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Capacity results for compound wiretap channels
Abstract
We derive a lower bound on the secrecy capacity of the compound wiretap
channel with channel state information at the transmitter which matches the
general upper bound on the secrecy capacity of general compound wiretap
channels given by Liang et al. and thus establishing a full coding theorem in
this case. We achieve this with a quite strong secrecy criterion and with a
decoder that is robust against the effect of randomisation in the encoding.
This relieves us from the need of decoding the randomisation parameter which is
in general not possible within this model. Moreover we prove a lower bound on
the secrecy capacity of the compound wiretap channel without channel state
information.
... This means that even if this criterion holds, one still does not know what a non-legitimate receiver can or cannot do to decode the confidential message. A criterion that can be given an operational meaning is the criterion of strong secrecy introduced by Maurer and Wolf in [11]: it was established in [12] [13] for the wiretap channel that under the strong secrecy criterion, the average decoding error at a non-legitimate receiver tends to one for any decoder it may use. This criterion is stronger than the one used so far. ...
... The observation of [12] [13] constitutes the main motivation to consider strong secrecy in bidirectional relay networks as depicted in Figure 1. Here a relay node establishes a bidirectional communication between two other nodes using a decode-and-forward protocol [14] [15] [16] [17] and at the same time transmits an additional confidential message to one node while keeping the other non-legitimate node completely ignorant of it. ...
... It is shown in [12] [13] ...
To increase the spectral efficiency of future wireless networks, it is important to wisely integrate multiple services at the physical layer. Here we study the efficient integration of confidential services in bidirectional relay networks, where a relay node establishes a bidirectional communication between two other nodes using a decode-and-forward protocol. In the broadcast phase the relay transmits an additional confidential message to one node while keeping the other node completely ignorant of it. We use the concept of strong information theoretic security to ensure that the non-legitimate node cannot decode the confidential message no matter what its computational resources are. This results in the study of the bidirectional broadcast channel with confidential messages for which we establish the strong secrecy capacity region.
... In [19] the authors required that the receiver's average error goes to zero and that the wiretapper is not able to detect the message using the same security criterion as in [32]. The result of [19] was improved in [8] by using a stronger condition for the limit of legitimate receiver's error, i.e., the maximal error should go to zero, as well as a stronger condition for the security criterion (c.f. Remark 1). ...
... [32] for wiretap channel's security criterion), is obtained if we replace (9) with max t∈θ 1 n I(X uni ; K n t ) ≤ ε . In this paper we will follow [8] and use (9). ...
... It was shown in [8] that for any positive ω, if we set ...
We determine the secrecy capacity of the compound channel with quantum
wiretapper and channel state information at the transmitter. Moreover, we
derive a lower bound on the secrecy capacity of this channel without channel
state information and determine the secrecy capacity of the compound
classical-quantum wiretap channel with channel state information at the
transmitter. We use this result to derive a new proof for a lower bound on the
entanglement generating capacity of compound quantum channel. We also derive a
new proof for the entanglement generating capacity of compound quantum channel
with channel state information at the encoder.
... It was shown in [5] that for any ω > 0, if we set ...
... In view of (5), one has (see [5]) the largest achievable rate, called capacity, of the compound wiretap channel with CSI at the transmitter C S,CSI , is given by ...
... P r Jn j=1 1 J n Ln l=1 1 L n W n t (D j (X) c |X j,l ) > √ T 2 −nω/2 ≤ √ T 2 −nω/2 . (7) Using (7) one can obtain (see [5] ...
We determine the capacity of the classical compound quantum wiretapper
channel with channel state information at the transmitter. Moreover we derive a
lower bound on the capacity of this channel without channel state information
and determine the capacity of the classical quantum compound wiretap channel
with channel state information at the transmitter.
... This means that even if this criterion holds, it is not clear what an eavesdropper can or cannot do to decode the confidential message. But recently, an operational meaning has been given to the strong secrecy criterion introduced by Maurer and Wolf [5]: it was established in [6] [7] for the wiretap channel that the strong secrecy criterion implies that the average decoding error at the eavesdropper tends to one for any decoder it may use. ...
