Fault tolerance in networks of bounded degree
STOC '86 Proceedings of the eighteenth annual ACM symposium on Theory of computing
STOC '87 Proceedings of the nineteenth 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
Verifiable secret sharing and multiparty protocols with honest majority
STOC '89 Proceedings of the twenty-first 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
Fully Polynomial Byzantine Agreement for Processors in Rounds
SIAM Journal on Computing
Reaching Agreement in the Presence of Faults
Journal of the ACM (JACM)
Reducibility and Completeness in Private Computations
SIAM Journal on Computing
The Byzantine Generals Problem
ACM Transactions on Programming Languages and Systems (TOPLAS)
A Continuum of Failure Models for Distributed Computing
WDAG '92 Proceedings of the 6th International Workshop on Distributed Algorithms
On 2-Round Secure Multiparty Computation
CRYPTO '02 Proceedings of the 22nd Annual International Cryptology Conference on Advances in Cryptology
Trading Correctness for Privacy in Unconditional Multi-Party Computation (Extended Abstract)
CRYPTO '98 Proceedings of the 18th Annual International Cryptology Conference on Advances in Cryptology
Perfectly Secure Message Transmission Revisited
EUROCRYPT '02 Proceedings of the International Conference on the Theory and Applications of Cryptographic Techniques: Advances in Cryptology
Almost everywhere secure computation
Almost everywhere secure computation
Protocols for secure computations
SFCS '82 Proceedings of the 23rd Annual Symposium on Foundations of Computer Science
Verifiable secret sharing and achieving simultaneity in the presence of faults
SFCS '85 Proceedings of the 26th Annual Symposium on Foundations of Computer Science
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
Asymptotically optimal two-round perfectly secure message transmission
CRYPTO'06 Proceedings of the 26th annual international conference on Advances in Cryptology
Round-Optimal and efficient verifiable secret sharing
TCC'06 Proceedings of the Third conference on Theory of Cryptography
Generalized privacy amplification
IEEE Transactions on Information Theory - Part 2
ICITS '08 Proceedings of the 3rd international conference on Information Theoretic Security
Secure Function Collection with Sublinear Storage
ICALP '09 Proceedings of the 36th Internatilonal Collogquium on Automata, Languages and Programming: Part II
Optimal secure message transmission by public discussion
ISIT'09 Proceedings of the 2009 IEEE international conference on Symposium on Information Theory - Volume 2
Truly efficient 2-round perfectly secure message transmission scheme
IEEE Transactions on Information Theory
Privacy-preserving computation of benchmarks on item-level data using RFID
Proceedings of the third ACM conference on Wireless network security
Almost-everywhere secure computation
EUROCRYPT'08 Proceedings of the theory and applications of cryptographic techniques 27th annual international conference on Advances in cryptology
From almost everywhere to everywhere: byzantine agreement with Õ(n³/²) bits
DISC'09 Proceedings of the 23rd international conference on Distributed computing
Brief announcement: realizing secure multiparty computation on incomplete networks
Proceedings of the 29th ACM SIGACT-SIGOPS symposium on Principles of distributed computing
Breaking the O(n2) bit barrier: scalable byzantine agreement with an adaptive adversary
Proceedings of the 29th ACM SIGACT-SIGOPS symposium on Principles of distributed computing
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
Breaking the O(n2) bit barrier: Scalable byzantine agreement with an adaptive adversary
Journal of the ACM (JACM)
Coordinated consensus in dynamic networks
Proceedings of the 30th annual ACM SIGACT-SIGOPS symposium on Principles of distributed computing
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
Secure message transmission with small public discussion
EUROCRYPT'10 Proceedings of the 29th Annual international conference on Theory and Applications of Cryptographic Techniques
Long distance quantum cryptography made simple
Quantum Information & Computation
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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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 almost-everywhere 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.