1,913 research outputs found
Randomized algorithms for reliable broadcast
Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2009.Includes bibliographical references (p. 82-85).In this thesis, we design randomized algorithms for classical problems in fault tolerant distributed computing in the full-information model. The full-information model is a strong adversarial model which imposes no restrictions on the computational power of the faulty players nor on the information available to them. Namely, the faulty players are infinitely powerful and are privy to all the communications in the network. Our main result is the construction of two efficient randomized protocols for Byzantine agreement, a classical problem in distributed computing. Byzantine agreement is the problem of simulating the reliable broadcast functionality in a network where all communication is person-to-person. We design two randomized Byzantine agreement protocols in a synchronous network with an expected round-complexity of O(log n) rounds. One of the protocols is resilient against an all-powerful, full-information adversary that corrupts less than a third of the number of players (whereas the other protocol is resilient against a fourth fraction of corruptions). Our protocols have the following additional features. * The fault-tolerance of our protocols can be increased to less a half fraction of faults, if there is a public-key infrastructure setup available that allows the players to compute (public-key) digital signatures. * Our protocols work even if the source of randomness is a "somewhat random" source (also called a Santha-Vazirani source). The price we pay is a decreased fault-tolerance. Our second result is the design of a compiler that transforms a randomized distributed protocol that tolerates benign, fail-stop faults into a protocol that tolerates malicious, Byzantine faults. Fail-stop faults follow the protocol specification, but may stop in the middle of the execution. On the other hand, Byzantine faults are arbitrarily malicious.(cont.) The resulting protocol has almost the same fault-tolerance and efficiency as the original protocol. Our compiler suggests a modular way to design distributed protocols: first, design a protocol that tolerates fail-stop faults, and use our compiler to "boost" the fault-tolerance to Byzantine faults. The design of the compiler is based on a new protocol technique that we develop, called "auditing" of distributed protocols.by Vinod Vaikuntanathan.Ph.D
Breaking the O(n^2) Bit Barrier: Scalable Byzantine agreement with an Adaptive Adversary
We describe an algorithm for Byzantine agreement that is scalable in the
sense that each processor sends only bits, where is
the total number of processors. Our algorithm succeeds with high probability
against an \emph{adaptive adversary}, which can take over processors at any
time during the protocol, up to the point of taking over arbitrarily close to a
1/3 fraction. We assume synchronous communication but a \emph{rushing}
adversary. Moreover, our algorithm works in the presence of flooding:
processors controlled by the adversary can send out any number of messages. We
assume the existence of private channels between all pairs of processors but
make no other cryptographic assumptions. Finally, our algorithm has latency
that is polylogarithmic in . To the best of our knowledge, ours is the first
algorithm to solve Byzantine agreement against an adaptive adversary, while
requiring total bits of communication
Minimizing Message Size in Stochastic Communication Patterns: Fast Self-Stabilizing Protocols with 3 bits
This paper considers the basic model of communication, in
which in each round, each agent extracts information from few randomly chosen
agents. We seek to identify the smallest amount of information revealed in each
interaction (message size) that nevertheless allows for efficient and robust
computations of fundamental information dissemination tasks. We focus on the
Majority Bit Dissemination problem that considers a population of agents,
with a designated subset of source agents. Each source agent holds an input bit
and each agent holds an output bit. The goal is to let all agents converge
their output bits on the most frequent input bit of the sources (the majority
bit). Note that the particular case of a single source agent corresponds to the
classical problem of Broadcast. We concentrate on the severe fault-tolerant
context of self-stabilization, in which a correct configuration must be reached
eventually, despite all agents starting the execution with arbitrary initial
states.
We first design a general compiler which can essentially transform any
self-stabilizing algorithm with a certain property that uses -bits
messages to one that uses only -bits messages, while paying only a
small penalty in the running time. By applying this compiler recursively we
then obtain a self-stabilizing Clock Synchronization protocol, in which agents
synchronize their clocks modulo some given integer , within rounds w.h.p., and using messages that contain bits only.
We then employ the new Clock Synchronization tool to obtain a
self-stabilizing Majority Bit Dissemination protocol which converges in time, w.h.p., on every initial configuration, provided that the
ratio of sources supporting the minority opinion is bounded away from half.
Moreover, this protocol also uses only 3 bits per interaction.Comment: 28 pages, 4 figure
On the Round Complexity of Randomized Byzantine Agreement
We prove lower bounds on the round complexity of randomized Byzantine agreement (BA) protocols, bounding the halting probability of such protocols after one and two rounds. In particular, we prove that:
1) BA protocols resilient against n/3 [resp., n/4] corruptions terminate (under attack) at the end of the first round with probability at most o(1) [resp., 1/2+ o(1)].
2) BA protocols resilient against n/4 corruptions terminate at the end of the second round with probability at most 1-Theta(1).
3) For a large class of protocols (including all BA protocols used in practice) and under a plausible combinatorial conjecture, BA protocols resilient against n/3 [resp., n/4] corruptions terminate at the end of the second round with probability at most o(1) [resp., 1/2 + o(1)].
The above bounds hold even when the parties use a trusted setup phase, e.g., a public-key infrastructure (PKI).
The third bound essentially matches the recent protocol of Micali (ITCS\u2717) that tolerates up to n/3 corruptions and terminates at the end of the third round with constant probability
Stabilizing Consensus with Many Opinions
We consider the following distributed consensus problem: Each node in a
complete communication network of size initially holds an \emph{opinion},
which is chosen arbitrarily from a finite set . The system must
converge toward a consensus state in which all, or almost all nodes, hold the
same opinion. Moreover, this opinion should be \emph{valid}, i.e., it should be
one among those initially present in the system. This condition should be met
even in the presence of an adaptive, malicious adversary who can modify the
opinions of a bounded number of nodes in every round.
We consider the \emph{3-majority dynamics}: At every round, every node pulls
the opinion from three random neighbors and sets his new opinion to the
majority one (ties are broken arbitrarily). Let be the number of valid
opinions. We show that, if , where is a
suitable positive constant, the 3-majority dynamics converges in time
polynomial in and with high probability even in the presence of an
adversary who can affect up to nodes at each round.
Previously, the convergence of the 3-majority protocol was known for
only, with an argument that is robust to adversarial errors. On
the other hand, no anonymous, uniform-gossip protocol that is robust to
adversarial errors was known for
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