... To date, there is only little work that incorporates both tasks: information theoretic security in interaction with channel uncertainty . The compound wiretap channel is analyzed in [6] [7] [10]. The MIMO compound wiretap channel is studied in [11] and the MIMO compound broadcast channel with confidential messages in [12]. ...
In this paper the compound broadcast channel with confidential messages is studied, where it is only known to the transmitter and receivers that the actual channel realization is fixed and from a pre-specified set of channels. An achievable rate region for the strong secrecy criterion is derived. Further, a multi-letter outer bound is given, which establishes, together with the achievable rate region, a multi-letter expression of the strong secrecy capacity region.
... However, the study of secure communications was not confined to the single-user channels and expanded to multi-terminal channels (Multiple access channels, Interference Channels, etc.). Some related works can be found in [4][5][6][7][8][9]. The basis of all the above models is sending private classical information over a noisy classical channel to one or more legitimate receivers at the presence of one or more passive eavesdroppers. ...
In this paper, the classical-quantum multiple access wiretap channel with a common message is studied under the one-shot setting.
... In the general wiretap channel, a transmitter wants to transmit its message to a legitimate receiver over a noisy channel reliably while keeping the message confidential from eavesdropping. In recent years, many types of wiretap channels have been introduced (see [3][4][5][6][7] and references therein). The multiple access wiretap channel (MA-WTC) was considered in [8] and [9] for the first time. ...
In this paper, the quantum wiretap channel (QWTC) and quantum multiple access channel (QMAC) are used so as to introduce the classical-quantum multiple access wiretap channel (C-QMA-WTC).
... There exist many combinations of these concepts. The classical compound wiretap channel was considered in [29] and [9]. The transmission capacity of the compound wiretap cqq-channel was given in [11]. ...
We study the identification capacity of classical-quantum channels ("cq-channels"), under channel uncertainty and privacy constraints. To be precise, we consider first compound memoryless cq-channels and determine their identification capacity; then we add an eavesdropper, considering compound memoryless wiretap cqq-channels, and determine their secret identification capacity. In the first case (without privacy), we find the identification capacity always equal to the transmission capacity. In the second case, we find a dichotomy: either the secrecy capacity (also known as private capacity) of the channel is zero, and then also the secrecy identification capacity is zero, or the secrecy capacity is positive and then the secrecy identification capacity equals the transmission capacity of the main channel without the wiretapper. We perform the same analysis for the case of arbitrarily varying wiretap cqq-channels (cqq-AVWC), with analogous findings, and make several observations regarding the continuity and super-additivity of the identification capacity in the latter case.
... we have enough resources allocated to saturate the eavesdropper to ensure that I(M ; Z n ) ≤ δ n holds, i.e., strong secrecy (4) is satisfied, cf. for example [26][27][28]. It remains to verify that the legitimate receiver can reliably decode the confidential message. ...
The problem of secure broadcasting with independent secret keys is studied. The particular scenario is analyzed in which a common message has to be broadcast to two legitimate receivers, while keeping an external eavesdropper ignorant of it. The transmitter shares independent secret keys of sufficiently high rates with both legitimate receivers, which can be used in different ways: they can be used as one-time pads to encrypt the common message, as fictitious messages for wiretap coding, or a hybrid of these. In this paper, capacity results are established when the broadcast channels involving the three receivers are degraded. If both legitimate channels are degraded versions of the eavesdropper channel, it is shown that the one-time pad approach is optimal for several cases yielding corresponding capacity expressions. Alternatively, the wiretap coding approach is shown to be optimal if the eavesdropper channel is degraded with respect to both legitimate channels establishing capacity in this case as well. If the eavesdropper channel is neither the strongest nor the weakest, an intricate scheme that carefully combines both concepts of one-time pad and wiretap coding with fictitious messages turns out to be capacity-achieving.
... Csiszár and Körner [2] considered a more general wiretap channel where the wiretap channel did not need to be a degraded version of the main channel, and common messages were also considered there. Other communication models of wiretap channels include wiretap channels with side information [3][4][5][6][7][8], compound wiretap channels [9][10][11][12] and arbitrarily-varying wiretap channels [13]. ...
