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Secret Key Agreement by Public Discussion From Common Information
 IEEE Transactions on Information Theory
, 1993
"... . The problem of generating a shared secret key S by two parties knowing dependent random variables X and Y , respectively, but not sharing a secret key initially, is considered. An enemy who knows the random variable Z, jointly distributed with X and Y according to some probability distribution PX ..."
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Cited by 440 (18 self)
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. The problem of generating a shared secret key S by two parties knowing dependent random variables X and Y , respectively, but not sharing a secret key initially, is considered. An enemy who knows the random variable Z, jointly distributed with X and Y according to some probability distribution PXY Z , can also receive all messages exchanged by the two parties over a public channel. The goal of a protocol is that the enemy obtains at most a negligible amount of information about S. Upper bounds on H(S) as a function of PXY Z are presented. Lower bounds on the rate H(S)=N (as N !1) are derived for the case where X = [X 1 ; : : : ; XN ], Y = [Y 1 ; : : : ; YN ] and Z = [Z 1 ; : : : ; ZN ] result from N independent executions of a random experiment generating X i ; Y i and Z i , for i = 1; : : : ; N . In particular it is shown that such secret key agreement is possible for a scenario where all three parties receive the output of a binary symmetric source over independent binary symmetr...
Generalized privacy amplification
 IEEE Transactions on Information Theory
, 1995
"... Abstract This paper provides a general treatment of privacy amplification by public discussion, a concept introduced by Bennett, Brassard, and Robert for a special scenario. Privacy amplification is a process that allows two parties to distill a secret key from a common random variable about which ..."
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Cited by 329 (19 self)
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Abstract This paper provides a general treatment of privacy amplification by public discussion, a concept introduced by Bennett, Brassard, and Robert for a special scenario. Privacy amplification is a process that allows two parties to distill a secret key from a common random variable about which an eavesdropper has partial information. The two parties generally know nothing about the eavesdropper’s information except that it satisfies a certain constraint. The results have applications to unconditionally secure secretkey agreement protocols and quantum cryptography, and they yield results on wiretap and broadcast channels for a considerably strengthened definition of secrecy capacity. Index Terms Cryptography, secretkey agreement, unconditional security, privacy amplification, wiretap channel, secrecy capacity, RCnyi entropy, universal hashing, quantum cryptography. I.
Secure Transmission with Multiple Antennas: The MISOME Wiretap Channel
, 2007
"... The role of multiple antennas for secure communication is investigated within the framework of Wyner’s wiretap channel. We characterize the secrecy capacity in terms of generalized eigenvalues when the sender and eavesdropper have multiple antennas, the intended receiver has a single antenna, and t ..."
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Cited by 235 (20 self)
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The role of multiple antennas for secure communication is investigated within the framework of Wyner’s wiretap channel. We characterize the secrecy capacity in terms of generalized eigenvalues when the sender and eavesdropper have multiple antennas, the intended receiver has a single antenna, and the channel matrices are fixed and known to all the terminals, and show that a beamforming strategy is capacityachieving. In addition, we show that in the high signaltonoise (SNR) ratio regime the penalty for not knowing eavesdropper’s channel is small—a simple “secure spacetime code ” that can be thought of as masked beamforming and radiates power isotropically attains nearoptimal performance. In the limit of large number of antennas, we obtain a realizationindependent characterization of the secrecy capacity as a function of the number β: the number of eavesdropper antennas per sender antenna. We show that the eavesdropper is comparatively ineffective when β < 1, but that for β≥2 the eavesdropper can drive the secrecy capacity to zero, thereby blocking secure communication to the intended receiver. Extensions to ergodic fading channels are also provided.
Gamal, “On the secrecy capacity of fading channels
 in Proc. IEEE Int. Symp. Information Theory (ISIT
"... We consider the secure transmission of information over an ergodic fading channel in the presence of an eavesdropper. Our eavesdropper can be viewed as the wireless counterpart of Wyner’s wiretapper. The secrecy capacity of such a system is characterized under the assumption of asymptotically long c ..."
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Cited by 203 (9 self)
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We consider the secure transmission of information over an ergodic fading channel in the presence of an eavesdropper. Our eavesdropper can be viewed as the wireless counterpart of Wyner’s wiretapper. The secrecy capacity of such a system is characterized under the assumption of asymptotically long coherence intervals. We first consider the full Channel State Information (CSI) case, where the transmitter has access to the channel gains of the legitimate receiver and the eavesdropper. The secrecy capacity under this full CSI assumption serves as an upper bound for the secrecy capacity when only the CSI of the legitimate receiver is known at the transmitter, which is characterized next. In each scenario, the perfect secrecy capacity is obtained along with the optimal power and rate allocation strategies. We then propose a lowcomplexity on/off power allocation strategy that achieves nearoptimal performance with only the main channel CSI. More specifically, this scheme is shown to be asymptotically optimal as the average SNR goes to infinity, and interestingly, is shown to attain the secrecy capacity under the full CSI assumption. Remarkably, our results reveal the positive impact of fading on the secrecy capacity and establish the critical role of rate adaptation, based on the main channel CSI, in facilitating secure communications over slow fading channels. 1
Secure communication over fading channels
, 2007
"... The fading broadcast channel with confidential messages (BCC) is investigated, where a source node has common information for two receivers (receivers 1 and 2), and has confidential information intended only for receiver 1. The confidential information needs to be kept as secret as possible from rec ..."
