Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1507.07091 · IEEE Transactions on Information Theory

The Wiretap Channel With Generalized Feedback: Secure Communication and Key Generation

Germán Bassi, Pablo Piantanida, Shlomo Shitz Shamai

Published Nov 26, 2018• 25 citations
arXivHTMLPDF

Abstract

It is a well-known fact that feedback does not increase the capacity of point-to-point memoryless channels, however, its effect in secure communications is not fully understood yet. In this paper, an achievable scheme for the wiretap channel with generalized feedback is presented. This scheme, which uses the feedback signal to generate a shared secret key between the legitimate users, encrypts the message to be sent at the bit level. New capacity results for a class of channels are provided, as well as some new insights into the secret key agreement problem. Moreover, this scheme recovers previously reported rate regions from the literature, and thus it can be seen as a generalization that unifies several results in the field.

DOI
10.1109/tit.2018.2883299

Related papers

The wiretap channel with generalized feedback: Secure communication and key generation

Germán Bassi, Pablo Piantanida, Shlomo Shitz Shamai

It is well-known that feedback does not increase the capacity of point-to-point memoryless channels, however, the advantage it poses to secure communications is not fully understood yet. In this work, an achievable scheme for the wiretap channel with generalized feedback is presented. This scheme employs the feedback signal to generate a secret key shared between the legitimate users, which is then used to encrypt the message to be sent. It is shown that the resulting achievable rate recovers previous results, thus it can be seen as a generalization and unification of several results in the field.

IEEE Information Theory Workshop (ITW)•Oct 1, 2015•4 citations

On the capacity of the wiretap channel with generalized feedback

Germán Bassi, Pablo Piantanida, Shlomo Shitz Shamai

It is well-known that feedback does not increase the capacity of point-to-point memoryless channels, however, its effect in secure communications is not fully understood yet. In this work, an achievable scheme for the wiretap channel with generalized feedback -based on joint source-channel coding- is presented. This scheme recovers previous results, thus it can be seen as a generalization and unification of several results in the field. Additionally, the Gaussian wiretap channel with noisy feedback is analyzed, and the scheme achieves positive secrecy rates even in unfavorable situations where the eavesdropper experiences a much better channel than the legitimate user.

IEEE International Symposium on Information Theory (ISIT)•Jun 1, 2015•7 citations

Wiretap Channel With Secure Rate-Limited Feedback

Ehsan Ardestanizadeh, Massimo Franceschetti, Tara Javidi +1 more

This paper studies the problem of secure communication over a wiretap channel p(y,z|x) with a secure feedback link of rate Rf, where X is the channel input, and Y and Z are channel outputs observed by the legitimate receiver and the eavesdropper, respectively. It is shown that the secrecy capacity, the maximum data rate of reliable communication while the intended message is not revealed to the eavesdropper, is upper bounded as Cs(Rf) les maxmin/p(x) {I(X;Y), I(X;Y |Z) + Rf}. The proof of the bound crucially depends on a recursive argument which is used to obtain the single-letter characterization. This upper bound is shown to be tight for the class of physically degraded wiretap channels. A capacity-achieving coding scheme is presented for this case, in which the receiver securely feeds back fresh randomness with rate Rf, generated independent of the received channel output symbols. The transmitter then uses this shared randomness as a secret key on top of Wyner's coding scheme for wiretap channels without feedback. Hence, when a feedback link is available, the receiver should allocate all resources to convey a new key rather than sending back the channel output.

IEEE Transactions on Information Theory•Nov 24, 2009•140 citations

Wiretap channel with rate-limited feedback

Ehsan Ardetsanizadeh, Massimo Franceschetti, Tara Javidi +1 more

This paper studies the problem of secure communication over a degraded wiretap channel p(y, z|x) = p(y|x)p(z|y) with secure feedback link of rate Rf, where X is the channel input, and Y and Z are channel outputs observed by the legitimate receiver and the wiretapper respectively. The secrecy capacity is characterized as Cs{Rf) = maxmin{I(X; Y), I(X; Y|Z) + Rf}. p(x)equation. A capacity-achieving coding scheme is presented, in which the receiver securely feeds back fresh randomness with rate Rf, independent of the received channel output. The transmitter then uses the shared randomness as a secret key on top of Wynerpsilas coding scheme for wiretap channel without feedback. Hence, when the receiver has a means of interacting with the transmitter, he should allocate all resources to convey a new key rather than sending back the channel output. For the converse, a recursive argument is used to obtain the single-letter characterization.