The secrecy capacity of an extended communication model of wiretap channelII is determined. In this channel model, the source message is encoded into a digital sequence of length N and transmitted to the legitimate receiver through a discrete memoryless channel (DMC). There exists an eavesdropper who is able to observe arbitrary μ = N α digital symbols from the transmitter through a second DMC, where 0 ≤ α ≤ 1 is a constant real number. A pair of an encoder and a decoder is designed to let the receiver be able to recover the source message with a vanishing decoding error probability and keep the eavesdropper ignorant of the message. This communication model includes a variety of wiretap channels as special cases. The coding scheme is based on that designed by Ozarow and Wyner for the classic wiretap channel II.
Common randomness (CR), as a resource, is not commonly exploited in existing practical communication systems. In the CR generation framework, both the sender and receiver aim to generate a common random variable observable to both, ideally with low error probability. The availability of this CR allows us to implement correlated random protocols that can lead to faster and more efficient algorithms. Previous work focused on CR generation over perfect channels with limited capacity. In our work, we consider the problem of CR generation from independent and identically distributed (i.i.d.) samples of a correlated finite source with one-way communication over a Gaussian channel. We first derive the CR capacity for single-input single-output (SISO) Gaussian channels. This result is then used for the derivation of the CR capacity in the multiple-input multiple-output (MIMO) case. CR plays a key role in the identification scheme since it may allow a significant increase in the identification capacity of channels. In the identification framework, the decoder is interested in knowing whether a specific message of special interest to him has been sent or not, rather than knowing what the received message is. In many new applications, such as several machine-to-machine and human-to-machine systems and the tactile internet, this post-Shannon scheme is more efficient than classical transmission. In our work, we also consider a CR-assisted secure identification scheme and develop a lower bound on the corresponding secure identification capacity.
Machine-to-machine and human-to-machine communications are essential aspects incorporated in the framework of fifth generation wireless connectivity.
We determine the identification capacity of compound channels in the presence of a wiretapper. It turns out that the secure identification capacity formula fulfills a dichotomy theorem: It is positive and equals the identification capacity of the channel if its message transmission secrecy capacity is positive. Otherwise, the secure identification capacity is zero. Thus, we show in the case that the secure identification capacity is greater than zero we do not pay a price for secure identification, i.e. the secure identification capacity is equal to the identification capacity. This is in strong contrast to the transmission capacity of the compound wiretap channel. We then use this characterization to investigate the analytic behavior of the secure identification capacity. In particular, it is practically relevant to investigate its continuity behavior as a function of the channels. We completely characterize this continuity behavior. We analyze the (dis-)continuity and (super-)additivity of the capacities. In [12] Alon gave a conjecture about maximal violation for the additivity of capacity functions in graphs.We show that this maximal violation as well holds for the secure identification capacity of compound wiretap channels. This is the first example of a capacity function exhibiting this behavior.
It is becoming more important that next-generation wireless networks wisely integrate multiple services at the physical layer to increase spectral efficiency. In this article, physical layer service integration in wireless networks is considered, where senders not only transmit individual data to certain receivers but also integrate additional multicast or confidential services that have to be kept secret from nonlegitimate receivers. In this context, physical layer security techniques are becoming a promising complement to cryptographic techniques since they establish security using only the physical properties of the wireless channel. State-of-the-art solutions for certain important communication scenarios are discussed, and signal processing challenges and promising research directions are identified.
For communication over arbitrarily varying channels (AVC), common randomness is an important resource to establish reliable communication, especially if the AVC is symmetrizable. In this paper the arbitrarily varying wiretap channel (AVWC) with active wiretapper is studied. Here the wiretapper is active in the sense that it can exploit the knowledge about the common randomness to control the channel conditions of the legitimate users. The common randomness assisted secrecy capacity of the AVWC with active wiretapper is analyzed and is related to the corresponding secrecy capacity of the AVWC with passive wiretapper. If the active secrecy capacity is positive, it equals the corresponding passive secrecy capacity. The case of zero active capacity is also studied.
