1 Prasad Narayana, Ruiming Chen, Yao Zhao, Yan Chen and Hai Zhou Northwestern University, Evanston IL Z. Judy Fu Motorola Labs, Schaumburg IL Funded by Motorola Center for Seamless Communications Automatic Vulnerability Checking of Wireless Protocols through TLA+

2 Outline Motivation Our approach Background on TLA+ General methods and challenges Results on WiMAX initial ranging and authentication Conclusions and future work

3 Motivation High-speed Wireless Metropolitan Area Networks (MAN) poised to become the Next Big Thing IEEE (WiMAX) with enormous backing from the industry is set to lead the broadband wireless network space Security is especially critical for open air wireless protocols However, security analysis of the IEEE protocol largely confined to manual analysis –Incomplete –Inaccurate

4 Motivation (II) Formal methods for automatic vulnerability checking highly desirable –With completeness and correctness guarantees Previous studies focus on security protocols and security properties only –CSP and FDR [Lowe96], MurØ [Shmatikov98], Symbolic traces and PS-LTL [Corin06] Non-security protocol analysis focus on resource exhaustion DoS attacks and ignore protocol malfunction attacks ! –[Yu88], [Meadow99], and [Meadow02]

5 Outline Motivation Our approach Background on TLA+ General methods and challenges Results on WiMAX initial ranging and authentication Conclusions and future work

6 Our Approach Systematic and automatic checking through formal methods. –Formally specify a protocol in TLA+ (Temporal Logic of Actions) –Formally model an attacker in TLA+ –Specify requested properties –Then automatically model-check for vulnerabilities Vulnerability analysis of e specs and WiMAX standards

7 Potential Benefits TLA+ specs of e can be used as golden model for implementations –Implementation correctness can be model-checked TLA+ attacker models and properties can be reused as test- benches when the protocol evolves –Correctness of modifications can be quickly checked

8 Outline Motivation Our approach Background on TLA+ General methods and challenges Results on WiMAX initial ranging and authentication Conclusions and future work

9 Why TLA+ A logic resulted from the past 20 years research on concurrent reactive systems One language for both system spec and proof logic Language is based on normal mathematics –Both abstract and detailed specs can be done at the right levels –System concepts are clean in math: composition: /\ nondeterministic: \/ implementation:  Modularity is employed for large specs Systems automatically model-checked by TLC

10 Intro to TLA+ TLA+ is a simple extension of linear temporal logic –Temporal operations: []—forever, <>—eventually –With primed variable (x’) for next state –A predicate with both non-primed and primed variables defines an action: x'=x-y /\ x>y A system is usually specified as Init /\ [] [Next] x −the system satisfies Init initially and satisfies Next for all transitions −Or simply, the system starts in Init and will do Next forever

11 TLA+ for Security A protocol can be specified as one monolithic system Or, it can be specified as a composition of many components: Protocol == CompA /\ CompB /\ \A i\in (1..n): Comp(i) An attacker can be specified similarly Checking security is to prove Protocol /\ Attacker  Property

12 Example: Simplifed SSL C  S: (C, VerC, SuiteC) S  C: (VerS, SuiteS, KeyS) C  S: (E KeyS (SecretC))

13 Protocol Spec Step 1: Client C sends message to server S: Step 2: Sever S responds to C with its public key KeyS: Step 3: Client C sends SecretC encrypted by KeyS:

14 Attacker Spec Intercept SC messages Intercept CS2 messages

15 Property of Secrecy Secrecy == [](secret=0) Model check: Protocol /\ Attacker  Secrecy

16 Result from TLC Error: Invariant Correctness is violated. The behavior up to this point is: STATE 1: /\ secret = 0 /\ msg = > STATE 2: /\ secret = 0 /\ msg = [type |-> "CS1", Name |-> "C", Ver |-> 1, Suite |-> 2] STATE 3: /\ secret = 0 /\ msg = [type |-> "SC", Ver |-> 6, Suite |-> 7, Key |-> 4] STATE 4: /\ secret = 0 /\ msg = [type |-> "SC", Ver |-> 6, Suite |-> 7, Key |-> 5] STATE 5: /\ secret = 0 /\ msg = [type |-> "CS2", Key |-> 5, Secret |-> 3] STATE 6: /\ secret = 3 /\ msg = [type |-> "CS2", Key |-> 4, Secret |-> 3] Secret is known by attacker Client and Sever do not know that the secret is not a “secret” now

17 Outline Motivation Our approach Background on TLA+ General methods and challenges Results on WiMAX initial ranging and authentication Conclusions and future work

18 TLA+ Vulnerability Checking Flow

19 TLA+ Protocol Specification Protocol specification in TLA+ can be easy or difficult –FSM easily translate to TLA+ –Tricky from English description to TLA+ spec: ambiguity, re-design, etc. Process of protocol specification: –Identify principals –Modularize principal behaviour using TLA+ –Combine principal specs to form a protocol spec

