Secure Multiplex Coding Attaining Channel Capacity in Wiretap Channels

Kobayashi, Daisuke; Yamamoto, Hirosuke; Ogawa, Tetsuhiro

doi:10.1109/tit.2013.2282673

Cited by 30 publications

(26 citation statements)

References 17 publications

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“…In order to get rid of this information rate loss, Yamamoto et al [22] proposed the secure multiplex coding, hereafter abbreviated as SMC, as a generalization of the wire-tap channel coding. The SMC can be used, for example, in the following case.…”

Section: A Overviewmentioning

confidence: 99%

“…, S T , and that Eve cannot obtain any information of the respective personal information. In order to keep the secrecy of the message S i from Eve, Yamamoto et al [22] proposed to use the remaining information S 1 , . .…”

Section: A Overviewmentioning

confidence: 99%

“…It is known that the application of the channel resolvability [13] yields the security of the wire-tap channel model [15]. Hence, employing this method, Yamamoto et al [22] proved the security of SMC.…”

Section: A Overviewmentioning

confidence: 99%

“…. , S T are personal information, they are not necessarily uniform random bits and might be dependent, while the existing papers [27], [22] assumed their uniformity and independence. Such assumption is difficult to be ensured in practice.…”

Section: A Overviewmentioning

confidence: 99%

“…The reader might also conceive that this problem could be solved by a straightforward combination of the coding for intrinsic randomness [33] and that for the original secure multiplex coding [22], [27]. We emphasize that this is false.…”

Section: A Overviewmentioning

confidence: 99%

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Secure Multiplex Coding With Dependent and Non-Uniform Multiple Messages

Hayashi

Matsumoto

2016

IEEE Trans. Inform. Theory

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Abstract-The secure multiplex coding (SMC) is a technique to remove rate loss in the coding for wire-tap channels and broadcast channels with confidential messages caused by the inclusion of random bits into transmitted signals. SMC replaces the random bits by other meaningful secret messages, and a collection of secret messages serves as the random bits to hide the rest of messages. In the previous researches, multiple secret messages were assumed to have independent and uniform distributions, which is difficult to be ensured in practice. We remove this restrictive assumption by a generalization of the channel resolvability technique.We also give practical construction techniques for SMC by using an arbitrary given error-correcting code as an ingredient, and channel-universal coding of SMC. By using the same principle as the channel-universal SMC, we give coding for the broadcast channel with confidential messages universal to both channel and source distributions.Index Terms-broadcast channel with confidential messages, information theoretic security, multiuser information theory, universal coding, the secure multiplex coding

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Section: A Overviewmentioning

confidence: 99%

Section: A Overviewmentioning

confidence: 99%

Section: A Overviewmentioning

confidence: 99%

Section: A Overviewmentioning

confidence: 99%

Section: A Overviewmentioning

confidence: 99%

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Secure Multiplex Coding With Dependent and Non-Uniform Multiple Messages

Hayashi

Matsumoto

2016

IEEE Trans. Inform. Theory

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Rényi Resolvability and Its Applications to the Wiretap Channel

Tan

2017

Lecture Notes in Computer Science

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The conventional channel resolvability problem refers to the determination of the minimum rate required for an input process so that the output distribution approximates a target distribution in either the total variation distance or the relative entropy. In contrast to previous works, in this paper, we use the (normalized or unnormalized) Rényi divergence (with the Rényi parameter in [0, 2] ∪ {∞}) to measure the level of approximation. We also provide asymptotic expressions for normalized Rényi divergence when the Rényi parameter is larger than or equal to 1 as well as (lower and upper) bounds for the case when the same parameter is smaller than 1. We characterize the Rényi resolvability, which is defined as the minimum rate required to ensure that the Rényi divergence vanishes asymptotically. The Rényi resolvabilities are the same for both the normalized and unnormalized divergence cases. In addition, when the Rényi parameter smaller than 1, consistent with the traditional case where the Rényi parameter is equal to 1, the Rényi resolvability equals the minimum mutual information over all input distributions that induce the target output distribution. When the Rényi parameter is larger than 1 the Rényi resolvability is, in general, larger than the mutual information. The optimal Rényi divergence is proven to vanish at least exponentially fast for both of these two cases, as long as the code rate is larger than the Rényi resolvability. The optimal exponential rate of decay for i.i.d. random codes is also characterized exactly. We apply these results to the wiretap channel, and completely characterize the optimal tradeoff between the rates of the secret and non-secret messages when the leakage measure is given by the (unnormalized) Rényi divergence. This tradeoff differs from the conventional setting when the leakage is measured by the traditional mutual information.

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Message randomization and strong security in quantum stabilizer-based secret sharing for classical secrets

Matsumoto

2020

Des. Codes Cryptogr.

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We improve the flexibility in designing access structures of quantum stabilizer-based secret sharing schemes for classical secrets, by introducing message randomization in their encoding procedures. We generalize the Gilbert-Varshamov bound for deterministic encoding to randomized encoding of classical secrets. We also provide an explicit example of a ramp secret sharing scheme with which multiple symbols in its classical secret are revealed to an intermediate set, and justify the necessity of incorporating strong security criterion of conventional secret sharing. Finally, we propose an explicit construction of strongly secure ramp secret sharing scheme by quantum stabilizers, which can support twice as large classical secrets as the McEliece-Sarwate strongly secure ramp secret sharing scheme of the same share size and the access structure. Keywords Secret sharing • Quantum error-correcting code • Gilbert-Varshamove bound • Strong security Mathematics Subject Classification 94A62 • 81P70 • 94B65 This is one of several papers published in Designs, Codes and Cryptography comprising the "Special Issue on Coding and Cryptography 2019".

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Secure Multiplex Coding Attaining Channel Capacity in Wiretap Channels

Cited by 30 publications

References 17 publications

Secure Multiplex Coding With Dependent and Non-Uniform Multiple Messages

Secure Multiplex Coding With Dependent and Non-Uniform Multiple Messages

Rényi Resolvability and Its Applications to the Wiretap Channel

Message randomization and strong security in quantum stabilizer-based secret sharing for classical secrets

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