Quantum Solution to the Byzantine Agreement Problem

This chapter addresses fault diagnosis agreement problem in a network with malicious members. The authors provide a new algorithm to reach an agreement among fault-free members about the faulty ones. The algorithm is designed for fully-connected networks and also can be easily adapted to partially connected networks. The authors contribution is to reduce bit complexity of Byzantine agreement process by detecting the same list of faulty units in all fault-free members. Therefore, the malicious units can be removed from other consensus processes. Also, each healthy unit detects a list of malicious units locally which results in lower packet transmission in the network. The authors provided algorithm solves fault diagnosis agreement problem in 2t+1 rounds and O(nt+1) bit complexity for each member.

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ALMOST-SAFE BYZANTINE AGREEMENT IN SPARSE NETWORKS WITH RANDOM FAULTS

Parallel Processing Letters ◽

10.1142/s0129626495000448 ◽

1995 ◽

Vol 05 (03) ◽

pp. 489-497

Author(s):

ANDRZEJ PELC

Keyword(s):

Large Class ◽

Maximum Degree ◽

Byzantine Agreement ◽

Fixed Probability ◽

Sparse Networks ◽

Agreement Protocols ◽

Agreement Problem

We consider the Byzantine Agreement problem by assuming that nodes of a network fail independently with fixed probability 0 < p < 1. The goal is to construct almost-safe agreement protocols working for classes of sparse n-node networks. For such protocols, the probability of reaching consensus, under any behavior of faulty nodes, must converge to 1 as n grows. For p < 1/3 and every function L: N → N growing faster than linear, we show n-node networks with L (n) links and an almost-safe Byzantine Agreement protocol working for these networks. We also construct such a protocol working for a large class of n-node networks of maximum degree O( log n). We show, further, that these networks are asymptotically sparsest possible to support almost-safe Byzantine Agreement.

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The Byzantine agreement problem: optimal early stopping

Proceedings of the 32nd Annual Hawaii International Conference on Systems Sciences. 1999. HICSS-32. Abstracts and CD-ROM of Full Papers ◽

10.1109/hicss.1999.772983 ◽

2003 ◽

Cited By ~ 4

Author(s):

A.W. Krings ◽

T. Feyer

Keyword(s):

Byzantine Agreement ◽

Early Stopping ◽

Agreement Problem

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Efficient Byzantine Agreement in Networks with Random Faults

Parallel Processing Letters ◽

10.1142/s0129626497000097 ◽

1997 ◽

Vol 07 (01) ◽

pp. 69-76 ◽

Cited By ~ 1

Author(s):

Adam Malinowski

Keyword(s):

Arbitrary Constant ◽

Byzantine Agreement ◽

Time Optimal ◽

Synchronous Network ◽

Agreement Problem

We consider the Byzantine Agreement problem under the assumption that nodes and links of a synchronous network fail independently with constant probabilities p < 1/3 and q< 1 - 1/2(1-p), respectively. In a unit of time any node can send or receive a single bit of information. We present an asymptotically time-optimal agreement protocol, whose probability of correctness exceeds 1 - n-∊, where n is the number of nodes and ∊ > 0 an arbitrary constant.

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