20 TLA+ Protocol Specification Challenges Challenge: Vagueness in English specification and the correctness in its translation to TLA+. Common problem for all approaches Solutions: –No easy solution exists! –Best designing protocols in TLA+ –Consult standards committee, product implementation teams among other things

21 Attacker Modelling Attacker capability model similar to Dolev-Yao model: Basically, attackers can: –Eavesdrop on and store messages. –Replay old messages. –Inject or spoof unprotected messages. –Corrupt messages on the channel by causing collisions. Assume the ideal cryptography: unforgeable signatures, safe encryption, and safe digest

22 Attacker Modelling Challenges Challenge: How to find all realistic attacks? –Model too strong: hide stealthy attacks –Model too weak: missing vulnerabilities Our solution: –Start with a relatively strong attacker model »TLC model-checks may yield unrealistic attacks. –Then weaken the attacker model »E.g.: the attacker can continuously corrupt a response from the BS. »Add restrictions on attacker to exclude such attacks. This dynamic modification of attacker model will end up with –a complete robustness proof OR –report of all attacks

23 Property Spec Focus on malfunction DoS attacks currently –Client needs to reach a termination <>[] (\A i\in PartySet: Party[i].state=ObjState) –Client may not terminate []<>(\A \in PartySet: Party[i].state=ObjState)

24 Property Spec Challenges Challenge: TLC cannot check all properties expressible in TLA+ Our Solution: Specify properties in restricted format

25 Model Checking by TLC TLC is a model checker for TLA+ Has both simulation mode and model checking mode –We run simulations before a complete model checking Terminate w/o violation: robustness proved Produce violation sequence: attack trace

26 Model Checking Challenges Challenge: State space explosions Our Solutions –Combine similar states without loss of functionality into one state –Identify symmetry in system, which will treat the different states as one common state. –Replace some random numbers with constants having some additional properties to simulate the effects of randomness

27 Outline Motivation Our approach Background on TLA+ General methods and challenges Results on WiMAX initial ranging and authentication Conclusions and future work

28 Case Studies Initial ranging Authentication process Choices based on the criticality of function and the probability of vulnerability

29 Initial Ranging Process Initial ranging: the first step an SS communicates with a BS via message exchanges. An SS acquires correct timing offset and power adjustments The request-response communication happens until the BS is satisfied with the ranging parameters. ’Actual’ data communication can happen only if the initial ranging is successful.

30 Property to Check SS can get service (getting into “Done” state) infinitely often []<>(SSstate = “Done”) –Need to make sure that such a property is true even without an attacker (weakest attacker model)

31 DOS during Initial Ranging (found by TLC Model Checking) DL Subframe Contention-based Initial Ranging Slots UL Subframe REQ

32 PKMv2 Authentication Process SS and BS mutually authenticate each other and exchange keys for data encryption PKMv2 is directed by two state machines in the SS –Authentication State Machine –TEK State Machine PKMv2 employs a SATEK three-way handshake for the BS and the SS to exchange security capabilities

33 Authentication – TLA Model Each key has a life time, so the SS needs to get authorized from time to time –SS will reach the “Authorized” state infinite times []<>(SSstate =”Authorized”) TLC encounters space explosion problem –We restrict the SS to reach “Authorized” state at most a given # of times. With our attacker model, TLC model checking completed w/o violation Hence, authentication process is resistant to any attempt under the given attacker model

34 Outline Motivation Our approach Background on TLA+ General methods and challenges Results on WiMAX initial ranging and authentication Conclusions and future work

35 Conclusions First step towards automatic vulnerability checking of WiMAX protocol with completeness and correctness guarantees Use TLA+/TLC to model malfunction DoS attacks –Avoid state space explosion in property checking –Model attackers’ capabilities for finding realistic attacks Analyzed initial ranging and authentication process in protocols

36 Future Work Development of a rigorous process in protocol specification using TLA+ Check vulnerabilities in other parts of standards such as mobility support and handoff procedures Exploration of more security properties: secrecy, resource exhaustion DoS

37 Thanks

38 Our Approach

39 Related Work (2) Automatically check with formal language –For security network protocols »CSP and FDR [Lowe96] »MurØ [Shmatikov98] »Symbolic traces and PS-LTL [Corin06] –For DoS attack »“A formal specification and verification method for the prevention of denial of service” [Yu88] »“Game-based analysis of denial-of-service prevention protocols” [Mahimkar05]

40 Example: Euclid's Algorithm Init == x=a /\ y=b Next == (x>y /\ x'=x-y) \/ (y>x /\ y'=y-x) Euclid(a,b) == Init /\ [][Next] Property == <>[](x=GCD(a,b)) Correct == (a>0 /\ b>0) /\ Euclid(a,b) =>Property

41 DOS during Initial Ranging (found by TLC Model Checking) DL Subframe Contention-based Initial Ranging Slots UL Subframe Attacker fills all slots, making its requests collide with requests from other SS, thereby denying all new SS a chance to complete ranging