# 1 Formal Modeling and Analysis of DoS Using Probabilistic Rewrite Theories Gul Agha Michael Greenwald Carl Gunter Sanjeev Khanna Jose Meseguer Koushik.

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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

2/28 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

3/28 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

4/28 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?

5/28 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

6/28 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 ?

7/28 Modeling and Analysis Probabilistic Rewrite Theories  Unified Algebraic Model  Probabilistic Object Model Properties in Continuous stochastic logic (CSL)  Statistical Model-checking [Sen et al. CAV’04, CAV’05, QEST’05] 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 [QAPL’05]

8/28 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

9/28 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%)

10/28 Attack Profile R S requires low b/w channel with high processing cost at R A loads this channel with bad packets S A

11/28 Selective Verification RA S

12/28 Selective Verification R R makes channels lossy S adds redundancy A gets reduced channel Tradeoff: bandwidth vs. processing S A

13/28 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

14/28 TCP/IP: 3-way handshake A: valid senderB: valid receiver SYN SYN + ACK ACK SYN Cache

15/28 TCP/IP: SYN Flood Attack A: valid senderB: valid receiver SYN SYN Cache X: attacker SYN SYN Cache Full Packet Dropped

16/28 TCP/IP: SYN Flood Attack A: valid senderB: valid receiver SYN Cache X: attacker SYN Drop packet with probability 0.75 SYN SYN + ACK ACK M Delap, M Greenwald, C Gunter, S Khanna, Y Xu 2004

17/28 Standard Rewrite Theories rules are of the form t(x) ! t’ (x) if cond t t’ cond

18/28 Probabilistic Rewrite Theories (PRTh) we add probability information to rules t(x) ! t’(x,y) if cond with probability y:=  (x) t cond t’ G Agha, J Meseguer, N Kumar, K Sen 2003

19/28 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), m+1i (XÃ SYN-ACK(B,m))

20/28 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), m+1i (XÃ SYN-ACK(B,m)) fi with probability drop? := BERNOULLI(p).

21/28 Availability Property Property: The probability that eventually the attacker X successfully fills up the SYN cache of B is less than 0.01. P <0.01 [§(sucessful_attack())] Statistical Model-checking using Vesta model-checker K Sen, M Viswanathan, G Agha 2005

22/28 Tools PMaude: Extends Maude with probabilistic rewrite theories [QAPL’05]  Monte Carlo simulation of probabilistic rewrite theories with on un-quantified non-determinism Vesta: Statistical model-checker for continuous stochastic logic [CAV’05]  Java implementation

23/28 Results Cache-size = 10,000 timeout = 10 seconds number of valid senders = 100

24/28 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 E[CountConnected()]

25/28 Linux Kernel Test Attack rate in SYNs/sec received at server Graph shows successful connections per 450 threads Defenseless kernel: >6 SYNs/sec shuts out client Aggregate connections Attack rate Model predicts cliff M Delap, M Greenwald, C Gunter, S Khanna, Y Xu 2004

26/28 Results Expected number of clients out of 100 clients that get connected with the server under DoS attack

27/28 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

28/28 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

29/28 SYN-flood defense: selective processing r X <= f B/t, then (1-f)B slots reserved for legit clients B B: size of SYN-cache t : timeout 0 < f < 1 r X : attacker rate p : probability of processing SYN at B M Delap, M Greenwald, C Gunter, S Khanna, Y Xu 2004

30/28 SYN-flood defense: selective processing r X <= f B/t, then (1-f)B slots reserved for legit clients Process SYNs with probability p <= f B/(t r X ) B p B: size of SYN-cache t : timeout 0 < f < 1 r X : attacker rate p : probability of processing SYN at B M Delap, M Greenwald, C Gunter, S Khanna, Y Xu 2004

31/28 SYN-flood defense: selective processing B p X 1/p Limited by net capacity. B: size of SYN-cache t : timeout 0 < f < 1 r X : attacker rate p : probability of processing SYN at B r X <= f B/t, then (1-f)B slots reserved for legit clients Process SYNs with probability p <= f B/(t r X ) Increase SYN packets sent by valid sender by 1/p M Delap, M Greenwald, C Gunter, S Khanna, Y Xu 2004

32/28 SYN-flood defense: selective processing r X <= f B/t, then (1-f)B slots reserved for legit clients Process SYNs with probability p <= f B/(t r X ) Increase SYN packets sent by valid sender by 1/p Attacker rate of p r X cannot fill more than f B slots B p p r A X 1/p rArA B: size of SYN-cache t : timeout 0 < f < 1 r X : attacker rate p : probability of processing SYN at B M Delap, M Greenwald, C Gunter, S Khanna, Y Xu 2004

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