Asymptotically Optimal Two-Round Perfectly Secure Message Transmission

Agarwal, Saurabh; Cramer, Ronald; Haan, Robbert de

doi:10.1007/11818175_24

Cited by 48 publications

(53 citation statements)

References 6 publications

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“…The goal is to send the message both privately and reliably. Since its introduction, SMT has been widely studied and optimized with respect to several different settings of parameters (for example, see [SA96,SNP04,ACH06,FFGV07,KS08]). …”

Section: Introductionmentioning

confidence: 99%

Secure Message Transmission with Small Public Discussion

Garay

Givens²,

Ostrovsky³

2010

Lecture Notes in Computer Science

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Abstract. In the problem of Secure Message Transmission in the public discussion model (SMT-PD), a Sender wants to send a message to a Receiver privately and reliably. Sender and Receiver are connected by n channels, up to t < n of which may be maliciously controlled by a computationally unbounded adversary, as well as one public channel, which is reliable but not private.The SMT-PD abstraction has been shown instrumental in achieving secure multi-party computation on sparse networks, where a subset of the nodes are able to realize a broadcast functionality, which plays the role of the public channel. However, the implementation of such public channel in point-to-point networks is highly costly and non-trivial, which makes minimizing the use of this resource an intrinsically compelling issue.In this paper, we present the first SMT-PD protocol with sublinear (i.e., logarithmic in m, the message size) communication on the public channel. In addition, the protocol incurs a private communication complexity of O( mn n−t ), which, as we also show, is optimal. By contrast, the best known bounds in both public and private channels were linear. Furthermore, our protocol has an optimal round complexity of (3, 2), meaning three rounds, two of which must invoke the public channel.Finally, we ask the question whether some of the lower bounds on resource use for a single execution of SMT-PD can be beaten on average through amortization. In other words, if Sender and Receiver must send several messages back and forth (where later messages depend on earlier ones), can they do better than the naïve solution of repeating an SMT-PD protocol each time? We show that amortization can indeed drastically reduce the use of the public channel: it is possible to limit the total number of uses of the public channel to two, no matter how many messages are ultimately sent between two nodes. (Since two uses of the public channel are required to send any reliable communication whatsoever, this is best possible.)

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Section: Introductionmentioning

confidence: 99%

Secure Message Transmission with Small Public Discussion

Garay

Givens²,

Ostrovsky³

2010

Lecture Notes in Computer Science

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“…More recently, Srinathan, Narayanan and Rangan [18] showed that, in order to achieve two-round PSMT, Ω(n ) bits must be communicated. This lower bound has been matched by the protocol by Agarwal, Cramer and de Haan [1], at the price, however, of requiring messages of length exponential in n. In [16], Patra, Choudhary, Srinathan and Rangan show that by using one additional round (i.e., three rounds in total), this communication bound can be achieved with polynomial message length.…”

Section: Introductionmentioning

confidence: 95%

“…Let Π 2 be the communication-optimal (but inefficient) two-round PSMT protocol in [1] (or even the communication-suboptimal protocol in [17]) for ν wires tolerating τ = ν−1 2 corrupted wires, where ν = O(1) (ν will be quantified later, based on the analysis below). Choosing ν = O(1) implies that protocol Π 2 's communication overhead is constant, and thus that Π 2 is communication-optimal.…”

Section: The Wire Virtualization Constructionmentioning

confidence: 99%

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Towards Optimal and Efficient Perfectly Secure Message Transmission

Fitzi

Franklin

Garay³

et al.

Lecture Notes in Computer Science

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Abstract. Perfectly secure message transmission (PSMT), a problem formulated by Dolev, Dwork, Waarts and Yung, involves a sender S and a recipient R who are connected by n synchronous channels of which up to t may be corrupted by an active adversary. The goal is to transmit, with perfect security, a message from S to R. PSMT is achievable if and only if n > 2t.For the case n > 2t, the lower bound on the number of communication rounds between S and R required for PSMT is 2, and the only known efficient (i.e., polynomial in n) two-round protocol involves a communication complexity of O(n 3 ) bits, where is the length of the message. A recent solution by Agarwal, Cramer and de Haan is provably communication-optimal by achieving an asymptotic communication complexity of O(n ) bits; however, it requires the messages to be exponentially large, i.e., = Ω(2 n ). In this paper we present an efficient communication-optimal tworound PSMT protocol for messages of length polynomial in n that is almost optimally resilient in that it requires a number of channels n ≥ (2 + ε)t, for any arbitrarily small constant ε > 0. In this case, optimal communication complexity is O( ) bits.

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“…We also already mentioned the relation of our tool for secure channels to the problem of perfectly secure message transmission [10], which has been further studied in, e.g., [28,8,29,1,12,24]. In [15], Franklin and Wright take a different approach and study the necessary and sufficient conditions for secure message transmissions over multicast lines.…”

Section: Introductionmentioning

confidence: 99%

Almost-Everywhere Secure Computation

Garay

Ostrovsky²

Advances in Cryptology – EUROCRYPT 2008

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Secure multi-party computation (MPC) is a central problem in cryptography. Unfortunately, it is well known that MPC is possible if and only if the underlying communication network has very large connectivity -in fact, Ω(t), where t is the number of potential corruptions in the network. This impossibility result renders existing MPC results far less applicable in practice, since many deployed networks have in fact a very small degree.In this paper, we show how to circumvent this impossibility result and achieve meaningful security guarantees for graphs with small degree (such as expander graphs and several other topologies). In fact, the notion we introduce, which we call almost-everywhere MPC, building on the notion of almosteverywhere agreement due to Dwork, Peleg, Pippenger and Upfal, allows the degree of the network to be much smaller than the total number of allowed corruptions. In essence, our definition allows the adversary to implicitly wiretap some of the good nodes by corrupting sufficiently many nodes in the "neighborhood" of those nodes. We show protocols that satisfy our new definition, retaining both correctness and privacy for most nodes despite small connectivity, no matter how the adversary chooses his corruptions.Instrumental in our constructions is a new model and protocol for the secure message transmission (SMT) problem, which we call SMT by public discussion, and which we use for the establishment of pairwise secure channels in limited connectivity networks.

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Asymptotically Optimal Two-Round Perfectly Secure Message Transmission

Cited by 48 publications

References 6 publications

Secure Message Transmission with Small Public Discussion

Secure Message Transmission with Small Public Discussion

Towards Optimal and Efficient Perfectly Secure Message Transmission

Almost-Everywhere Secure Computation

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