELECTRICAL AND COMPUTER ENGINEERING 2017 ii THIS THESIS FOR THE MASTER OF SCIENCE DEGREE BY JAYADEV VASANTH NAIR HAS BEEN APPROVED FOR THE DEPARTMENT OF ELECTRICAL AND COMPUTER ENGINEERING BY WILLIE K. HARRISON,CHAIR MARK A. WICKERT M. SCOTT TRIMBOLI Date 05/04/2017 iii Vasanth Nair, Jayadev (M.S. Electrical Engineering) A Study of Secrecy Codes and Their Real-World Performance Thesis directed by Assistant Professor Willie K. Harrison ABSTRACT This paper presents established works in the physical-layer security and information theory domain, discussing concepts and definitions relevant to the experimental setup. We discuss the wiretap channel model, its relevance, and the secrecy coding methods employed. These methods are then utilized with specific code constructions like LDPC, and Reed-Muller codes, and their performance over binary erasure channels (BEC) and binary symmetric chan- nels (BSC), using error rate curves, are studied. This is then expanded to a Gaussian channel with the help of radios and the transmission performance is studied. With this information, we seek to arrive at a ranking of codes, to determine if there is a better code suited to secrecy applications. iv ACKNOWLEDGEMENTS I would like to express my sincere gratitude to my advisor Dr. Willie Har- rison, for his guidance, support, and enthusiasm. Dr. Harrison’s willingness to help out with every roadblock I’ve hit through this research, has been im- mense and it has gone a long way in helping me achieve my goals. I would also like to thank Sam Schmidt, for his endless and patient sup- port during my Master’s course, and for always being only a phone call away for help. Above all, I would like to thank my family: my better half Lekshmi Prathap, my parents Jayashree Narayanan and Vasanth Kumar Nair, my brother Jayanth Nair, for all that they have blessed me with. v TABLE OF CONTENTS CHAPTER IINTRODUCTION .............................. 1 II PHYSICAL LAYER SECURITY ...................... 4 Linear Block Codes . 4 Wiretap Channel . 8 Secrecy and Secrecy Coding Fundamentals . 11 III CODING STRATEGY ........................... 16 Syndrome Coding. 16 Linear Codes to be Used in Secrecy Designs . 20 Low-Density Parity Check Codes. 20 Reed-Muller Codes . 23 Other Codes . 26 Bit Error Rate (BER) Curves . 26 IV EXPERIMENTS AND RESULTS ..................... 28 System Description . 28 LDPC Construction. 29 Reed-Muller Code Construction . 30 Random and Worst Code Constructions . 30 Simulation Setup . 31 Radio Transmission Setup . 33 Results . 35 Simulation Results . 35 Radio Transmission Results . 38 VCONCLUSION AND FUTURE WORK . 40 Conclusion . 40 Future Work . 42 BIBLIOGRAPHY .............................. 43 vi LIST OF FIGURES FIGURE 2.1 A standard array table [21]. 8 2.2 The wiretap channel model. 9 2.3 The BSC wiretap channel model. 10 3.1 The BEC channel model. 17 3.2 Syndrome table [21] with M number of codewords per coset, and N cosets. 18 3.3 Tanner graph for the parity check matrix in (3.7). The nodes on the right hand side are the check nodes, while the nodes on the left are the variable nodes. 21 3.4 Reed-Muller code is found to have the highest equivocation rates amongst all (8, 4) codes. 25 4.1 GNU Radio transmitter flowgraph. 34 4.2 GNU Radio receiver flowgraph. 34 4.3 Error performance of all (8, 4) codes over the binary erasure channel. 35 4.4 Error performance of all (128, 64) codes over the binary erasure channel. 36 4.5 Error performance of all (8, 4) codes over the binary symmetric channel. 37 4.6 Error performance of all (128, 64) codes over the binary sym- metric channel. 37 1 CHAPTER I INTRODUCTION Cryptography, in general, has taken on several different methods of im- plementation given the varying requirements for privacy and confidentiality today. With the Internet continually growing in complexity, calls for mea- sures that guarantee data security are more prominent. One of the earliest forms of encryption was in using mono-alphabetic substitution ciphers, and it has since evolved to much larger, and more complex forms with the advent of military strategies, and technology in general. Regardless of complexity, when attempting to transmit data, the two criteria relevant to this discussion are ‘reliability’ and ‘security’; how reliably can data be sent across a channel, such that the intended receiver is able to correctly decipher and decode the data, and how well does that encryption scheme guarantee that the data is not compromised to a third-party? Unlike other implementations of cryptography, physical layer security is a technique that specifically targets the physical layer of a communication system; exploiting characteristics like thermal noise, interference, and the time-varying nature of fading channels [3]. This technique also envelopes the addition of coding strategies to the transmitted