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Nonlinear network coding is necessary to combat general byzantine attacks
- in 47th Annual Allerton Conference on Communication, Control, and Computing
, 2009
"... Abstract — We consider the problem of achieving capacity through network coding when some of the nodes act covertly as Byzantine adversaries. For several case-study networks, we investigate rates of reliable communication through network coding and upper bounds on capacity. We show that linear codes ..."
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Cited by 29 (4 self)
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Abstract — We consider the problem of achieving capacity through network coding when some of the nodes act covertly as Byzantine adversaries. For several case-study networks, we investigate rates of reliable communication through network coding and upper bounds on capacity. We show that linear codes are inadequate in general, and a slight augmentation of the class of linear codes can increase throughput. Furthermore, we show that even this nonlinear augmentation may not be enough to achieve capacity. We introduce a new class of codes known as bounded-linear that make use of distributions defined over bounded sets of integers subject to linear constraints using real arithmetic. I.
Polytope Codes Against Adversaries in Networks”-
- IEEE Transactions on Information Theory,
, 2014
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A Multi-hop Multi-source Algebraic Watchdog
- IEEE INFORMATION THEORY WORKSHOP- ITW 2010 DUBLIN
, 2010
"... In our previous work (‘An Algebraic Watchdog for Wireless Network Coding’), we proposed a new scheme in which nodes can detect malicious behaviors probabilistically, police their downstream neighbors locally using overheard messages; thus, provide a secure global self-checking network. As the first ..."
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Cited by 6 (1 self)
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In our previous work (‘An Algebraic Watchdog for Wireless Network Coding’), we proposed a new scheme in which nodes can detect malicious behaviors probabilistically, police their downstream neighbors locally using overheard messages; thus, provide a secure global self-checking network. As the first building block of such a system, we focused on a two-hop network, and presented a graphical model to understand the inference process by which nodes police their downstream neighbors and to compute the probabilities of misdetection and false detection. In this paper, we extend the Algebraic Watchdog to a more general network setting, and propose a protocol in which we can establish trust in coded systems in a distributed manner. We develop a graphical model to detect the presence of an adversarial node downstream within a general two-hop network. The structure of the graphical model (a trellis) lends itself to well-known algorithms, such as Viterbi algorithm, that can compute the probabilities of misdetection and false detection. Using this as a building block, we generalize our scheme to multi-hop networks. We show analytically that as long as the min-cut is not dominated by the Byzantine adversaries, upstream nodes can monitor downstream neighbors and allow reliable communication with certain probability. Finally, we present preliminary simulation results that support our analysis.
Capacity of Byzantine Agreement (Preliminary Draft – Work in Progress)
, 2010
"... Caveat: This report represents work-in-progress, and provides some of our early results on the topic. A more complete version of this report, with additional results not presented in this draft, and improved description of the algorithms and analysis, will be released later this year. This draft ver ..."
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Cited by 2 (2 self)
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Caveat: This report represents work-in-progress, and provides some of our early results on the topic. A more complete version of this report, with additional results not presented in this draft, and improved description of the algorithms and analysis, will be released later this year. This draft version contains known problems with clarity/readability and the descriptions are incomplete/imprecise in some places. The draft is being released nevertheless to seek early feedback from other researchers. 1
Split Null Keys: A Null Space Based Defense for Pollution Attacks in Wireless Network Coding
"... Abstract—Recent work in defending against pollution attacks for intra-flow network coding systems proposed a null spaces based algebraic approach which has a smaller computation cost than previous pollution defenses. The approach requires the source to distribute keys periodically, but in order to s ..."
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Cited by 1 (0 self)
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Abstract—Recent work in defending against pollution attacks for intra-flow network coding systems proposed a null spaces based algebraic approach which has a smaller computation cost than previous pollution defenses. The approach requires the source to distribute keys periodically, but in order to scale involves forwarder nodes in the creation of new keys and their distribution. As a result the key distribution is secure only in specific network topologies such as those created by large-scale peer to peer systems, and is not secure in wireless networks where such topologies do not exist. We propose Split Null Keys, which splits the keys such that only a small portion of the key is updated periodically. The small updates allow for a scalable key distribution scheme that does not involve forwarder nodes in creating keys and thus does not rely its security on constraints imposed on the network topology. We prove that our scheme is secure despite splitting the key and we show that when compared with existing defenses our scheme imposes lower communication and computation overhead, is resilient to colluding adversaries, and does not require time synchronization. I.
