Towards Scalable and Robust Overlay Networks

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Towards Scalable and Robust Overlay Networks

• Christian Scheideler
• Institut für Informatik
• Technische Universität München

Baruch Awerbuch Dept. of Computer Science Johns
Hopkins University
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Motivation

• Peer-to-peer systems have attracted a lot of
  attention in recent years
• Many structured peer-to-peer systems use overlay
  networks based on virtual space

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Example

• Chord
• Each peer assigned to (pseudo-)random point in
  0,1)
• Each peer at point x connects to peers closest to
  x1/2, x1/4, x1/8,(mod 1)

0
1
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Basic Goals

• Scalability
• Network has (poly-)logarithmic diameter
• Peers have (poly-)logarithmic degree
• Join/leave require (poly-)logarithmic work
• Robustness
• Network robust against insider and outsider
  attacks (minimal goal honest peers form single
  connected component)

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Join-Leave Attacks

• In open peer-to-peer systems
• Goal make abuse of join and leave operations hard

• peers may frequently join and leave

• not all peers are honest/reliable

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Join-Leave Model

• n honest peers
• ?n adversarial peers, ?lt1
• Operations
• Join(v) peer v joins the system
• Leave(v) peer v leaves the system
• Goal maintain scalability and robustness for
  any sequence of polynomially many rejoin
  (leavejoin) requests

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Join-Leave Model

• Goal maintain scalability and robustness for any
  sequence of polynomially many rejoin (leavejoin)
  requests
• Adversary can decide adaptively which peer
  (honest or adversarial) has to rejoin

time
Rejoin(v1)
Rejoin(v2)
Rejoin(v3)
Rejoin(v4)
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More specific goal

• n honest peers, ?n adversarial peers
• every peer has point in 0,1) (Chord)
• For any interval I ½ 0,1) of size (c log n)/n
• Balancing condition ?(log n) peers in I
• Majority condition honest peers in majority

c log n / n
I
0
1
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How to satisfy conditions?

• (1) use pseudo-random (cryptographic) hash
  function to map peers to points in 0,1)
• randomly distributes honest peers
• does not randomly distribute adversarial peers

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How to satisfy conditions?

• (2) map peers to random points in 0,1)

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How to satisfy conditions?

• (3) Group spreading AS04
• Map peers to random points in 0,1)
• Limit lifetime of peers

Too expensive!
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Only adversarial peers rejoin

• Rule that works k-cuckoo rule AS06

n honest ?n adversarial
evict k/n-region
? lt 1-1/k
Rejoin leave and join via k-cuckoo rule
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Limitation of k-cuckoo rule

• Only works for any sequence of rejoin requests of
  adversarial peers.
• Does not work for any sequence of rejoin
  requests.

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Local Load Balancing

• Works quite effectively to maintain overlay
  network if all peers are honest KSW05

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Random Filling/Flipping

• Fill position of leaving peer with random peer
• Flip k/n-region of leaving peer with random
  k/n-region

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Random-Neighbor-Flipping

• Flip random among c log n neighboring k/n-regions
  with random k/n-region

Analysisdifficult!
flip
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k-cuckooflip rule

• Join as before (k-cuckoo rule)
• Leave random k/n-region among c log n
  neighboring k/n-regions, empty flip it with
  random k/n-region

Rejoin viak-cuckoo rule
n honest ?n adversarial
flip
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Main Result

• Theorem For any constants ? and k with ?lt1/4-(2
  log k1)/k, the cuckooflip rule satisfies the
  balancing and majority conditions for a poly
  number of rejoin requests, w.h.p.
• Proofvia several worst-case high-concentration
  results for honest and adversarial peers

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Conclusions

• Algorithmic solutions are possible to counter
  join-leave attacks with constant factor overhead
• Concurrent join-leave operations fine with rate
  limit enforced by peers
• Massive departure of adversarial peers not a
  problem due to balancing condition

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Conclusions

• Problem strategy is high-level and only covers
  legal attacks on overlay network (resp. DoS
  attacks on one honest node at a time)
• Low-level protocols
• Most critical issue is random number gen.
• Low-level protocol for that in AS06b(works
  unlike VSS - for public channels)

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Conclusions

• Problem strategy is high-level and only covers
  legal attacks on overlay network (resp. DoS
  attacks on one honest node at a time)
• Illegal attacks
• Biggest problem low-level DoS attacks
• Only oblivious or relatively weak adaptive
  attackers can be handled so far

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Questions?