IEEE International Symposium on Information Theory (ISIT)•Jul 1, 2008•8 citations

Multi-user and wiretap channels including feedback

S. Leung-Yan-Cheong

The concept of the wiretap channel was first proposed by Wyner. He considered the case in which data is to be transmitted reliably over a discrete memoryless main channel to a legitimate receiver. The wiretapper views the output of the main channel through another discrete memoryless channel. It is assumed that the wiretapper knows the code being used and his only handicap is the additional noise in his signal. The problem is to maximize the transmission rate R to the legitimate receiver and the equivocation d of the wiretapper. In this dissertation, the additive white Gaussian noise wiretap channel is introduced and the set of all achievable (R,d) pairs is determined explicitly through the use of certain special properties of the Gaussian channel. Some useful characterizations of a special class of wiretap channels are also explored. A model of the wiretap channel with feedback is proposed. It turns out that with the introduction of feedback, even when the main channel is inferior to the wiretapper's channel, it is still possible to reliably communicate with the legitimate receiver in complete secrecy. The binary erasure wiretap channel with feedback is examined and inner and outer bounds on the achievable (R,d) region are given. Finally, a scheme for enlarging the capacity region of multiple-access channels using feedback is analyzed. It is shown that conditions under which an enlargement is possible are fairly weak, indicating that feedback can almost increase the capacity region. (Author)

•Jan 1, 1976•19 citations

The Wiretap Channel With Feedback: Encryption Over the Channel

Lifeng Lai, Hesham El Gamal, H. Vincent Poor

In this work, the critical role of noisy feedback in enhancing the secrecy capacity of the wiretap channel is established. Unlike previous works, where a noiseless public discussion channel is used for feedback, the feed-forward and feedback signals share the same noisy channel in the present model. Quite interestingly, this noisy feedback model is shown to be more advantageous in the current setting. More specifically, the discrete memoryless modulo-additive channel with a full-duplex destination node is considered first, and it is shown that the judicious use of feedback increases the secrecy capacity to the capacity of the source-destination channel in the absence of the wiretapper. In the achievability scheme, the feedback signal corresponds to a private key, known only to the destination. In the half-duplex scheme, a novel feedback technique that always achieves a positive perfect secrecy rate (even when the source-wiretapper channel is less noisy than the source-destination channel) is proposed. These results hinge on the modulo-additive property of the channel, which is exploited by the destination to perform encryption over the channel without revealing its key to the source. Finally, this scheme is extended to the continuous real valued modulo-Lambda channel where it is shown that the secrecy capacity with feedback is also equal to the capacity in the absence of the wiretapper.