The wiretap channel models the communication scenario where two legitimate users want to communicate in such a way that an external wiretapper is kept ignorant. In this paper, the wiretap channel with side information is studied, where the wiretapper has additional side information about the transmitted message available for post-processing. The secrecy of the message is modeled by the decoding performance of the wiretapper. It is required for the wiretapper to have worst behavior of decoding performance regardless of the decoding strategy that is used. The secrecy capacity is derived and shown to be equal to the one of the classical wiretap channel without side information available at the wiretapper. Further, the corresponding optimal transceiver design is characterized.
In this work the arbitrarily varying wiretap channel AVWC under the average error criterion and the strong secrecy criterion is studied. We show that in the case of a non-symmetrisable channel to the legitimate receiver the deterministic code secrecy capacity equals the random code secrecy capacity and thus we establish a result for the AVWC similar to that of Ahlswede's dichotomy for ordinary AVCs. We derive a lower bound on the random code secrecy capacity in the case of a best channel to the eavesdropper. We further prove upper bounds on the deterministic code secrecy capacity, which in special cases results in explicit expressions of the secrecy capacity.
Secret key generation describes the problem of generating common randomness between two terminals without giving any information about it to an eavesdropper. In this paper we study secret key generation using compound sources where the terminals have access to correlated components of a compound source and can further use a noiseless public channel for discussion which is open to eavesdroppers. We establish the key-capacity and analyze for different classes of communication protocols the corresponding costs of public communication that are needed for secret key generation using compound sources. Finally, we discuss the case where a wiretapper also observes a correlated component of the source.
In this work, the bidirectional broadcast channel (BBC) with confidential messages is studied. The problem is motivated by the concept of bidirectional relaying in a three-node network, where a half-duplex relay node establishes a bidirectional communication between two other nodes using a decode-and-forward protocol and thereby transmits additional confidential information to one of them in the broadcast phase. The corresponding confidential message is transmitted at a certain secrecy level which characterizes the amount of information that can be kept secret from the non-legitimate node. The capacity-equivocation and secrecy capacity regions of the BBC with confidential messages are established where the latter characterizes the communication scenario with perfect secrecy, which means that the confidential information is completely hidden from the non-legitimate node. Thereby, it is shown that the optimal processing exploits ideas and concepts of the BBC with common messages and of the classical broadcast channel with confidential messages.
In order to increase spectral efficiency, it is becoming more and more important that next generation wireless networks wisely integrate multiple services such as transmissions of private, common, and confidential messages at the physical layer. This is referred to as physical layer service integration, and in this paper is being studied for bidirectional relay networks. Here, a relay node establishes a bidirectional communication between two other nodes using a decode-and-forward protocol. This is also known as two-way relaying. In the broadcast phase, the relay efficiently integrates additional common and confidential services at the physical layer, which then requires the study of the bidirectional broadcast channel (BBC) with common and confidential messages. The entire secrecy capacity regions for discrete memoryless and MIMO Gaussian channels are established. These results further unify previous partial results such as the BBC with common messages or the classical broadcast channel with common and confidential messages, where the relay node provides only some of the services.
We analyze physical-layer security based on the premise that the coding mechanism for secrecy over noisy channels is tied to the notion of channel resolvability. Instead of considering capacity-based constructions, which associate to each message a subcode that operates just below the capacity of the eavesdropper's channel, we consider channel-resolvability-based constructions, which associate to each message a subcode that operates just above the resolvability of the eavesdropper's channel. Building upon the work of Csiszár and Hayashi, we provide further evidence that channel resolvability is a powerful and versatile coding mechanism for secrecy by developing results that hold for strong secrecy metrics and arbitrary channels. Specifically, we show that at least for symmetric wiretap channels, random capacity-based constructions fail to achieve the strong secrecy capacity, while channel-resolvability-based constructions achieve it. We then leverage channel resolvability to establish the secrecy-capacity region of arbitrary broadcast channels with confidential messages and a cost constraint for strong secrecy metrics. Finally, we specialize our results to study the secrecy capacity of wireless channels with perfect channel state information (CSI), mixed channels, and compound channels with receiver CSI, as well as the secret-key capacity of source models for secret-key agreement. By tying secrecy to channel resolvability, we obtain achievable rates for strong secrecy metrics with simple proofs.