signal which further ex- ploit the channel properties to ensure that a third-party, also termed an eaves- dropper, is unable to detect or decode the message. Such a method allows for the physical location of the eavesdropper to be detrimental in its attempt to Chapter I. INTRODUCTION 2 decipher the message. The wiretap channel model introduced by Wyner in [24] is an example of a system that exploits channel conditions to ensure that the eavesdropper is not able to read any transmitted message. This model works on the assump- tion that the channel between the sender and the eavesdropper is ‘noisier’ than the channel between the sender and the legitimate receiver. For discrete memoryless channels, a channel property that is often related to its ‘noisi- ness’ is its crossover/erasure probability, i.e., the probability with which a transmitted bit is flipped or lost. Therefore, if the sender-eavesdropper chan- nel has a greater chance of a bit-flip or a bit-loss than the sender-receiver channel, then that channel is said to be ‘noisier’. As [23] describes, there are two major reasons why a wiretap channel set- ting is of relevance: (1) no assumptions are made regarding the eavesdrop- per’s computational ability, and (2) there is no key distribution between the sender and receiver. Reason (1) essentially implies information-theoretic secu- rity, where the eavesdropper, even with unlimited computational power, can never have enough information to retrieve the message. The eavesdropper could also potentially have access to the encoding/decoding scheme that is followed. Therefore, the intention behind using a wiretap model is solely to disarm the eavesdropper’s ability to decipher the correct message, by using channel noise to distort the message. Secrecy codes are generally designed for such a channel model, and this is where the two criteria that we introduced earlier, reliability and security, come into play. The aim of any secrecy code would be to not only meet the reliabil- ity criterion, but also to ensure that in doing so, security is not compromised. The channel capacity, as Shannon describes in [18], is the maximum rate at which the reliability criterion can be met. The maximum achievable rate that also meets the security criterion, in a wiretap channel model, was found to Chapter I. INTRODUCTION 3 be the difference between the receiver channel capacity and the eavesdrop- per (or wiretapper’s) channel capacity, under certain specific conditions [23]. This rate is labeled as the secrecy capacity. This capacity was shown to be zero, unless the eavesdropper’s channel is noisier than the main channel, in [8]. Wyner in [24], explained how secrecy capacity is achieved by means of an encoder that separates codewords into cosets, allowing one message to be mapped to one of several random codewords within a large coset. This allows for data to be reliably decoded by the legitimate receiver, while guar- anteeing secrecy through the randomness that each sub-code provides. This forms the basis for the coding scheme that is relevant to our discussion, coset coding. In this paper, we attempt to study different code constructions, imple- mented through coset coding, and their performance over certain channels, in an effort to discern if there is a better or best code under fixed block lengths, for secrecy applications. The paper discusses the expected perfor- mances, determined by simulated error curves, and attempts to corroborate these with results from a real-world environment test using Universal Soft- ware Radio Peripheral (USRP) boards. 4 CHAPTER II PHYSICAL LAYER SECURITY Physical layer security, as introduced earlier, focuses on the physical layer of a communication system, to achieve security. This technique exploits char- acteristics like noise and interference, such that the channel statistics of a receiver allow system designers to make information-theoretic security guar- antees, implying that the eavesdropper can never have enough information to successfully decode the message. This chapter will provide a background into how this can be achieved in a communication system, and how the ad- dition of certain coding methods can improve secrecy. Before we begin describing the systems and code constructions we em- ploy in this paper, it is perhaps vital to know and understand what comprises a code. 2.1 Linear Block Codes In our experiments, and in coding theory in general, the transmitter aims to encode a certain message into a codeword, transmit over a channel, and subsequently have the receiver decode the message without error, even when the channel is noisy. Linear codes determine how a message is mapped to a codeword. Through this paper we aim to use only binary alphabets in {0, 1}, to represent our messages and codewords.
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