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IEICE Communications Express

Secrecy capacity of wiretap channels with the bit error rate criterion

Ryutaroh Matsumoto

Published Jan 1, 2016• 0 citations
Publisher

Abstract

The coding problem over wiretap channels is to realize an encoder and a decoder such that the legitimate receiver can correctly decode transmitted secret messages while the eavesdropper knows little about the secret messages. Traditionally, the secrecy of messages to the eavesdropper has been measured in terms of mutual information. Recently, several researches on the wiretap channels employ the bit error rate after decoding by the eavesdropper as a secrecy measure. In this note, we show that the secrecy capacity with respect to the bit error rate criterion is different from that with the traditional mutual information criterion. In addition to that, the encoder can be deterministic for the bit error rate criterion, while it must be stochastic for the mutual information criterion.

DOI
10.1587/comex.2016xbl0129

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The coding problem over wiretap channels is to realize an encoder and a decoder such that the legitimate receiver can correctly decode transmitted secret messages while the eavesdropper knows little about the secret messages. Traditionally, the secrecy of messages to the eavesdropper has been measured in terms of mutual information. Recently, several researches on the wiretap channels employ the bit error rate after decoding by the eavesdropper as a secrecy measure. In this note, we show that the secrecy capacity with respect to the bit error rate criterion is different from that with the traditional mutual information criterion. In addition to that, the encoder can be deterministic for the bit error rate criterion, while it must be stochastic for the mutual information criterion.
This paper considers the problem of proof for the secrecy capacity region of the Gaussian wiretap channel. In this channel, the transmitter sends confidential messages to the legitimate receivers, which need to be kept asymptotically perfectly secret from the eavesdropper. We characterize the secrecy capacity region of this channel and give a converse proof by using the fundamental relationship between information theory and the estimation theory in the Gaussian channel, relating the derivative of the mutual information to the minimum mean-square-error (MMSE). Our proof is different from the superposition coding and the random binning. We obtain that using the relationship between MMSE and mutual information one can provide insightful and simple proofs for multiuser single antenna problems and the secrecy capacity problem, such as broadcast channel.
In this paper we consider a wiretap channel with a secret key buffer. We use the coding scheme of [1] to enhance the secrecy rate to the capacity of the main channel, while storing each securely transmitted message in the secret key buffer. We use the oldest secret bits from the buffer to be used as a secret key to transmit a message in a slot and then remove those bits. With this scheme we are able to prove stronger results than those in [1]. i.e., not only the message which is being transmitted currently, but all the messages transmitted in last N1N_1N1​ slots are secure with respect to all the information that the eavesdropper possesses, where N1N_1N1​ can be chosen arbitrarily large.
The wiretap channel models the communication scenario where two legitimate users want to communicate in such a way that a wiretapper is kept ignorant. In this paper, the wiretap channel with side information is studied, where the wiretapper has additional side information available. This side information allows the wiretapper to restrict the transmitted message to a certain subset of messages before further postprocessing. Two different criteria are employed to model the secrecy of the confidential message: the information theoretic criterion of strong secrecy and a signal-processing-inspired criterion based on the decoding performance of the wiretapper. For the latter, the wiretapper is required to have the worst decoding performance regardless of the specific decoding strategy that is used. It is shown that both criteria are equivalent in terms of secrecy capacity. Furthermore, the secrecy capacity equals the one of the classical wiretap channel without side information available at the wiretapper. In addition, the corresponding capacity-achieving code structure and optimal transceiver design are characterized and properties are identified. Finally, extensions to channel uncertainty and multiple wiretappers are discussed.
This paper considers an extension of wiretap channel II, where the source message W is transmitted to the legitimate receiver via a discrete memoryless main channel (DMC). Receiving YN, the receiver needs to recover W with small error probability. Meanwhile, an eavesdropper is able to observe arbitrary subsequence of YNwith size μ = Nα, where 0 <; α <; 1 is a constant real number. The encoding-decoding scheme is designed to satisfy a strong secrecy criterion, i.e. the information of each block (instead of each bit) exposed to the eavesdropper is negligible or arbitrarily close to 0 when N is sufficiently large. We focus on the secrecy capacity of this model.
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.
The secrecy capacity problems over the general arbitrarily varying wiretap channel (AVWC), with respect to the maximal decoding error probability and strong secrecy criterion, are considered, where the channel state sequence may be known or unknown at the receiver. In the mean time, it is always assumed that the channel state sequence is known at the eavesdropper and unknown at the transmitter. Capacity results of both stochastic code (with random encoder and deterministic decoder) and random code (with random encoder and decoder) are discussed. This model includes the previous models of classic AVWC as special cases. Single-letter lower bounds on the secrecy capacities are given, which are proved to be the secrecy capacities when the main channel is less noisy than the wiretap channel. The coding scheme is based on Csiszar's almost independent coloring scheme and Ahlswede's elimination technique. Moreover, a new kind of typical sequence with respect to states is defined for this coding scheme. It is concluded that the secrecy capacity of stochastic code is identical to that of random code when the receiver knows the state sequence. Meanwhile, random code may achieve larger secrecy capacity when the state sequence is unknown by the receiver.