It is known that a message can be transmitted safely against any wiretapper via a noisy channel without a secret key if the coding rate is less than the so-called secrecy capacity CS, which is usually smaller than the channel capacity C. In order to remove the loss C-CS, we propose a multiplex coding scheme with plural independent messages. In this paper, it is shown that the proposed multiplex coding scheme can attain the channel capacity as the total rate of the plural messages and the perfect secrecy for each massage. Several bounds of achievable multiplex coding rate region are derived for general wiretap channels in the sense of information-spectral methods, by extending Hayashi's proof, in which the coding of the channel resolvability is applied to wiretap channels. Furthermore, the exact region for deterministic coding is determined for stationary memoryless full-rank wiretap channels.It is known that a message can be transmitted safely against any wiretapper via a noisy channel without a secret key if the coding rate is less than the so-called secrecy capacity CS, which is usually smaller than the channel capacity C. In order to remove the loss C-CS, we propose a multiplex coding scheme with plural independent messages. In this paper, it is shown that the proposed multiplex coding scheme can attain the channel capacity as the total rate of the plural messages and the perfect secrecy for each massage. Several bounds of achievable multiplex coding rate region are derived for general wiretap channels in the sense of information-spectral methods, by extending Hayashi's proof, in which the coding of the channel resolvability is applied to wiretap channels. Furthermore, the exact region for deterministic coding is determined for stationary memoryless full-rank wiretap channels.

IEEE Transactions on Information TheoryJan 1, 20141 citation

Secure multiplex coding to attain the channel capacity in wiretap channels

Daisuke Kobayashi, H. Yamamoto, Tomohiro Ogawa

It is known that a message can be transmitted safely against any wiretapper via a noisy channel without a secret key if the coding rate is less than the so-called secrecy capacity $C_S$ , which is usually smaller than the channel capacity $C$ . In order to remove the loss $C - C_S$ , we propose a multiplex coding scheme with plural independent messages. In this paper, it is shown that the proposed multiplex coding scheme can attain the channel capacity as the total rate of the plural messages and the perfect secrecy for each message. The coding theorem is proved by extending Hayashi's proof, in which the coding of the channel resolvability is applied to wiretap channels.It is known that a message can be transmitted safely against any wiretapper via a noisy channel without a secret key if the coding rate is less than the so-called secrecy capacity $C_S$, which is usually smaller than the channel capacity $C$. In order to remove the loss $C - C_S$, we propose a multiplex coding scheme with plural independent messages. In this paper, it is shown that the proposed multiplex coding scheme can attain the channel capacity as the total rate of the plural messages and the perfect secrecy for each message. The coding theorem is proved by extending Hayashi's proof, in which the coding of the channel resolvability is applied to wiretap channels.

arXiv:cs/0509047Sep 16, 20050 citations

How to attain the ordinary channel capacity securely in wiretap channels

Daisuke Kobayashi, H. Yamamoto, Tomohiro Ogawa

It is known that a message can be transmitted safely against any wiretap per via a noisy channel without a secret key if the coding rate is less than the so-called secrecy capacity Cs, which is usually smaller than the channel capacity C. In order to remove the loss C - Cs, we propose a multiplex coding scheme with plural independent messages. In this paper, it is shown that the proposed multiplex coding scheme can attain the channel capacity as the total rate of the plural messages and the perfect secrecy for each message. The coding theorem is proved by extending Hayashi's proof, in which the coding of the channel resolvability is applied to the wiretap channel.It is known that a message can be transmitted safely against any wiretap per via a noisy channel without a secret key if the coding rate is less than the so-called secrecy capacity Cs, which is usually smaller than the channel capacity C. In order to remove the loss C - Cs, we propose a multiplex coding scheme with plural independent messages. In this paper, it is shown that the proposed multiplex coding scheme can attain the channel capacity as the total rate of the plural messages and the perfect secrecy for each message. The coding theorem is proved by extending Hayashi's proof, in which the coding of the channel resolvability is applied to the wiretap channel.