To increase the spectral efficiency of future wireless networks, it is important to wisely integrate multiple services at the physical layer. Here the efficient integration of confidential services in the three-node bidirectional relay channel is studied. A relay node establishes a bidirectional communication between two other nodes using a decode-and-forward protocol, which is also known as two-way relaying. In the broadcast phase, the relay transmits not only the two bidirectional messages it received in the previous multiple access phase, but also an additional confidential message to one node while keeping the other node completely ignorant of it. The concept of strong information theoretic secrecy is used to ensure that the nonlegitimate node cannot decode the confidential message no matter what its computational resources are. Moreover, this implies that the average decoding error at the nonlegitimate node goes exponentially fast to one for any decoding strategy it may use. This results in the study of the bidirectional broadcast channel with confidential messages for which the strong secrecy capacity region is established. Furthermore, it is shown that the efficient integration of confidential messages with strong secrecy extends to such scenarios, where the relay further transmits an additional common message to both nodes.
In this work the arbitrarily varying wiretap channel AVWC is studied. We
derive a lower bound on the random code secrecy capacity for the average error
criterion and the strong secrecy criterion in the case of a best channel to the
eavesdropper by using Ahlswede's robustification technique for ordinary AVCs.
We show that in the case of a non-symmetrisable channel to the legitimate
receiver the deterministic code secrecy capacity equals the random code secrecy
capacity, a result similar to Ahlswede's dichotomy result for ordinary AVCs.
Using this we can derive that the lower bound is also valid for the
deterministic code capacity of the AVWC. The proof of the dichotomy result is
based on the elimination technique introduced by Ahlswede for ordinary AVCs. We
further prove upper bounds on the deterministic code secrecy capacity in the
general case, which results in a multi-letter expression for the secrecy
capacity in the case of a best channel to the eavesdropper. Using techniques of
Ahlswede, developed to guarantee the validity of a reliability criterion, the
main contribution of this work is to integrate the strong secrecy criterion
into these techniques.
Bidirectional relaying is a promising approach to improve the performance in wireless networks such as sensor, ad-hoc, and even cellular systems. Bidirectional relaying applies to three-node networks, where a relay establishes a bidirectional communication between two other nodes using a decode-and-forward protocol. First, the two nodes transmit their messages to the relay which decodes them. Then, the relay broadcasts a reencoded message in such a way that both nodes can decode their intended message using their own message as side information. We consider uncertainty in the channel state information (CSI) and assume that all nodes only know that the channel over which the transmission takes place is from a pre-specified set of channels. In this work, we concentrate on the second phase, which is called the compound bidirectional broadcast channel. We present a robust coding strategy which enables reliable communication under channel uncertainty and show that this strategy actually achieves the compound capacity. Further, we analyze scenarios where either the receivers or the transmitter have perfect CSI. We show that CSI at the receivers does not affect the maximal achievable rates, while CSI at the transmitter improves the capacity region. A numerical example and a game-theoretic interpretation complete this work.
This paper considers the compound wiretap channel, which generalizes Wyner's wiretap model to allow the channels to the (legitimate) receiver and to the eavesdropper to take a number of possible states. No matter which states occur, the transmitter guarantees that the receiver decodes its message and that the eavesdropper is kept in full ignorance about the message. The compound wiretap channel can also be viewed as a multicast channel with multiple eavesdroppers, in which the transmitter sends information to all receivers and keeps the information secret from all eavesdroppers. For the discrete memoryless channel, lower and upper bounds on the secrecy capacity are derived. The secrecy capacity is established for the degraded channel and the semideterministic channel with one receiver. The parallel Gaussian channel is further studied. The secrecy capacity and the secrecy degree of freedom (s.d.o.f.) are derived for the degraded case with one receiver. Schemes to achieve the s.d.o.f. for the case with two receivers and two eavesdroppers are constructed to demonstrate the necessity of a prefix channel in encoder design. Finally, the multi-antenna (i.e., MIMO) compound wiretap channel is studied. The secrecy capacity is established for the degraded case and an achievable s.d.o.f. is given for the general case.
