Secure Message Transmission With Small Public Discussion

Garay, Juan A.; Givens, Clint; Ostrovsky, Rafail

doi:10.1109/tit.2014.2307309

Cited by 5 publications

(13 citation statements)

References 35 publications

(20 reference statements)

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“…Our construction also has two steps: a key establishment, followed by encrypting the message and sending it over the public discussion channel. This is also the approach in [9] (Protocol I) and [16]. The model of adversarial wiretap in [14,15] extends wiretap II to include active (jamming) adversarial noise.…”

Section: Related Workmentioning

confidence: 98%

“…In Section 6 we compare these results with the known bounds and constructions of SMT-PD. The message round lower bound for (ǫ, δ)-SMT [ow−s] -PD also lower bounds the message round complexity of general SMT-PD (two-way communication over wires) and so can be compared with the round complexity bounds in [9,16]. Similarly the construction of (ǫ, δ)-SMT [ow−s] -PD can be compared with those in [9].…”

Section: Relation With Smt-pdmentioning

confidence: 99%

“…Proof. We use the notations in [9]. From [9], we have log |W i | ≥ N , N = K 1−D , K = kmin n−t + λ, k min = m, and log |M| = m. This gives the information rate,…”

Section: C2 Detail Of Bounding C 1 and Cmentioning

confidence: 99%

“…Access to a public discussion channel in SMT was considered by Garay et.al. [9] who showed that secure message tranmission will be possible when N ≥ t + 1 while without a PD , N ≥ 2t + 1. We allow communicants to interact over the PD but assume communication over the AWTP channel is one-way and from Alice to Bob.…”

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confidence: 99%

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Adversarial wiretap channel with public discussion

Wang

2015

2015 IEEE Conference on Communications and Network Security (CNS)

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Wyner's elegant model of wiretap channel exploits noise in the communication channel to provide perfect secrecy against a computationally unlimited eavesdropper without requiring a shared key. We consider an adversarial model of wiretap channel proposed in [18,19] where the adversary is active: it selects a fraction ρr of the transmitted codeword to eavesdrop and a fraction ρw of the codeword to corrupt by "adding" adversarial error. It was shown that this model also captures network adversaries in the setting of 1-round Secure Message Transmission [8]. It was proved that secure communication (1-round) is possible if and only if ρr + ρw < 1. In this paper we show that by allowing communicants to have access to a public discussion channel (authentic communication without secrecy) secure communication becomes possible even if ρr + ρw > 1. We formalize the model of AWTP PD protocol and for two efficiency measures, information rate and message round complexity derive tight bounds. We also construct a rate optimal protocol family with minimum number of message rounds. We show application of these results to Secure Message Transmission with Public Discussion (SMT-PD), and in particular show a new lower bound on transmission rate of these protocols together with a new construction of an optimal SMT-PD protocol.Alice and Bob are connected by N node disjoint paths, a subset of which is controlled by a computationally unlimited adversary and the goal is to provide secrecy and reliability for the communication. The adversary in AWTP channel is more general (powerful) than the widely studied threshold SMT adversary and can choose different subsets for eavesdropping and corruption.Motivation It was proved [18] that perfect secrecy and reliability for AWTP in 1round communication is possible if and only if, ρ r + ρ w < 1. We consider a scenario where in addition to the AWTP channel, a public discussion channel denoted by PD, is available to the communicants. We call this model AWTP with public discussion (or AWTP PD for short). Our goal is to see if the use of this extra resource can make secure communication possible when ρ r + ρ w > 1 (for example ρ r = ρ w = 0.9). Public discussion channels had been considered in wiretap and SMT models, both. In wiretap setting it was shown [11,2] that a public discussion channel substantially expands the range of scenarios in which secure communication is possible. In particular secure communication becomes possible even if the eavesdroper channel is less noisy than the main channel. A similar result holds for SMT. Access to a public discussion channel in SMT was considered by Garay et.al. [9] who showed that secure message tranmission will be possible when N ≥ t + 1 while without a PD , N ≥ 2t + 1. We allow communicants to interact over the PD but assume communication over the AWTP channel is one-way and from Alice to Bob. This restriction is to simplify our analysis and as we will show, will still allow us to construct protocols that are optimal.The assumption is also natural in setting...