IEEE Information Theory Workshop (ITW)Dec 10, 200521 citations

Secrecy from Resolvability

Matthieu R. Bloch, J. Nicholas Laneman

We investigate an approach to physical-layer security based on the premise that the coding mechanism for secrecy over noisy channels is fundamentally tied to the notion of resolvability. Instead of considering capacity-based constructions, which associate to each message a sub-code whose rate approaches the capacity of the eavesdropper’s channel, we consider resolvability-based constructions, which associate to each message a sub-code whose rate is beyond the resolvability of the eavesdropper’s channel. We provide evidence that resolvability is a more powerful and perhaps more fundamental coding mechanism for secrecy by developing results that hold for strong secrecy metrics and arbitrary channels. Specifically, we show that, at least for binary symmetric wiretap channels, random capacity-based constructions fail to approach the strong secrecy capacity while resolvability-based constructions achieve it. We then obtain the secrecy-capacity region of arbitrary broadcast channels with confidential messages and a cost constraint for strong secrecy metrics, which generalizes existing results. Finally, we specialize our results to study the secrecy capacity of wireless channels with perfect channel state information, compound and mixed channels, as well as the secret-key capacity of source models for secret-key agreement. By tying secrecy to resolvability, we obtain achievable rates for stronger secrecy metrics and with simpler proofs than previously derived. Index Terms information-theoretic security, wiretap channel, secret-key agreement, information-spectrum, resolv-ability, wireless channels.We investigate an approach to physical-layer security based on the premise that the coding mechanism for secrecy over noisy channels is fundamentally tied to the notion of resolvability. Instead of considering capacity-based constructions, which associate to each message a sub-code whose rate approaches the capacity of the eavesdropper’s channel, we consider resolvability-based constructions, which associate to each message a sub-code whose rate is beyond the resolvability of the eavesdropper’s channel. We provide evidence that resolvability is a more powerful and perhaps more fundamental coding mechanism for secrecy by developing results that hold for strong secrecy metrics and arbitrary channels. Specifically, we show that, at least for binary symmetric wiretap channels, random capacity-based constructions fail to approach the strong secrecy capacity while resolvability-based constructions achieve it. We then obtain the secrecy-capacity region of arbitrary broadcast channels with confidential messages and a cost constraint for strong secrecy metrics, which generalizes existing results. Finally, we specialize our results to study the secrecy capacity of wireless channels with perfect channel state information, compound and mixed channels, as well as the secret-key capacity of source models for secret-key agreement. By tying secrecy to resolvability, we obtain achievable rates for stronger secrecy metrics and with simpler proofs than previously derived. Index Terms information-theoretic security, wiretap channel, secret-key agreement, information-spectrum, resolv-ability, wireless channels.

May 26, 201119 citations

Multiplex Coding of Bit Commitment Based on a Discrete Memoryless Channel

H. Yamamoto, Daichi Isami

The bit commitment can be realized by using a noisy channel. Winter-Nascimento-Imai showed that the bit commitment capacity of a noisy channel is given by Cb= maxpNH(X\Y) where X and Y are the input and output of the channel. In this paper, the idea of a multiplex coding, which was first introduced into the coding problem of a wiretap channel by Kobayashi-Yamamoto-Ogawa, is applied to the bit commitment coding. The coding theorem is proved for the multiplex coding of bit commitment based on a noisy channel, and it is shown that several mutually independent secrets can be committed at the same time via a nosiy channel attaining the perfect secrecy of each secret with the total coding rate log \X\, where \X\ is the cardinality of channel input alphabet.The bit commitment can be realized by using a noisy channel. Winter-Nascimento-Imai showed that the bit commitment capacity of a noisy channel is given by Cb= maxpNH(X\Y) where X and Y are the input and output of the channel. In this paper, the idea of a multiplex coding, which was first introduced into the coding problem of a wiretap channel by Kobayashi-Yamamoto-Ogawa, is applied to the bit commitment coding. The coding theorem is proved for the multiplex coding of bit commitment based on a noisy channel, and it is shown that several mutually independent secrets can be committed at the same time via a nosiy channel attaining the perfect secrecy of each secret with the total coding rate log \X\, where \X\ is the cardinality of channel input alphabet.

