A rate-distortion based secrecy system with side information at the decoders

2016 IEEE International Symposium on Information Theory (ISIT)

Permuter

2016

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The secrecy capacity of the type II wiretap channel (WTC II) with a noisy main channel is currently an open problem. Herein its secrecy-capacity is derived and shown to be equal to its semantic-security (SS) capacity. In this setting, the legitimate users communicate via a discrete-memoryless (DM) channel in the presence of an eavesdropper that has perfect access to a subset of its choosing of the transmitted symbols, constrained to a fixed fraction of the blocklength. The secrecy criterion is achieved simultaneously for all possible eavesdropper subset choices. The SS criterion demands negligible mutual information between the message and the eavesdropper's observations even when maximized over all message distributions.A key tool for the achievability proof is a novel and stronger version of Wyner's soft covering lemma. Specifically, a random codebook is shown to achieve the soft-covering phenomenon with high probability. The probability of failure is doublyexponentially small in the blocklength. Since the combined number of messages and subsets grows only exponentially with the blocklength, SS for the WTC II is established by using the union bound and invoking the stronger soft-covering lemma. The direct proof shows that rates up to the weak-secrecy capacity of the classic WTC with a DM erasure channel (EC) to the eavesdropper are achievable. The converse follows by establishing the capacity of this DM wiretap EC as an upper bound for the WTC II. From a broader perspective, the stronger soft-covering lemma constitutes a tool for showing the existence of codebooks that satisfy exponentially many constraints, a beneficial ability for many other applications in information theoretic security.Index Terms-Erasure wiretap channel, information theoretic security, semantic-security, soft-covering lemma, wiretap channel of type II.

mentioning

confidence: 99%

Semantic-security capacity for wiretap channels of type II

Goldfeld

2016 IEEE International Symposium on Information Theory (ISIT)

Permuter

2016

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mentioning

confidence: 99%

Semantic-Security Capacity for Wiretap Channels of Type II

Goldfeld

IEEE Trans. Inform. Theory

Permuter

2016

Self Cite

Abstract-The secrecy capacity of the type II wiretap channel (WTC II) with a noisy main channel is currently an open problem. Herein its secrecy-capacity is derived and shown to be equal to its semantic-security (SS) capacity. In this setting, the legitimate users communicate via a discrete-memoryless (DM) channel in the presence of an eavesdropper that has perfect access to a subset of its choosing of the transmitted symbols, constrained to a fixed fraction of the blocklength. The secrecy criterion is achieved simultaneously for all possible eavesdropper subset choices. The SS criterion demands negligible mutual information between the message and the eavesdropper's observations even when maximized over all message distributions.A key tool for the achievability proof is a novel and stronger version of Wyner's soft covering lemma. Specifically, a random codebook is shown to achieve the soft-covering phenomenon with high probability. The probability of failure is doublyexponentially small in the blocklength. Since the combined number of messages and subsets grows only exponentially with the blocklength, SS for the WTC II is established by using the union bound and invoking the stronger soft-covering lemma. The direct proof shows that rates up to the weak-secrecy capacity of the classic WTC with a DM erasure channel (EC) to the eavesdropper are achievable. The converse follows by establishing the capacity of this DM wiretap EC as an upper bound for the WTC II. From a broader perspective, the stronger soft-covering lemma constitutes a tool for showing the existence of codebooks that satisfy exponentially many constraints, a beneficial ability for many other applications in information theoretic security.Index Terms-Erasure wiretap channel, information theoretic security, semantic-security, soft-covering lemma, wiretap channel of type II.

“…The likelihood encoder also simplifies analysis in secrecy settings, though this was not demonstrated within this paper. In the secrecy settings [17], [32], [33], a superposition codebook together with a superposition version of the soft-covering lemma is typically required.…”

Section: Discussionmentioning

confidence: 99%

“…where (34) follows from Property 1(e) and (35) follows from (31), (32) and Property 1(d). By Property 1(b),…”

Section: B Achievability Proof Using the Likelihood Encodermentioning

confidence: 99%

The Likelihood Encoder for Lossy Compression

Song

IEEE Trans. Inform. Theory

Poor

2016

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Abstract-A likelihood encoder is studied in the context of lossy source compression. The analysis of the likelihood encoder is based on the soft-covering lemma. It is demonstrated that the use of a likelihood encoder together with the soft-covering lemma yields simple achievability proofs for classical source coding problems. The cases of the point-to-point rate-distortion function, the rate-distortion function with side information at the decoder (i.e. the Wyner-Ziv problem), and the multi-terminal source coding inner bound (i.e. the Berger-Tung problem) are examined in this paper. Furthermore, a non-asymptotic analysis is used for the point-to-point case to examine the upper bound on the excess distortion provided by this method. The likelihood encoder is also related to a recent alternative technique using properties of random binning.