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Cited by 188 (21 self)
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The fading broadcast channel with confidential messages (BCC) is investigated, where a source node has common information for two receivers (receivers 1 and 2), and has confidential information intended only for receiver 1. The confidential information needs to be kept as secret as possible from receiver 2. The broadcast channel from the source node to receivers 1 and 2 is corrupted by multiplicative fading gain coefficients in addition to additive Gaussian noise terms. The channel state information (CSI) is assumed to be known at both the transmitter and the receivers. The parallel BCC with independent subchannels is first studied, which serves as an informationtheoretic model for the fading BCC. The secrecy capacity region of the parallel BCC is established. This result is then specialized to give the secrecy capacity region of the parallel BCC with degraded subchannels. The secrecy capacity region is then established for the parallel Gaussian BCC, and the optimal source power allocations that achieve the boundary of the secrecy capacity region are derived. In particular, the secrecy capacity region is established for the basic Gaussian BCC. The secrecy capacity results are then
Quantum cryptography
 Rev. Mod. Phys
, 2002
"... Quantum cryptography could well be the first application of quantum mechanics at the individual quanta level. The very fast progress in both theory and experiments over the recent years are reviewed, with emphasis on open questions and technological issues. Contents I ..."
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Cited by 182 (6 self)
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Quantum cryptography could well be the first application of quantum mechanics at the individual quanta level. The very fast progress in both theory and experiments over the recent years are reviewed, with emphasis on open questions and technological issues. Contents I
Discrete memoryless interference and broadcast channels with confidential messages: secrecy rate regions
 IEEE Transactions on Information Theory
, 2008
"... Abstract — Discrete memoryless interference and broadcast channels in which independent confidential messages are sent to two receivers are considered. Confidential messages are transmitted to each receiver with perfect secrecy, as measured by the equivocation at the other receiver. In this paper, w ..."
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Cited by 161 (12 self)
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Abstract — Discrete memoryless interference and broadcast channels in which independent confidential messages are sent to two receivers are considered. Confidential messages are transmitted to each receiver with perfect secrecy, as measured by the equivocation at the other receiver. In this paper, we derive inner and outer bounds for the achievable rate regions for these two communication systems. I.
Wireless informationtheoretic security  part I: Theoretical aspects
 IEEE Trans. on Information Theory
, 2006
"... In this twopart paper, we consider the transmission of confidential data over wireless wiretap channels. The first part presents an informationtheoretic problem formulation in which two legitimate partners communicate over a quasistatic fading channel and an eavesdropper observes their transmissi ..."
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Cited by 155 (12 self)
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In this twopart paper, we consider the transmission of confidential data over wireless wiretap channels. The first part presents an informationtheoretic problem formulation in which two legitimate partners communicate over a quasistatic fading channel and an eavesdropper observes their transmissions through another independent quasistatic fading channel. We define the secrecy capacity in terms of outage probability and provide a complete characterization of the maximum transmission rate at which the eavesdropper is unable to decode any information. In sharp contrast with known results for Gaussian wiretap channels (without feedback), our contribution shows that in the presence of fading informationtheoretic security is achievable even when the eavesdropper has a better average signaltonoise ratio (SNR) than the legitimate receiver — fading thus turns out to be a friend and not a foe. The issue of imperfect channel state information is also addressed. Practical schemes for wireless informationtheoretic security are presented in Part II, which in some cases comes close to the secrecy capacity limits given in this paper.
The relayeavesdropper channel: Cooperation for secrecy
 IEEE Trans. on Inf. Theory
, 2006
"... This paper establishes the utility of user cooperation in facilitating secure wireless communications. In particular, the fourterminal relayeavesdropper channel is introduced and an outerbound on the optimal rateequivocation region is derived. Several cooperation strategies are then devised and ..."
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Cited by 153 (6 self)
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This paper establishes the utility of user cooperation in facilitating secure wireless communications. In particular, the fourterminal relayeavesdropper channel is introduced and an outerbound on the optimal rateequivocation region is derived. Several cooperation strategies are then devised and the corresponding achievable rateequivocation region are characterized. Of particular interest is the novel NoiseForwarding (NF) strategy, where the relay node sends codewords independent of the source message to confuse the eavesdropper. This strategy is used to illustrate the deaf helper phenomenon, where the relay is able to facilitate secure communications while being totally ignorant of the transmitted messages. Furthermore, NF is shown to increase the secrecy capacity in the reversely degraded scenario, where the relay node fails to offer performance gains in the classical setting. The gain offered by the proposed cooperation strategies is then proved theoretically and validated numerically in the additive White Gaussian Noise (AWGN) channel. I.
Coding for Computing
 IEEE Transactions on Information Theory
, 1998
"... A sender communicates with a receiver who wishes to reliably evaluate a function of their combined data. We show that if only the sender can transmit, the number of bits required is a conditional entropy of a naturally defined graph. We also determine the number of bits needed when the communicators ..."
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Cited by 142 (0 self)
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A sender communicates with a receiver who wishes to reliably evaluate a function of their combined data. We show that if only the sender can transmit, the number of bits required is a conditional entropy of a naturally defined graph. We also determine the number of bits needed when the communicators exchange two messages. 1 Introduction Let f be a function of two random variables X and Y . A sender PX knows X, a receiver PY knows Y , and both want PY to reliably determine f(X; Y ). How many bits must PX transmit? Embedding this communicationcomplexity scenario (Yao [22]) in the standard informationtheoretic setting (Shannon [17]), we assume that (1) f(X; Y ) must be determined for a block of many independent (X; Y )instances, (2) PX transmits after observing the whole block of X instances, (3) a vanishing block error probability is allowed, and (4) the problem's rate L f (XjY ) is the number of bits transmitted for the block, normalized by the number of instances. Two simple bou...