Broadcast channels with confidential messages

Csiszár, Imre; Körner, János

doi:10.1109/tit.1978.1055892

Cited by 3,106 publications

(3,285 citation statements)

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“…A fundamental problem is the generation of a mutual key about which an adversary has virtually no information. Wyner [18] and later Csiszár and Körner [10] considered the natural message-transmission scenarios in which the legitimate partners Alice and Bob, as well as the adversary Eve, are connected by noisy channels. In Csiszár and Körner's setting, Alice sends information (given by the random variable X) to Bob (receiving Y ) and to the opponent Eve (who obtains Z) over a noisy broadcast channel characterized by the conditional distribution P Y Z|X .…”

Section: Models Of Information-theoretic Secret-key Agreementmentioning

confidence: 99%

Information-Theoretic Key Agreement: From Weak to Strong Secrecy for Free

Maurer

Wolf

2000

Lecture Notes in Computer Science

400

469

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Abstract. One of the basic problems in cryptography is the generation of a common secret key between two parties, for instance in order to communicate privately. In this paper we consider information-theoretically secure key agreement. Wyner and subsequently Csiszár and Körner described and analyzed settings for secret-key agreement based on noisy communication channels. Maurer as well as Ahlswede and Csiszár generalized these models to a scenario based on correlated randomness and public discussion. In all these settings, the secrecy capacity and the secret-key rate, respectively, have been defined as the maximal achievable rates at which a highly-secret key can be generated by the legitimate partners. However, the privacy requirements were too weak in all these definitions, requiring only the ratio between the adversary's information and the length of the key to be negligible, but hence tolerating her to obtain a possibly substantial amount of information about the resulting key in an absolute sense. We give natural stronger definitions of secrecy capacity and secret-key rate, requiring that the adversary obtains virtually no information about the entire key. We show that not only secret-key agreement satisfying the strong secrecy condition is possible, but even that the achievable key-generation rates are equal to the previous weak notions of secrecy capacity and secret-key rate. Hence the unsatisfactory old definitions can be completely replaced by the new ones. We prove these results by a generic reduction of strong to weak key agreement. The reduction makes use of extractors, which allow to keep the required amount of communication negligible as compared to the length of the resulting key.

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Section: Models Of Information-theoretic Secret-key Agreementmentioning

confidence: 99%

Information-Theoretic Key Agreement: From Weak to Strong Secrecy for Free

Maurer

Wolf

2000

Lecture Notes in Computer Science

400

469

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“…As mentioned in the introduction, Theorem 1 has already been known to hold for general (not necessarily efficient) protocols [3,1].…”

Section: A General Expression For the One-way Secret-key Ratementioning

confidence: 96%

“…For one-way communication, it is already implied by a result in [3] and has later been shown in [1] that the secret-key rate S → (X; Y |Z) is given by the supremum of H(U |ZV ) − H(U |Y V ), taken over all possible random variables U and V obtained from X. 1 However, as this is a purely information-theoretic result, it does not directly imply that there exists an efficient key-agreement protocol.…”

Section: Secret-key Agreementmentioning

confidence: 97%

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One-Way Secret-Key Agreement and Applications to Circuit Polarization and Immunization of Public-Key Encryption

Holenstein

Renner

2005

Lecture Notes in Computer Science

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Abstract. Secret-key agreement between two parties Alice and Bob, connected by an insecure channel, can be realized in an informationtheoretic sense if the parties share many independent pairs of correlated and partially secure bits. We study the special case where only one-way communication from Alice to Bob is allowed and where, for each of the bit pairs, with a certain probability, the adversary has no information on Alice's bit. We give an expression which, for this situation, exactly characterizes the rate at which Alice and Bob can generate secret key bits.This result can be used to analyze a slightly restricted variant of the problem of polarizing circuits, introduced by Sahai and Vadhan in the context of statistical zero-knowledge, which we show to be equivalent to secret-key agreement as described above. This provides us both with new constructions to polarize circuits, but also proves that the known constructions work for parameters which are tight.As a further application of our results on secret-key agreement, we show how to immunize single-bit public-key encryption schemes from decryption errors and insecurities of the encryption, a question posed and partially answered by Dwork, Naor, and Reingold. Our construction works for stronger parameters than the known constructions.

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“…After that, Wyner [5] and Csiszár and Körner [6] showed that it is possible to securely communicate between Alice and Bob, under the assumption of the presence of noise in communication channels from Alice to Bob, and to an adversary Eve. By taking various assumptions on the adversary's ability, many applications have been derived in the field of physical layer security.…”

Section: Related Workmentioning

confidence: 99%

Generalized Upper Bound of Agreement Probability for Extracting Common Random Bits From Correlated Sources

Kim¹,

Lim²

2014

Appl. Math. Inf. Sci.

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Suppose that both Alice and Bob receive independent random bits without any bias, which are influenced by an independent noise. From the received random bits, Alice and Bob are willing to extract common randomness, without any communication. The extracted common randomness can be used for authentication or secrets. Recently, Bogdanov and Mossel derived an upper bound of the agreement probability, based on the min-entropy of outputs. In this paper, we derive a generalized upper bound of the probability of extracting common random bits from correlated sources, using the Rènyi entropy of order 1/(1 − ε), where ε is the error probability of the binary symmetric noise. It is shown that the generalized upper bound is always less than or equal to the previous bound.

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Broadcast channels with confidential messages

Cited by 3,106 publications

References 6 publications

Information-Theoretic Key Agreement: From Weak to Strong Secrecy for Free

Information-Theoretic Key Agreement: From Weak to Strong Secrecy for Free

One-Way Secret-Key Agreement and Applications to Circuit Polarization and Immunization of Public-Key Encryption

Generalized Upper Bound of Agreement Probability for Extracting Common Random Bits From Correlated Sources

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