arXiv:0704.2259•IEEE Transactions on Information Theory•Oct 22, 2008•167 citations
It is a well-known fact that feedback does not increase the capacity of point-to-point memoryless channels, however, its effect in secure communications is not fully understood yet. In this paper, an achievable scheme for the wiretap channel with generalized feedback is presented. This scheme, which uses the feedback signal to generate a shared secret key between the legitimate users, encrypts the message to be sent at the bit level. New capacity results for a class of channels are provided, as well as some new insights into the secret key agreement problem. Moreover, this scheme recovers previously reported rate regions from the literature, and thus it can be seen as a generalization that unifies several results in the field.
It is well-known that feedback does not increase the capacity of point-to-point memoryless channels, however, the advantage it poses to secure communications is not fully understood yet. In this work, an achievable scheme for the wiretap channel with generalized feedback is presented. This scheme employs the feedback signal to generate a secret key shared between the legitimate users, which is then used to encrypt the message to be sent. It is shown that the resulting achievable rate recovers previous results, thus it can be seen as a generalization and unification of several results in the field.
It is well-known that feedback does not increase the capacity of point-to-point memoryless channels, however, its effect in secure communications is not fully understood yet. In this work, an achievable scheme for the wiretap channel with generalized feedback -based on joint source-channel coding- is presented. This scheme recovers previous results, thus it can be seen as a generalization and unification of several results in the field. Additionally, the Gaussian wiretap channel with noisy feedback is analyzed, and the scheme achieves positive secrecy rates even in unfavorable situations where the eavesdropper experiences a much better channel than the legitimate user.
This paper studies the problem of secure communication over a wiretap channel p(y,z|x) with a secure feedback link of rate Rf, where X is the channel input, and Y and Z are channel outputs observed by the legitimate receiver and the eavesdropper, respectively. It is shown that the secrecy capacity, the maximum data rate of reliable communication while the intended message is not revealed to the eavesdropper, is upper bounded as Cs(Rf) les maxmin/p(x) {I(X;Y), I(X;Y |Z) + Rf}. The proof of the bound crucially depends on a recursive argument which is used to obtain the single-letter characterization. This upper bound is shown to be tight for the class of physically degraded wiretap channels. A capacity-achieving coding scheme is presented for this case, in which the receiver securely feeds back fresh randomness with rate Rf, generated independent of the received channel output symbols. The transmitter then uses this shared randomness as a secret key on top of Wyner's coding scheme for wiretap channels without feedback. Hence, when a feedback link is available, the receiver should allocate all resources to convey a new key rather than sending back the channel output.
This paper studies the problem of secure communication over a degraded wiretap channel p(y, z|x) = p(y|x)p(z|y) with secure feedback link of rate Rf, where X is the channel input, and Y and Z are channel outputs observed by the legitimate receiver and the wiretapper respectively. The secrecy capacity is characterized as Cs{Rf) = maxmin{I(X; Y), I(X; Y|Z) + Rf}. p(x)equation. A capacity-achieving coding scheme is presented, in which the receiver securely feeds back fresh randomness with rate Rf, independent of the received channel output. The transmitter then uses the shared randomness as a secret key on top of Wynerpsilas coding scheme for wiretap channel without feedback. Hence, when the receiver has a means of interacting with the transmitter, he should allocate all resources to convey a new key rather than sending back the channel output. For the converse, a recursive argument is used to obtain the single-letter characterization.
The concept of the wiretap channel was first proposed by Wyner. He considered the case in which data is to be transmitted reliably over a discrete memoryless main channel to a legitimate receiver. The wiretapper views the output of the main channel through another discrete memoryless channel. It is assumed that the wiretapper knows the code being used and his only handicap is the additional noise in his signal. The problem is to maximize the transmission rate R to the legitimate receiver and the equivocation d of the wiretapper. In this dissertation, the additive white Gaussian noise wiretap channel is introduced and the set of all achievable (R,d) pairs is determined explicitly through the use of certain special properties of the Gaussian channel. Some useful characterizations of a special class of wiretap channels are also explored. A model of the wiretap channel with feedback is proposed. It turns out that with the introduction of feedback, even when the main channel is inferior to the wiretapper's channel, it is still possible to reliably communicate with the legitimate receiver in complete secrecy. The binary erasure wiretap channel with feedback is examined and inner and outer bounds on the achievable (R,d) region are given. Finally, a scheme for enlarging the capacity region of multiple-access channels using feedback is analyzed. It is shown that conditions under which an enlargement is possible are fairly weak, indicating that feedback can almost increase the capacity region. (Author)
In this work, the critical role of noisy feedback in enhancing the secrecy capacity of the wiretap channel is established. Unlike previous works, where a noiseless public discussion channel is used for feedback, the feed-forward and feedback signals share the same noisy channel in the present model. Quite interestingly, this noisy feedback model is shown to be more advantageous in the current setting. More specifically, the discrete memoryless modulo-additive channel with a full-duplex destination node is considered first, and it is shown that the judicious use of feedback increases the secrecy capacity to the capacity of the source-destination channel in the absence of the wiretapper. In the achievability scheme, the feedback signal corresponds to a private key, known only to the destination. In the half-duplex scheme, a novel feedback technique that always achieves a positive perfect secrecy rate (even when the source-wiretapper channel is less noisy than the source-destination channel) is proposed. These results hinge on the modulo-additive property of the channel, which is exploited by the destination to perform encryption over the channel without revealing its key to the source. Finally, this scheme is extended to the continuous real valued modulo-Lambda channel where it is shown that the secrecy capacity with feedback is also equal to the capacity in the absence of the wiretapper.