A fast mutual exclusion algorithm
ACM Transactions on Computer Systems (TOCS)
Fault tolerance in networks of bounded degree
STOC '86 Proceedings of the eighteenth annual ACM symposium on Theory of computing
Completeness theorems for non-cryptographic fault-tolerant distributed computation
STOC '88 Proceedings of the twentieth annual ACM symposium on Theory of computing
Multiparty unconditionally secure protocols
STOC '88 Proceedings of the twentieth annual ACM symposium on Theory of computing
Tolerating linear number of faults in networks of bounded degree
PODC '92 Proceedings of the eleventh annual ACM symposium on Principles of distributed computing
Perfectly secure message transmission
Journal of the ACM (JACM)
Efficient perfectly secure message transmission in synchronous networks
Information and Computation
An Optimal Probabilistic Protocol for Synchronous Byzantine Agreement
SIAM Journal on Computing
Fully Polynomial Byzantine Agreement for Processors in Rounds
SIAM Journal on Computing
Simplified VSS and fast-track multiparty computations with applications to threshold cryptography
PODC '98 Proceedings of the seventeenth annual ACM symposium on Principles of distributed computing
Fast consensus in networks of bounded degree
Distributed Computing
On the Optimal Communication Complexity of Multiphase Protocols for Perfect Communication
SP '07 Proceedings of the 2007 IEEE Symposium on Security and Privacy
Deterministic Extractors for Bit-Fixing Sources and Exposure-Resilient Cryptography
SIAM Journal on Computing
Fuzzy Extractors: How to Generate Strong Keys from Biometrics and Other Noisy Data
SIAM Journal on Computing
Optimal secure message transmission by public discussion
ISIT'09 Proceedings of the 2009 IEEE international conference on Symposium on Information Theory - Volume 2
Towards optimal and efficient perfectly secure message transmission
TCC'07 Proceedings of the 4th conference on Theory of cryptography
Almost-everywhere secure computation
EUROCRYPT'08 Proceedings of the theory and applications of cryptographic techniques 27th annual international conference on Advances in cryptology
Truly efficient 2-round perfectly secure message transmission scheme
EUROCRYPT'08 Proceedings of the theory and applications of cryptographic techniques 27th annual international conference on Advances in cryptology
Asymptotically optimal two-round perfectly secure message transmission
CRYPTO'06 Proceedings of the 26th annual international conference on Advances in Cryptology
On expected constant-round protocols for byzantine agreement
CRYPTO'06 Proceedings of the 26th annual international conference on Advances in Cryptology
Secure message transmission by public discussion: a brief survey
IWCC'11 Proceedings of the Third international conference on Coding and cryptology
Public discussion must be back and forth in secure message transmission
ICISC'10 Proceedings of the 13th international conference on Information security and cryptology
Unconditionally-Secure robust secret sharing with compact shares
EUROCRYPT'12 Proceedings of the 31st Annual international conference on Theory and Applications of Cryptographic Techniques
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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 tn 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 $O(\frac{mn}{n-t})$, 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.)