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
In information-theoretic models of secure transmission or cooperative secret key generation, the usual secrecy criterion is per letter mutual information. For familiar models, the same secrecy capacity is shown to be achievable with a much stronger criterion. The main tool is a general theorem about a function of a random variable almost uniformly distributed on a large set and almost independent of another random variable, a consequence of a recent result of R. Ahlswede and the author about robust uniform randomness [Common randomness in information theory and cryptography. II: CR capacity, IEEE Trans. Inform. Theory 44, No. 1, 225-240 (1998)].
Csiszár and Körner’s book is widely regarded as a classic in the field of information theory, providing deep insights and expert treatment of the key theoretical issues. It includes in-depth coverage of the mathematics of reliable information transmission, both in two-terminal and multi-terminal network scenarios. Updated and considerably expanded, this new edition presents unique discussions of information theoretic secrecy and of zero-error information theory, including the deep connections of the latter with extremal combinatorics. The presentations of all core subjects are self contained, even the advanced topics, which helps readers to understand the important connections between seemingly different problems. Finally, 320 end-of-chapter problems, together with helpful solving hints, allow readers to develop a full command of the mathematical techniques. It is an ideal resource for graduate students and researchers in electrical and electronic engineering, computer science and applied mathematics. © Akadémiai Kiadó, Budapest 1981 and Cambridge University Press 2011.
We consider the situation in which digital data is to be reliably transmitted over a discrete, memoryless channel (DMC) that is subjected to a wire-tap at the receiver. We assume that the wire-tapper views the channel output via a second DMC. Encoding by the transmitter and decoding by the receiver are permitted. However, the code books used in these operations are assumed to be known by the wire-tapper. The designer attempts to build the encoder-decoder in such a way as to maximize the transmission rate R, and the equivocation d of the data as seen by the wire-tapper. In this paper, we find the trade-off curve between R and d, assuming essentially perfect (“error-free”) transmission. In particular, if d is equal to H s, the entropy of the data source, then we consider that the transmission is accomplished in perfect secrecy. Our results imply that there exists a C8 > 0, such that reliable transmission at rates up to CS is possible in approximately perfect secrecy.
One of the basic problems in cryptography is the generation of a common secret key between two parties, for instance in order
to communicate privately. In this paper we consider information-theoretically secure key agreement. Wyner and subsequently
Csiszár and Körner described and analyzed settings for secret-key agreement based on noisy communication channels. Maurer
as well as Ahlswede and Csiszár generalized these models to a scenario based on correlated randomness and public discussion.
In all these settings, the secrecy capacity and the secret-key rate, respectively, have been defined as the maximal achievable
rates at which a highly-secret key can be generated by the legitimate partners. However, the privacy requirements were too
weak in all these definitions, requiring only the ratio between the adversary’s information and the length of the key to be
negligible, but hence tolerating her to obtain a possibly substantial amount of information about the resulting key in an
absolute sense. We give natural stronger definitions of secrecy capacity and secret-key rate, requiring that the adversary
obtains virtually no information about the entire key. We show that not only secret-key agreement satisfying the strong secrecy
condition is possible, but even that the achievable key-generation rates are equal to the previous weak notions of secrecy
capacity and secret-key rate. Hence the unsatisfactory old definitions can be completely replaced by the new ones. We prove
these results by a generic reduction of strong to weak key agreement. The reduction makes use of extractors, which allow to
keep the required amount of communication negligible as compared to the length of the resulting key.
Following Schumacher and Westmoreland, we address the problem of the capacity of a quantum wiretap channel. We first argue that, in the definition of the so-called quantum privacy, Holevo quantities should be used instead of classical mutual informations. The argument actually shows that the security condition in the definition of a code should limit the wiretappers Holevo quantity. Then we show that this modified quantum privacy is the optimum achievable rate of secure transmission.
