Network Coding and Wireless Physical-layer ... - Jacobs University

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Chapter 7: Physical-layer Key Encoding for Wireless Physical-layer Secret-key Generation (WPSG) with Unequal Security Protection (USP) 109 With the summation ∑ 3 i=1 Y i known by wiretapping, and K 1 ⊕ K 3 ⊕ K 5 known if K 1 , K 3 , and K 5 are vulnerable symbols, the enemy knows the summation ∑ 3 i=1 X i. This means, by guessing two bits out of three bits X i , i = 1, 2, 3, correctly, the enemy knows all the three bits. The probability of guessing two bits correctly is 0.25, corresponding to the requirement p t2 = 0.25. We can see that there is no way to derive any three bits with more guessing success probability than 0.25. Therefore, the first condition is not met, meaning that our encryption will be considered scalably secure if the second condition is not met either. By checking every possible way for the enemy to derive all four plaintext bits X i , i = 1, 2, 3, 4, we see that the maximum guessing success probability is 0.125. Since 0.125 = p ti · ( 1 |F| )χ i−c i = 0.25 · ( 1 2 )4−3 , the second condition is not met and our encryption is therefore scalably secure according to the requirement. One may observe that, by using the given scalable security requirement instead of the perfect secrecy requirement, we reduce the number of original symbols I K needed by 40%. 7.8 Conclusion and Future Research We have proposed physical-layer key encoding for the WPSG cryptosystem with onetime pad encryptor. Four theorems indicate the required properties of the codes in order to achieve perfect secrecy of the secret data. After that, we discuss a scalable security framework specifying the degrees of security weakness that can be allowed in lower-priority data. Our framework applies to weakly secure network coding as well as our physicallayer key encoding in a WPSG cryptosystem and, indeed, any key encoding schemes for one-time pad cryptosystems having vulnerable key bits. We show that the number of original key bits needed can be significantly reduced if weak security is allowed. In future, we hope that some algorithms are developed such that, given any scalable security requirement, the code can be systematically designed.
Chapter 8 Summary, Conclusion, and Future Works 8.1 Summary and Conclusion Physical key encoding has been presented in Chapter 7 as a means to protect security in the presence of vulnerable key symbols. The encoded output key is shorter than the input, thus sacrificing some key length for the sake of security. The counterpart of physical key encoding is Slepian-Wolf coding, which adds some redundancy to the quantized key such that legitimate receivers are protected against key mismatch due to channel estimation error. The relationship between physical key encoding and Slepian-Wolf coding in WPSG is similar to source coding and channel coding in a communication system in such a way that the latter expands what the former contracts. It is proved that optimality can be achieved when the source coding and the channel coding in a communication perform their tasks separately. It is yet to be proved whether such optimality holds with the separation of physical key encoding and Slepian-Wolf coding in WPSG. Just as channel coding has an unequal-error-protection (UEP) capability, physical key encoding has an unequal-security-protection (USP) capability. The concept of USP or scalable security has been previously discussed [22, 27, 32, 72], but it is more precisely 110
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Network Coding and Wireless Physica
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Abstract The general abstraction of
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Contents Abstract i Abstract ii Dec
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vi CONTENTS 5.4 Degree Distribution
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List of Figures 2.1 A basic digital
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x LIST OF FIGURES 5.11 Comparison o
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Part I Motivation, Overview, and In
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Chapter 1: Motivation and Overview
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Chapter 2 Introduction to Digital C
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Chapter 2: Introduction to Digital
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33 The emergence of scalable video
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Chapter 4: Unequal Erasure Protecti
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Page 132 and 133: Bibliography [1] 3GPP, “3GPP; Tec
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Page 138 and 139: BIBLIOGRAPHY 125 [63] S. Jaggi, P.
Page 140: BIBLIOGRAPHY 127 [81] X. Sun, X. Wu
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