Reaching Agreement in the Presence of Faults

Abstract

ABSTRACT. The problem addressed here concerns a set of isolated processors, some unknown subset of which may be faulty, that communicate only by means of two-party messages. Each nonfaulty processor has a private value of reformation that must be communicated to each other nonfanlty processor. Nonfaulty processors always communicate honestly, whereas faulty processors may lie The problem is to devise an algorithm in which processors communicate their own values and relay values received from others that allows each nonfaulty processor to refer a value for each other processor The value referred for a nonfanlty processor must be that processor's private value, and the value inferred for a faulty one must be consistent wRh the corresponding value inferred by each other nonfanlty processor It is shown that the problem is solvable for, and only for, n >_ 3m + 1, where m IS the number of faulty processors and n is the total number. It is also shown that if faulty processors can refuse to pass on reformation but cannot falsely relay information, the problem is solvable for arbitrary n _> m _> 0. This weaker assumption can be approxunated m practice using cryptographic methods

Fast Access to Distributed Atomic Memory

“…We consider a general model of computation where t among the set S of server processes on which the data structure is implemented can fail; in this paper, we assume t ≥ 1. A server can fail by crashing, or even by deviating arbitrarily from its algorithm and be malicious (also called Byzantine [26]). We denote by b the number of arbitrary server failures, where 0 ≤ b ≤ t. In this paper, we consider the authenticated arbitrary failure model in which processes can rely on unforgeable digital signatures [28].…”

“…On invoking a write, the writer increments its timestamp (initialized to 0) and sends a write message with the timestamp to all servers (lines 4-5). Upon receiving the message, servers update the timestamp and send writeack messages back to the writer (lines [22][23][24][25][26][27][28][29]. The writer returns ok once it has received writeack messages from S − t servers (lines 6-7).…”

“…At least one of those must have been received by r j in read rd that immediately precedes rd . Hence, maxT S rd = k, and maxT S in line 12 of rd equals k. Finally, S − t servers send readack to rd with the timestamp equal to k and the set updated that contains {r j } (see lines [22][23][24][25][26], i.e., k is admissible with degree 1 in rd . Finally, to help distinguish read and readack messages from different reads of the same reader, we implicitly (for better readability of pseudocode) assume that every reader r j maintains a local variable rdCnt j that r j increments at the beginning of every read invocation.…”

Communication Complexity of Consensus in Anonymous Message Passing Systems

“…Most of the literature on consensus concerns the presence of processor faults, that can be either crash or Byzantine, starting from the seminal paper [22]; see the recent book [23] for a comprehensive survey. In [18] the authors showed a randomized consensus for crash faults with optimal communication complexity.…”

Global, Unpredictable Bit Generation Without Broadcast

“…For many applications, such as Byzantine Agreement [13,4,16) -the problem of agreeing on a common value in a network with unreliable nodes -randomness itself is simultaneously not enough and too much. Secret sharing, multiparty protocols, reliable decentralized databases, multicasts, and even timestamping protocols can depend very strongly on agreed-upon information in a system.…”