12,335 research outputs found
On Compact Routing for the Internet
While there exist compact routing schemes designed for grids, trees, and
Internet-like topologies that offer routing tables of sizes that scale
logarithmically with the network size, we demonstrate in this paper that in
view of recent results in compact routing research, such logarithmic scaling on
Internet-like topologies is fundamentally impossible in the presence of
topology dynamics or topology-independent (flat) addressing. We use analytic
arguments to show that the number of routing control messages per topology
change cannot scale better than linearly on Internet-like topologies. We also
employ simulations to confirm that logarithmic routing table size scaling gets
broken by topology-independent addressing, a cornerstone of popular
locator-identifier split proposals aiming at improving routing scaling in the
presence of network topology dynamics or host mobility. These pessimistic
findings lead us to the conclusion that a fundamental re-examination of
assumptions behind routing models and abstractions is needed in order to find a
routing architecture that would be able to scale ``indefinitely.''Comment: This is a significantly revised, journal version of cs/050802
MPC for MPC: Secure Computation on a Massively Parallel Computing Architecture
Massively Parallel Computation (MPC) is a model of computation widely believed to best capture realistic parallel computing architectures such as large-scale MapReduce and Hadoop clusters. Motivated by the fact that many data analytics tasks performed on these platforms involve sensitive user data, we initiate the theoretical exploration of how to leverage MPC architectures to enable efficient, privacy-preserving computation over massive data. Clearly if a computation task does not lend itself to an efficient implementation on MPC even without security, then we cannot hope to compute it efficiently on MPC with security. We show, on the other hand, that any task that can be efficiently computed on MPC can also be securely computed with comparable efficiency. Specifically, we show the following results:
- any MPC algorithm can be compiled to a communication-oblivious counterpart while asymptotically preserving its round and space complexity, where communication-obliviousness ensures that any network intermediary observing the communication patterns learn no information about the secret inputs;
- assuming the existence of Fully Homomorphic Encryption with a suitable notion of compactness and other standard cryptographic assumptions, any MPC algorithm can be compiled to a secure counterpart that defends against an adversary who controls not only intermediate network routers but additionally up to 1/3 - ? fraction of machines (for an arbitrarily small constant ?) - moreover, this compilation preserves the round complexity tightly, and preserves the space complexity upto a multiplicative security parameter related blowup.
As an initial exploration of this important direction, our work suggests new definitions and proposes novel protocols that blend algorithmic and cryptographic techniques
Space-Efficient Routing Tables for Almost All Networks and the Incompressibility Method
We use the incompressibility method based on Kolmogorov complexity to
determine the total number of bits of routing information for almost all
network topologies. In most models for routing, for almost all labeled graphs
bits are necessary and sufficient for shortest path routing. By
`almost all graphs' we mean the Kolmogorov random graphs which constitute a
fraction of of all graphs on nodes, where is an arbitrary
fixed constant. There is a model for which the average case lower bound rises
to and another model where the average case upper bound
drops to . This clearly exposes the sensitivity of such bounds
to the model under consideration. If paths have to be short, but need not be
shortest (if the stretch factor may be larger than 1), then much less space is
needed on average, even in the more demanding models. Full-information routing
requires bits on average. For worst-case static networks we
prove a lower bound for shortest path routing and all
stretch factors in some networks where free relabeling is not allowed.Comment: 19 pages, Latex, 1 table, 1 figure; SIAM J. Comput., To appea
On the robustness of bucket brigade quantum RAM
We study the robustness of the bucket brigade quantum random access memory
model introduced by Giovannetti, Lloyd, and Maccone [Phys. Rev. Lett. 100,
160501 (2008)]. Due to a result of Regev and Schiff [ICALP '08 pp. 773], we
show that for a class of error models the error rate per gate in the bucket
brigade quantum memory has to be of order (where is the
size of the memory) whenever the memory is used as an oracle for the quantum
searching problem. We conjecture that this is the case for any realistic error
model that will be encountered in practice, and that for algorithms with
super-polynomially many oracle queries the error rate must be
super-polynomially small, which further motivates the need for quantum error
correction. By contrast, for algorithms such as matrix inversion [Phys. Rev.
Lett. 103, 150502 (2009)] or quantum machine learning [Phys. Rev. Lett. 113,
130503 (2014)] that only require a polynomial number of queries, the error rate
only needs to be polynomially small and quantum error correction may not be
required. We introduce a circuit model for the quantum bucket brigade
architecture and argue that quantum error correction for the circuit causes the
quantum bucket brigade architecture to lose its primary advantage of a small
number of "active" gates, since all components have to be actively error
corrected.Comment: Replaced with the published version. 13 pages, 9 figure
Security and Privacy Issues in Wireless Mesh Networks: A Survey
This book chapter identifies various security threats in wireless mesh
network (WMN). Keeping in mind the critical requirement of security and user
privacy in WMNs, this chapter provides a comprehensive overview of various
possible attacks on different layers of the communication protocol stack for
WMNs and their corresponding defense mechanisms. First, it identifies the
security vulnerabilities in the physical, link, network, transport, application
layers. Furthermore, various possible attacks on the key management protocols,
user authentication and access control protocols, and user privacy preservation
protocols are presented. After enumerating various possible attacks, the
chapter provides a detailed discussion on various existing security mechanisms
and protocols to defend against and wherever possible prevent the possible
attacks. Comparative analyses are also presented on the security schemes with
regards to the cryptographic schemes used, key management strategies deployed,
use of any trusted third party, computation and communication overhead involved
etc. The chapter then presents a brief discussion on various trust management
approaches for WMNs since trust and reputation-based schemes are increasingly
becoming popular for enforcing security in wireless networks. A number of open
problems in security and privacy issues for WMNs are subsequently discussed
before the chapter is finally concluded.Comment: 62 pages, 12 figures, 6 tables. This chapter is an extension of the
author's previous submission in arXiv submission: arXiv:1102.1226. There are
some text overlaps with the previous submissio
Internet's Critical Path Horizon
Internet is known to display a highly heterogeneous structure and complex
fluctuations in its traffic dynamics. Congestion seems to be an inevitable
result of user's behavior coupled to the network dynamics and it effects should
be minimized by choosing appropriate routing strategies. But what are the
requirements of routing depth in order to optimize the traffic flow? In this
paper we analyse the behavior of Internet traffic with a topologically
realistic spatial structure as described in a previous study (S-H. Yook et al.
,Proc. Natl Acad. Sci. USA, {\bf 99} (2002) 13382). The model involves
self-regulation of packet generation and different levels of routing depth. It
is shown that it reproduces the relevant key, statistical features of
Internet's traffic. Moreover, we also report the existence of a critical path
horizon defining a transition from low-efficient traffic to highly efficient
flow. This transition is actually a direct consequence of the web's small world
architecture exploited by the routing algorithm. Once routing tables reach the
network diameter, the traffic experiences a sudden transition from a
low-efficient to a highly-efficient behavior. It is conjectured that routing
policies might have spontaneously reached such a compromise in a distributed
manner. Internet would thus be operating close to such critical path horizon.Comment: 8 pages, 8 figures. To appear in European Journal of Physics B (2004
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