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Section: Related Workmentioning

confidence: 98%

Section: Relation With Smt-pdmentioning

confidence: 99%

“…Proof. We use the notations in [9]. From [9], we have log |W i | ≥ N , N = K 1−D , K = kmin n−t + λ, k min = m, and log |M| = m. This gives the information rate,…”

Section: C2 Detail Of Bounding C 1 and Cmentioning

confidence: 99%

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confidence: 99%

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Adversarial wiretap channel with public discussion

Wang

2015

2015 IEEE Conference on Communications and Network Security (CNS)

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“…Robust secret sharing has also direct application to secure message transmission (SMT). In an unconditionally secure SMT [12,14,15], a sender is connected to a receiver through n wires such that up to t of which are controlled by an adversary. The goal of an SMT protocol is to ensure that the message sent by the sender is received correctly by the receiver, and no information about the message is leaked to the adversary.…”

Section: Introductionmentioning

confidence: 99%

Unconditionally-secure ideal robust secret sharing schemes for threshold and multilevel access structure

Jhanwar

2013

Journal of Mathematical Cryptology

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An n-player .t; ı/-secure robust secret sharing scheme is a .t; n/-threshold secret sharing scheme with the additional property that the secret can be recovered, with probability at least 1 ı, from the set of all shares even if up to t players provide incorrect shares. The existing constructions of robust secret sharing schemes for the range n 3 Ä t < n 2 have the share size larger than the secret size. An important goal in this area is to minimize the share size. In the paper, we propose a new unconditionally-secure robust secret sharing scheme for the case n 2t C 2 with share size equal to the secret size. This is the minimum possible size as dictated by the perfect secrecy of the scheme. We further extend our scheme to realize a class of multilevel access structures that satisfy a special condition. The property that the share size is equal to secret size is preserved in the extended scheme. The proposed scheme is the first known robust secret sharing scheme realizing multilevel access structure.

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Unconditionally-Secure Robust Secret Sharing with Compact Shares

Cevallos

Fehr

Ostrovsky³

et al. 2012

Advances in Cryptology – EUROCRYPT 2012

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We consider the problem of reconstructing a shared secret in the presence of faulty shares, with unconditional security. We require that any t shares give no information on the shared secret, and reconstruction is possible even if up to t out of the n shares are incorrect. The interesting setting is n/3 ≤ t < n/2, where reconstruction of a shared secret in the presence of faulty shares is possible, but only with an increase in the share size, and only if one admits a small failure probability. The goal of this work is to minimize this overhead in the share size. Known schemes either have a Ω(κn)-overhead in share size, where κ is the security parameter, or they have a close-to-optimal overhead of order O(κ + n) but have an exponential running time (in n). In this paper, we propose a new scheme that has a close-to-optimal overhead in the share size of orderÕ(κ + n), and a polynomial running time. Interestingly, the shares in our new scheme are prepared in the very same way as in the well-known scheme by Rabin and Ben-Or, which relies on message authentication, but we use a message authentication code with short tags and keys and with correspondingly weak security. The short tags and keys give us the required saving in the share size. Surprisingly, we can compensate for the weakened security of the authentication and achieve an exponentially small (in κ) failure probability by means of a more sophisticated reconstruction procedure.

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Secure Message Transmission With Small Public Discussion

Cited by 5 publications

References 35 publications

Adversarial wiretap channel with public discussion

Adversarial wiretap channel with public discussion

Unconditionally-secure ideal robust secret sharing schemes for threshold and multilevel access structure

Unconditionally-Secure Robust Secret Sharing with Compact Shares

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