Fault tolerance in networks of bounded degree
STOC '86 Proceedings of the eighteenth annual ACM symposium on Theory of computing
Privacy amplification by public discussion
SIAM Journal on Computing - Special issue on cryptography
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
Reaching Agreement in the Presence of Faults
Journal of the ACM (JACM)
The Byzantine Generals Problem
ACM Transactions on Programming Languages and Systems (TOPLAS)
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
ICITS '08 Proceedings of the 3rd international conference on Information Theoretic Security
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
Improved fault tolerance and secure computation on sparse networks
ICALP'10 Proceedings of the 37th international colloquium conference on Automata, languages and programming: Part II
Secure message transmission with small public discussion
EUROCRYPT'10 Proceedings of the 29th Annual international conference on Theory and Applications of Cryptographic Techniques
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
Generalized privacy amplification
IEEE Transactions on Information Theory - Part 2
Unconditionally-Secure robust secret sharing with compact shares
EUROCRYPT'12 Proceedings of the 31st Annual international conference on Theory and Applications of Cryptographic Techniques
Edge fault tolerance on sparse networks
ICALP'12 Proceedings of the 39th international colloquium conference on Automata, Languages, and Programming - Volume Part II
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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 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. In this short survey paper, after formally defining the SMT-PD problem, we overview the basic constructions starting with the first, rather communication-inefficient solutions to the problem, and ending with the most efficient solutions known to-date--optimal private communication and sublinear public communication. These complexities refer to resource use for a single execution of an SMT-PD protocol. We also review the amortized complexity of the problem, which would arise in natural use-case scenarios where S and R must send several messages back and forth, where later messages depend on earlier ones.