Fault tolerance in networks of bounded degree
STOC '86 Proceedings of the eighteenth annual ACM symposium on Theory of computing
An O(lg n) expected rounds randomized Byzantine generals protocol
STOC '85 Proceedings of the seventeenth 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
Distributed consensus revisited
Information Processing Letters
Simple and efficient leader election in the full information model
STOC '94 Proceedings of the twenty-sixth annual ACM symposium on Theory of computing
Agreement in the presence of faults, on networks of bounded degree
Information Processing Letters
Randomness-optimal sampling, extractors, and constructive leader election
STOC '96 Proceedings of the twenty-eighth annual ACM symposium on Theory of 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 (Extended Abstract)
WDAG '90 Proceedings of the 4th International Workshop on Distributed Algorithms
Asymptotically Optimal Distributed Consensus (Extended Abstract)
ICALP '89 Proceedings of the 16th International Colloquium on Automata, Languages and Programming
Bounds on information exchange for Byzantine Agreement
PODC '82 Proceedings of the first ACM SIGACT-SIGOPS symposium on Principles of distributed computing
Efficient player-optimal protocols for strong and differential consensus
Proceedings of the twenty-second annual symposium on Principles of distributed computing
Towards Secure and Scalable Computation in Peer-to-Peer Networks
FOCS '06 Proceedings of the 47th Annual IEEE Symposium on Foundations of Computer Science
The Effect of Faults on Network Expansion
Theory of Computing Systems
Almost Euclidean subspaces of ℓN1 via expander codes
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
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
From almost everywhere to everywhere: byzantine agreement with Õ(n³/²) bits
DISC'09 Proceedings of the 23rd international conference on 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
Edge fault tolerance on sparse networks
ICALP'12 Proceedings of the 39th international colloquium conference on Automata, Languages, and Programming - Volume Part II
TCC'13 Proceedings of the 10th theory of cryptography conference on Theory of Cryptography
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In the problem of almost-everywhere agreement (denoted a.e. agreement), introduced by Dwork, Peleg, Pippenger, and Upfal [STOC '86], n parties want to reach agreement on an initially held value, despite the possible disruptive and malicious behavior of up to t of them. So far this is reminiscent of the classical Byzantine agreement problem, except that in the alternative formulation the underlying connectivity graph is sparse--i.e., not all parties share point-to-point reliable channels--thus modeling the actual connectivity of real communication networks. In this setting, one may not be able to guarantee agreement amongst all honest parties, and some of them, say x, must be given up. Thus, in this line of work the goal is to be able to tolerate a high value for t (a constant fraction of n is the best possible) while minimizing x. As shown in the original paper, the dependency on d, the degree of the network, to achieve this goal is paramount. Indeed, the best polynomial-time a.e. agreement protocol tolerating a constant fraction of corruptions t = αn, for some constant α 0 (presented in the original paper, over two decades ago) has parameters, d = nεfor constant ε 0 and x = µt for some constant µ 1. In this work, we significantly improve on the above parameters obtaining a protocol with t = αn, d = O(logq n), for constant q 0 and x = O(t/log n). Our approach follows that of Dwork et al. of reducing the a.e. agreement problem to constructing a reliable transmission scheme between pairs of nodes for a large fraction of them; however, given our setting's more stringent conditions--poly-logarithmic degree and a linear number of corruptions, such a task is significantly harder. We also consider the problem of secure computation on partially connected networks, as formulated by Garay and Ostrovsky [Eurocrypt '08], and as a corollary to our main result obtain an almost-everywhere secure multi-party computation protocol with the same parameters as above, again significantly improving on the bound on the number of left-out parties--x = O(t/log n) for t ≤ αn corruptions, as opposed to x = O(t) in the original work.