IEEE International Symposium on Information Theory (ISIT)Jun 1, 20077 citations

A New Wiretap Channel Model and Its Strong Secrecy Capacity

Mohamed Nafea, Aylin Yener

In this paper, a new wiretap channel model is proposed, where the legitimate transmitter and receiver communicate over a discrete memoryless channel. The wiretapper has perfect access to a fixed-length subset of the transmitted code word symbols of her choosing. Additionally, she observes the remainder of the transmitted symbols through a discrete memoryless channel. This new model subsumes the classical wiretap channel and wiretap channel II with noisy main channel as its special cases, and is termed as the generalized wiretap channel for that reason. The strong secrecy capacity of the proposed channel model is identified. Achievability is established by solving a dual secret key agreement problem in the source model, and converting the solution to the original channel model using probability distribution approximation arguments. In the dual problem, a source encoder and decoder, who observe random sequences independent and identically distributed according to the input and output distributions of the legitimate channel in the original problem, communicate a confidential key over a public error-free channel using a single forward transmission, in the presence of a compound wiretapping source who has perfect access to the public discussion. The security of the key is guaranteed for the exponentially many possibilities of the subset chosen at the wiretapper by deriving a lemma which provides a doubly-exponential convergence rate for the probability that, for a fixed choice of the subset, the key is uniform and independent from the public discussion and the wiretapping source's observation. The converse is derived by using Sanov's theorem to upper bound the secrecy capacity of the generalized wiretap channel by the secrecy capacity when the tapped subset is randomly chosen by nature.In this paper, a new wiretap channel model is proposed, where the legitimate transmitter and receiver communicate over a discrete memoryless channel. The wiretapper has perfect access to a fixed-length subset of the transmitted code word symbols of her choosing. Additionally, she observes the remainder of the transmitted symbols through a discrete memoryless channel. This new model subsumes the classical wiretap channel and wiretap channel II with noisy main channel as its special cases, and is termed as the generalized wiretap channel for that reason. The strong secrecy capacity of the proposed channel model is identified. Achievability is established by solving a dual secret key agreement problem in the source model, and converting the solution to the original channel model using probability distribution approximation arguments. In the dual problem, a source encoder and decoder, who observe random sequences independent and identically distributed according to the input and output distributions of the legitimate channel in the original problem, communicate a confidential key over a public error-free channel using a single forward transmission, in the presence of a compound wiretapping source who has perfect access to the public discussion. The security of the key is guaranteed for the exponentially many possibilities of the subset chosen at the wiretapper by deriving a lemma which provides a doubly-exponential convergence rate for the probability that, for a fixed choice of the subset, the key is uniform and independent from the public discussion and the wiretapping source's observation. The converse is derived by using Sanov's theorem to upper bound the secrecy capacity of the generalized wiretap channel by the secrecy capacity when the tapped subset is randomly chosen by nature.

IEEE Transactions on Information TheoryDec 22, 201726 citations

It is known that a message can be transmitted safely against any wiretapper via a noisy channel without a secret key if the coding rate is less than the so-called secrecy capacity

C_S

, which is usually smaller than the channel capacity

C

. In order to remove the loss

C - C_S

, we propose a multiplex coding scheme with plural independent messages. In this paper, it is shown that the proposed multiplex coding scheme can attain the channel capacity as the total rate of the plural messages and the perfect secrecy for each message. The coding theorem is proved by extending Hayashi's proof, in which the coding of the channel resolvability is applied to wiretap channels.