Formal Modeling and Analysis of DoS Using Probabilistic Rewrite Theories

1
Formal Modeling and Analysis of DoS Using
Probabilistic Rewrite Theories

• Gul Agha
• Michael Greenwald
• Carl Gunter
• Sanjeev Khanna

Jose Meseguer Koushik Sen Prasanna Thati
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Formal Analysis of Cryptographic Protocols

• Integrity and Confidentiality
• Recipient not fooled or leaks information
• algebraic techniques
• assumes idealized cryptographic primitives
• complexity-theoretic techniques
• based on complexity assumptions

3
Availability Attack

• Availability threats
• whether recipient available to valid sender
• algebraic and/or complexity theoretic methods are
  not suitable for finding availability threats
• assumes adversary can insert, delete, or replay
  messages
• availability attack is assured as the adversary
  can delete any valid packet

4
Availability Attack

• Availability threats
• whether recipient available to valid sender
• algebraic and/or complexity theoretic methods are
  not suitable for finding availability threats
• assumes adversary can insert, delete, or replay
  messages
• availability attack is assured as the adversary
  can delete any valid packet
• How to model and analyze availability formally?

5
Our Goal

• Given a protocol P, let properties T hold for P
• P is a traditional non-deterministic
  specification
• T is a set of integrity and confidentiality
  properties
• Extend P to P and T to T
• P is DoS hardened P
• T includes availability properties in addition
  to T
• Goal
• Prove that T hold for P
• without re-proving that T hold for P

6
Our Results

• Given a protocol P, let properties T hold for P
• P is a traditional non-deterministic
  specification
• T is a set of integrity and confidentiality
  properties
• Extend P to P and T to T
• P is DoS hardened P
• T includes availability properties in addition
  to T
• Goal
• Prove that T hold for P
• without re-proving that T hold for P

?
7
Modeling and Analysis

• Probabilistic Rewrite Theories
• Unified Algebraic Model
• Probabilistic Object Model
• Properties in Continuous stochastic logic (CSL)
• Statistical Model-checking Sen et al. CAV04,
  CAV05, QEST05
• using Monte Carlo simulation
• and statistical hypothesis testing
• QuaTEx
• Quantitative Temporal Expressions
• Query language to gain quantitative insight about
  a model
• Statistical computation of QuaTEx QAPL05

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DoS Models and Counter-measures

• Shared Memory model
• adversary cannot delete packet
• adversary can replay or insert message in the
  network
• Asymmetry Paradigm
• adversary attacks by recognizing
• certain operations at recipient are expensive
• whereas invoking them is easy
• so it uses all of its bandwidth to invoke
  expensive operations
• creates a difference (asymmetry)
• receiver can increase the burden on attacker
• selective verification is our approach

C Gunter, S Khanna, K Tan, S Venkatesh 2004
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Selective Sequential Verification

• The signature stream is vulnerable to signature
  flooding the adversary can devote his entire
  channel to fake signature packets
• Countermeasure
• Valid sender sends multiple copies of the
  signature packet
• receiver checks each incoming signature packet
  with some probability (say, 25 or 1)

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Attack Profile
R
A
S
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Selective Verification
R
A
S
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Selective Verification
R makes channels lossy
R
A
Tradeoff bandwidth vs. processing
S
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TCP/IP A case study

• Common
• Susceptible to DoS attacks
• SYN flood and others
• Existing solutions as benchmark
• Increase size of SYN cache, random drop, SYN
  cookies

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TCP/IP 3-way handshake
A valid sender
B valid receiver
SYN
SYN ACK
SYN Cache
ACK
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TCP/IP SYN Flood Attack
A valid sender
B valid receiver
X attacker
SYN
SYN
SYN Cache
SYN Cache Full Packet Dropped
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TCP/IP SYN Flood Attack
A valid sender
B valid receiver
X attacker
SYN
SYN
SYN Cache
SYN ACK
ACK
M Delap, M Greenwald, C Gunter, S Khanna, Y Xu
2004
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Standard Rewrite Theories

• rules are of the form
• t(x) ! t (x) if cond

t
t
cond
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Probabilistic Rewrite Theories (PRTh)

• we add probability information to rules
• t(x) ! t(x,y) if cond with probability
  y?(x)

t
t
cond
G Agha, J Meseguer, N Kumar, K Sen 2003
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Model TCP/IP 3-way handshake using PRwTh

