By exploiting multipath fading channels as a source of common randomness, physical layer (PHY) based key generation protocols allow two terminals with correlated observations to generate secret keys with information-theoretical security. The state of the art, however, still suffers from major limitations, e.g., low key generation rate, lower entropy of key bits and a high reliance on node mobility. In this paper, a novel cooperative key generation protocol is developed to facilitate high-rate key generation in narrowband fading channels, where two keying nodes extract the phase randomness of the fading channel with the aid of relay node(s). For the first time, we explicitly consider the effect of estimation methods on the extraction of secret key bits from the underlying fading channels and focus on a popular statistical method--maximum likelihood estimation (MLE). The performance of the cooperative key generation scheme is extensively evaluated theoretically. We successfully establish both a theoretical upper bound on the maximum secret key rate from mutual information of correlated random sources and a more practical upper bound from Cramer-Rao bound (CRB) in estimation theory. Numerical examples and simulation studies are also presented to demonstrate the performance of the cooperative key generation system. The results show that the key rate can be improved by a couple of orders of magnitude compared to the existing approaches.
The PHY based key generation can be traced back to the original information-theoretic formulation of secure communication due to @cite_0 . Building on information theory, @cite_7 @cite_8 @cite_20 characterized the fundamental bounds and showed the feasibility of generating keys using external random source-channel impulse response. To the best of our knowledge, the first key generation scheme suitable for wireless network was proposed in @cite_6 . In @cite_6 , the differential phase between two frequency tones is encoded for key generation. Error control coding techniques are used for enhancing the reliability of key generation. Similar to @cite_6 , a technique of using random phase for extracting secret keys in an OFDM system through channel estimation and quantization was recently proposed in @cite_21 . This paper characterized the probability of generating the same bit vector between two nodes as a function of signal-to-interference-and-noise (SINR) and quantization levels.
@cite_7 @cite_8 @cite_21 @cite_6 @cite_0 @cite_20
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All information-theoretically secure key agreement protocols (e.g. based on quantum cryptography or on noisy channels) described in the literature are secure only against passive adversaries in the sense that they assume the existence of an authenticated public channel. The goal of this paper is to investigate information-theoretic security even against active adversaries with complete control over the communication channel connecting the two parties who want to agree on a secret key. Several impossibility results are proved and some scenarios are characterized in which secret-key agreement secure against active adversaries is possible. In particular, when each of the parties, including the adversary, can observe a sequence of random variables that are correlated between the parties, the rate at which key agreement against active adversaries is possible is characterized completely: it is either 0 or equal to the rate achievable against passive adversaries, and the condition for distinguishing between the two cases is given. This is the first part of a three-part paper on secret-key agreement secure against active adversaries. In all three parts, we address the question whether two parties, knowing some correlated pieces of information X and Y, respectively, can generate a string S about which an adversary, knowing some information Z and having read and write access to the communication channel used by the legitimate partners, is almost completely ignorant. Whether such key agreement is possible, and if yes at which rate, is an inherent property of the joint probability distribution PXYZ. In this part, we first prove a number of general impossibility results. We then consider the important special case where the legitimate partners as well as the adversary have access to the outcomes of many independent repetitions of a fixed tripartite random experiment. In this case, the result characterizing the possibility of secret-key agreement secure against active adversaries is of all-or-nothing nature: either a secret key can be generated at the same rate as in the (well-studied) passive-adversary case, or such secret-key agreement is completely impossible. The exact condition characterizing the two cases is presented. Secure wireless communications is a challenging problem due to the shared nature of the wireless medium. Most existing security protocols apply cryptographic techniques for bit scrambling at the application layer by exploiting a shared secret key between pairs of communicating nodes. However, more recent research argues that multipath propagation - a salient feature of wireless channels - provides a physical resource for secure communications. In this context, we propose a protocol that exploits the inherent randomness in multipath wireless channels for generating secret keys through channel estimation and quantization. Our approach is particularly attractive in wideband channels which exhibit a large number of statistically independent degrees of freedom (DoF), thereby enabling the generation of large, more-secure, keys. We show that the resulting keys are distinct for distinct pairwise links with a probability that increases exponentially with the key-size channel DoF. We also characterize the probability that the two users sharing a common link generate the same key. This characterization is used to analyze the energy consumption in successful acquisition of a secret key by the two users. For a given key size, our results show that there is an optimum transmit power, and an optimum quantization strategy, that minimizes the energy consumption. The proposed approach to secret key generation through channel quantization also obviates the problem of key pre-distribution inherent to many existing cryptographic approaches. Abstract Hassan, A. A., Stark, W. E., Hershey, J. E., and Chennakeshu, S., Cryptographic Key Agreement for Mobile Radio, Digital Signal Processing 6 (1996), 207–212. The problem of establishing a mutually held secret cryptographic key using a radio channel is addressed. The performance of a particular key distribution system is evaluated for a practical mobile radio communications system. The performance measure taken is probabilistic, and different from the Shannon measure of perfect secrecy. In particular, it is shown that by using a channel decoder, the probability of two users establishing a secret key is close to one, while the probability of an adversary generating the same key is close to zero. The number of possible keys is large enough that exhaustive search is impractical. THE problems of cryptography and secrecy systems furnish an interesting application of communication theory.1 In this paper a theory of secrecy systems is developed. The approach is on a theoretical level and is intended to complement the treatment found in standard works on cryptography.2 There, a detailed study is made of the many standard types of codes and ciphers, and of the ways of breaking them. We will be more concerned with the general mathematical structure and properties of secrecy systems. As the first part of a study of problems involving common randomness at distance locations, information-theoretic models of secret sharing (generating a common random key at two terminals, without letting an eavesdropper obtain information about this key) are considered. The concept of key-capacity is defined. Single-letter formulas of key-capacity are obtained for several models, and bounds to key-capacity are derived for other models. >