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
Distributed consensus revisited
Information Processing Letters
Reaching Agreement in the Presence of Faults
Journal of the ACM (JACM)
The Byzantine Generals Problem
ACM Transactions on Programming Languages and Systems (TOPLAS)
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
Almost-everywhere secure computation
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 by public discussion: a brief survey
IWCC'11 Proceedings of the Third international conference on Coding and cryptology
TCC'13 Proceedings of the 10th theory of cryptography conference on Theory of Cryptography
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Byzantine agreement, which requires n processors (nodes) in a completely connected network to agree on a value dependent on their initial values and despite the arbitrary, possible malicious behavior of some of them, is perhaps the most popular paradigm in fault-tolerant distributed systems. However, partially connected networks are far more realistic than fully connected networks, which led Dwork, Peleg, Pippenger and Upfal [STOC'86] to formulate the notion of almost-everywhere (a.e.) agreement which shares the same aim with the original problem, except that now not all pairs of nodes are connected by reliable and authenticated channels. In such a setting, agreement amongst all correct nodes cannot be guaranteed due to possible poor connectivity with other correct nodes, and some of them must be given up. The number of such nodes is a function of the underlying communication graph and the adversarial set of nodes. In this work we introduce the notion of almost-everywhere agreement with edge corruptions which is exactly the same problem as described above, except that we additionally allow the adversary to completely control some of the communication channels between two correct nodes--i.e., to "corrupt" edges in the network. While it is easy to see that an a.e. agreement protocol for the original node-corruption model is also an a.e. agreement protocol tolerating edge corruptions (albeit for a reduced fraction of edge corruptions with respect to the bound for node corruptions), no polynomial-time protocol is known in the case where a constant fraction of the edges can be corrupted and the degree of the network is sub-linear. We make progress on this front, by constructing graphs of degree O(nε) (for arbitrary constant 0εμn (for some constant 0μ In addition, building upon the work of Garay and Ostrovsky [Eurocrypt'08], we obtain a protocol for a.e. secure computation tolerating edge corruptions on the above graphs.