• P
• Receiver h B buf , mi
• Message (X Ã content)
• Rules
• drop packet
• h B buf , mi (BÃ SYN(X,n)) ) h B buf, mi
• process packet
• h B buf , mi (BÃ SYN(X,n)) )
• h B buf TCB(X,m) , m1i (XÃ SYN-ACK(B,m))

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Model TCP/IP 3-way handshake using PRwTh

• P
• Receiver h B buf , mi
• Message (X Ã content)
• One Rule (selective verification)
• h B buf , mi (BÃ SYN(X,n))
• )
• if drop?
• then
• h B buf, mi
• else
• h B buf TCB(X,m) , m1i (XÃ SYN-ACK(B,m))
• fi
• with probability drop? BERNOULLI(p) .

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Availability Property

• Property The probability that eventually the
  attacker X successfully fills up the SYN cache of
  B is less than 0.01.
• Plt0.01(sucessful_attack())
• Statistical Model-checking using Vesta
  model-checker

K Sen, M Viswanathan, G Agha 2005
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Tools

• PMaude Extends Maude with probabilistic rewrite
  theories QAPL05
• Monte Carlo simulation of probabilistic rewrite
  theories with on un-quantified non-determinism
• Vesta Statistical model-checker for continuous
  stochastic logic CAV05
• Java implementation

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Results

• Cache-size 10,000
• timeout 10 seconds
• number of valid senders 100

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Quantitative Queries Using QuaTEx

• What is the expected number of clients that
  successfully connect to S out of 100 clients?
• What is the probability that a client connected
  to S within 10 seconds after it initiated the
  connection request?
• CountConnected() if completed() then count()
  else (CountConnected()) fi
• eval ECountConnected()

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Linux Kernel Test

• Attack rate in SYNs/sec received at server
• Graph shows successful connections per 450
  threads
• Defenseless kernel gt6 SYNs/sec shuts out client

Aggregate connections
Attack rate
Model predicts cliff
M Delap, M Greenwald, C Gunter, S Khanna, Y Xu
2004
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Results
Expected number of clients out of 100 clients
that get connected with the server under DoS
attack
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Conclusion

• A general framework for modeling and verifying
  DoS properties of communication protocols.
• Capable of expressing and proving key
  availability properties.
• Performance limitations require us to use scaled
  down version of parameters.
• Future Work
• Addressing efficiency limitations
• Verifying the properties for general systems

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Summary

• Given a protocol P, let properties T hold for P
• P is a traditional non-deterministic
  specification
• T is a set of integrity and confidentiality
  properties
• Extend P to P and T to T
• P is DoS hardened P
• T includes availability properties in addition
  to T
• Goal
• Prove that T hold for P
• without re-proving that T hold for P

29
SYN-flood defense selective processing
B size of SYN-cache t timeout 0 lt f lt 1 rX
attacker rate p probability of processing SYN
at B
B

• rX lt f B/t, then (1-f)B slots reserved for
  legit clients

M Delap, M Greenwald, C Gunter, S Khanna, Y Xu
2004
30
SYN-flood defense selective processing
B size of SYN-cache t timeout 0 lt f lt 1 rX
attacker rate p probability of processing SYN
at B
B
p

• rX lt f B/t, then (1-f)B slots reserved for
  legit clients
• Process SYNs with probability p lt f B/(t rX)

M Delap, M Greenwald, C Gunter, S Khanna, Y Xu
2004
31
SYN-flood defense selective processing
B size of SYN-cache t timeout 0 lt f lt 1 rX
attacker rate p probability of processing SYN
at B
X 1/p
Limited by net capacity.
B
p
X 1/p

• rX lt f B/t, then (1-f)B slots reserved for
  legit clients
• Process SYNs with probability p lt f B/(t rX)
• Increase SYN packets sent by valid sender by 1/p

M Delap, M Greenwald, C Gunter, S Khanna, Y Xu
2004
32
SYN-flood defense selective processing
B size of SYN-cache t timeout 0 lt f lt 1 rX
attacker rate p probability of processing SYN
at B
rA
p rA
B
p
X 1/p

• rX lt f B/t, then (1-f)B slots reserved for
  legit clients
• Process SYNs with probability p lt f B/(t rX)
• Increase SYN packets sent by valid sender by 1/p
• Attacker rate of p rX cannot fill more than f B
  slots

M Delap, M Greenwald, C Gunter, S Khanna, Y Xu
2004