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IEEE International Symposium on Information Theory (ISIT)

The Gelfand-Pinsker wiretap channel: Higher secrecy rates via a novel superposition code

Ziv Goldfeld, Paul Cuff, Haim Henri Permuter

Published Jun 1, 2017• 0 citations
Publisher

Abstract

We study the state-dependent (SD) wiretap channel (WTC) with non-causal channel state information (CSI) at the encoder. This model subsumes all other instances of CSI availability as special cases, and calls for an efficient utilization of the state sequence both for reliability and security purposes. A lower bound on the secrecy-capacity, that improves upon the previously best known result by Chen and Han Vinck, is derived based on a novel superposition coding scheme. The improvement over the Chen and Han Vinck result is strict for some SD-WTCs. Specializing the lower bound to the case where CSI is also available to the decoder reveals that it is at least as good as the achievable formula by Chia and El-Gamal, which is already known to outperform the adaptation of the Chen and Han Vinck code to the encoder and decoder CSI scenario. The results are derived under the strict semantic-security metric that requires negligible information leakage for all message distributions. The proof of achievability relies on a stronger version of the soft-covering lemma for superposition codes.

DOI
10.1109/isit.2017.8006870

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We study the state-dependent (SD) wiretap channel (WTC) with non-causal channel state information (CSI) at the encoder. This model subsumes all other instances of CSI availability as special cases, and calls for an efficient utilization of the state sequence both for reliability and security purposes. A lower bound on the secrecy-capacity, that improves upon the previously best known result by Chen and Han Vinck, is derived based on a novel superposition coding scheme. The improvement over the Chen and Han Vinck result is strict for some SD-WTCs. Specializing the lower bound to the case where CSI is also available to the decoder reveals that it is at least as good as the achievable formula by Chia and El-Gamal, which is already known to outperform the adaptation of the Chen and Han Vinck code to the encoder and decoder CSI scenario. The results are derived under the strict semantic-security metric that requires negligible information leakage for all message distributions. The proof of achievability relies on a stronger version of the soft-covering lemma for superposition codes.
We study the state-dependent (SD) wiretap channel (WTC) with non-causal channel state information (CSI) at the encoder. This model subsumes all instances of CSI availability as special cases, and calls for an efficient utilization of the state sequence for both reliability and security purposes. A lower bound on the secrecy-capacity, that improves upon the previously best known result published by Prabhakaran et al., is derived based on a novel superposition coding scheme. Our achievability gives rise to the exact secrecy-capacity characterization of a class of SD-WTCs that decompose into a product of two WTCs, one independent of the state and the other depends only on the state. The results are derived under the strict semantic-security metric that requires negligible information leakage for all message distributions.
We study the trade-off between secret message (SM) and secret key (SK) rates, simultaneously achievable over a state-dependent (SD) wiretap channel (WTC) with non-causal channel state information (CSI) at the encoder. This model subsumes other instances of CSI availability as special cases, and calls for efficient utilization of the state sequence for both reliability and security purposes. An inner bound on the semantic-security (SS) SM-SK capacity region is derived based on a superposition coding scheme inspired by a past work of the authors. The region is shown to attain capacity for a certain class of SD-WTCs. SS is established by virtue of two versions of the strong soft-covering lemma. The derived region yields an improvement upon the previously best known SM-SK trade-off result reported by Prabhakaran et al., and, to the best of our knowledge, upon all other existing lower bounds for either SM or SK for this setup, even if the semantic security requirement is relaxed to weak secrecy. It is demonstrated that our region can be strictly larger than those reported in the preceding works.
The state-dependent (SD) wiretap channel (WTC) with non-causal channel state information (CSI) available at the encoder is considered. An inner bound on the trade-off region between admissible secret key (SK) and secret message (SM) rates is provided. The result is derived under the stringent semantic-security metric. Our inner bound recovers the best-known achievability results for either SK generation, SM transmission, or simultaneous execution of both. Since some of these past benchmarks were derived under weaker security metrics, our results imply that an upgrade to semantic-security is possible without inflicting any rate loss. It is shown that for certain instances of the considered SD-WTC, the derived region is strictly larger than the previously best-known SK-SM trade-off region reported by Prabhakaran et al., and that a recently reported SK rate for this setup cannot be achieved.
The coding problem for wiretap channels with causal channel state information (CSI) available at the encoder (Alice) and/or the decoder (Bob) is studied. We are concerned here particularily with the problem of achievable secret-message secret-key rate pairs under the semantic security criterion. Our main result extends all the previous results on achievable rates as given by Chia and El Gamal [10], Fujita [11], and Han and Sasaki [23]. In order to do this, we first derive a unifying theorem (Theorem 2) with causal CSI at Alice, which follows immediately by leveraging the unifying seminal theorem for wiretap channels with non-causal CSI at Alice as recently established by Bunin et al. [22]. The only thing to do here is just to re-interpret the latter non-causal one in a causal manner. A prominent feature of this approach is that we are able to dispense with the block-Markov encoding scheme as used in the previous works. Also, the exact secret-message key capacity region for wiretap channels with non-causal CSI at both Alice and Bob is given.
The coding problem for wiretap channels (WTCs) with causal and/or non-causal channel state information (CSI) available at the encoder (Alice) and/or the decoder (Bob) is studied, particularly focusing on achievable secret-message secret-key (SM-SK) rate pairs under the semantic security criterion. One of our main results is summarized as Theorem 3 on causal inner bounds for SM-SK rate pairs, which follows immediately by leveraging the unified seminal theorem for WTCs with non-causal CSI at Alice that has been recently established by Bunin et al.. The only thing to do here is just to re-interpret the latter non-causal scheme in a causal manner by restricting the range of auxiliary random variables appearing in non-causal encoding to a subclass of auxiliary random variables for the causal encoder. This technique is referred to as “plugging.” Then, we are able to dispense with the block-Markov encoding scheme used in the previous works by Chia and El Gamal, Fujita, and Han and Sasaki and then extend all the known results on achievable rates. The other main results include the exact SM-SK capacity region for WTCs with non-causal CSI at “both” Alice and Bob (Theorem 2), a “tighter” causal SM-SK outer bound for state-reproducing coding schemes with CSI at Alice (Proposition 4), and the exact SM-SK capacity region for degraded WTCs with causal/non-causal CSI at both Alice and Bob (Theorem 4).
Channel state information (CSI) is differently available at each terminal in state-dependent wiretap channels (SD-WTCs). Considering a random channel state non-causally available only at the encoder, this paper investigates an explicit polar coding scheme for the discrete and memoryless SD-WTC, where Alice aims to transmit a secret message (SM) and a secret key (SK) to Bob while concealing them from Eve. Based on a two-layer superposition coding, which includes an inner layer and an outer layer, the proposed polar coding scheme can achieve the inner bound of the current optimal SM-SK capacity region for the discrete and memoryless SD-WTC with CSI non-causally available only at the encoder. A cross-layer construction is proposed to address the issue where the regular chaining construction used in wiretap polar codes cannot be applied in the inner layer. Results show that the decoding error probability (DEP) of the legitimate decoder vanishes to zero as the block length increases. In addition, the proposed scheme is proven to satisfy strong secrecy.