We investigate the fundamental secrecy limits of arbitrary wiretap channels using the information-spectrum approach and we provide a random coding theorem for the secrecy capacity under various secrecy metrics. We show how our result specializes to several recent results, e.g., compound channels, parallel channels, and fading channels. As a side benefit, our analysis shows that earlier results hold under more stringent secrecy metrics than previously established.
We derive a lower bound on the secrecy capacity of the compound wiretap
channel with channel state information at the transmitter which matches the
general upper bound on the secrecy capacity of general compound wiretap
channels given by Liang et al. and thus establishing a full coding theorem in
this case. We achieve this with a stronger secrecy criterion and the maximum
error probability criterion, and with a decoder that is robust against the
effect of randomisation in the encoding. This relieves us from the need of
decoding the randomisation parameter which is in general not possible within
this model. Moreover we prove a lower bound on the secrecy capacity of the
compound wiretap channel without channel state information and derive a
multi-letter expression for the capacity in this communication scenario.
Shannon's basic theorem on the capacity of a channel is generalized to the case of a class of memoryless channels. A generalized capacity is defined and is shown to be the supremum of attainable transmission rates when the coding and decoding procedure must be satisfactory for every channel in the class.
A formula for the capacity of a quantum channel for transmitting private classical information is derived. This is shown to be equal to the capacity of the channel for generating a secret key, and neither capacity is enhanced by forward public classical communication. Motivated by the work of Schumacher and Westmoreland on quantum privacy and quantum coherence, parallels between private classical information and quantum information are exploited to obtain an expression for the capacity of a quantum channel for generating pure bipartite entanglement. The latter implies a new proof of the quantum channel coding theorem and a simple proof of the converse. The coherent information plays a role in all of the above mentioned capacities
We present a simple proof of the strong converse for
identification via discrete memoryless quantum channels, based on a
novel covering lemma. The new method is a generalization to quantum
communication channels of Ahlswede's (1979, 1992) approach to classical
channels. It involves a development of explicit large deviation
estimates to the case of random variables taking values in self-adjoint
operators on a Hilbert space. This theory is presented separately in an
appendix, and we illustrate it by showing its application to quantum
generalizations of classical hypergraph covering problems
One of the basic problems in cryptography is the generation of a common secret key between two parties, e.g., in order to communicate privately. In this paper we consider information-theoretically secure key agreement. Wyner and subsequently Csiszár and Korner described and analyzed settings for secret-key agreement based on noisy communication channels. Maurer as well as Ahlswede and Csiszár generalized these models to a scenario based on correlated randomness and public discussion. In all these settings, the secrecy capacity and the secret-key rate, respectively, have been defined as the maximal achievable rates at which a highly-secret key can be generated by the legitimate partners. However, the privacy requirements were too weak in all these definitions, requiring only the adversary's ratio of information to be negligible, but hence tolerating her to obtain a possibly substantial amount of information about the resulting key. It has been unknown previously how to generate keys about which the adversary has virtually no information. We give natural new definitions of secrecy capacity and secret-key rate satisfying this stronger requirement and show that not only secret-key agreement is possible with respect to the strong secrecy condition, but even that the achievable key-generation rates are equal to the previous weak notions of secrecy capacity and secret-key rate. Hence the unsatisfactory old definitions can be completely replaced by the new ones. The proofs require novel privacy-amplification techniques based on extractor functions.
On the secrecy capacity of arbitrary wiretap channel Forty-Sixth Annual Allerton Conference
- M Bloch
- J N Laneman
M. Bloch and J.N. Laneman, " On the secrecy capacity of arbitrary wiretap channel, " Forty-Sixth Annual Allerton Conference, Allerton House, Illinois, USA, Sep. 2008.
Secrecy results for compound wiretap channels," submitted to Problems of Information Transmission
- I Bjelacović
- H Boche
- J Sommerfeld
The wire-tap channel The Bell System Tech
- A Wyner