Going Beyond Pollution Attacks: Forcing Byzantine Clients to Code Correctly
, 2011
"... Network coding achieves optimal throughput in multicast networks. However, throughput optimality relies on the network nodes or routers to code correctly. A Byzantine node may introduce junk packets in the network (thus polluting downstream packets and causing the sinks to receive the wrong data) or ..."
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Cited by 1 (0 self)
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Network coding achieves optimal throughput in multicast networks. However, throughput optimality relies on the network nodes or routers to code correctly. A Byzantine node may introduce junk packets in the network (thus polluting downstream packets and causing the sinks to receive the wrong data) or may choose coding coefficients in a way that significantly reduces the throughput of the network. Most prior work focused on the problem of Byzantine nodes polluting packets. However, even if a Byzantine node does not pollute packets, he can still affect significantly the throughput of the network by not coding correctly. No previous work attempted to verify if a certain node coded correctly using random coefficients over all of the packets he was supposed to code over. We provide two novel protocols (which we call PIP and Log-PIP) for detecting whether a node coded correctly over all the packets received (i.e., according to a random linear network coding algorithm). Our protocols enable any node in the network to examine a packet received from another node by running a “verification test”. With our protocols, the worst an adversary can do and still pass the packet verification test is in fact equivalent to random linear network coding, which has
ADVERSARIES IN NETWORKS
, 2010
"... As systems become more distributed, they are vulnerable to new forms of attack. An adversary could seize control of several nodes in a network and reprogram them, unbeknownst to the rest of the network. Strategies are needed that can ensure robust performance in the presence of these sorts of attack ..."
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As systems become more distributed, they are vulnerable to new forms of attack. An adversary could seize control of several nodes in a network and reprogram them, unbeknownst to the rest of the network. Strategies are needed that can ensure robust performance in the presence of these sorts of attacks. This thesis studies the adversarial problem in three scenarios. First is the problem of network coding, in which a source seeks to send data to a destination through a network of intermediate nodes that may perform arbitrarily complicated coding functions. When an adversary controls nodes in the network, achievable rates and upper bounds on capacity are found, and Polytope Codes are introduced, which are a nonlinear class of codes specially designed to handle adversaries in a network coding framework. Second, multiterminal source coding is studied, in which several nodes make correlated measurements, independently encode them, and transmit their encodings to a common decoder, which attempts to recover some information. Two special cases of this problem are studied when several of the nodes may be con-
I. COUNTER EXAMPLE FOR PREVIOUS CONJECTURE IN
, 2009
"... In our previous work [1] and [2] we showed by example that linear network coding cannot achieve secure network capacity for error detection. To the best of our knowledge, it was the first work that identified the insufficiency of linear network codes in achieving secure capacity, even for unicast. S ..."
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In our previous work [1] and [2] we showed by example that linear network coding cannot achieve secure network capacity for error detection. To the best of our knowledge, it was the first work that identified the insufficiency of linear network codes in achieving secure capacity, even for unicast. Some recent works [3], [4] also discovered (independently) the necessity of non-linear network codes to achieve secure capacity.
When Watchdog Meets Coding II
, 2009
"... In this paper, we study the problem of misbe-havior detection in wireless networks. A commonly adopted approach is to utilize the broadcast nature of the wireless medium and have nodes monitor their neighborhood. We call such nodes the Watchdogs. We propose a lightweight misbehavior detection scheme ..."
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In this paper, we study the problem of misbe-havior detection in wireless networks. A commonly adopted approach is to utilize the broadcast nature of the wireless medium and have nodes monitor their neighborhood. We call such nodes the Watchdogs. We propose a lightweight misbehavior detection scheme which integrates the idea of watchdogs and error detection coding. We show that even if the watchdog can only observe a fraction of packets, by choosing the encoder properly, an attacker will be detected with high probability while achieving throughput arbitrarily close to optimal. Such properties reduce the incentive for the attacker to attack. We then consider the problem of locating the misbehaving node and propose a simple protocol, which correctly locates the misbehaving node with high probability. The protocol requires exactly two watchdogs per unreliable relay node.
