Modeling Ad-hoc Rushing Attack in a Negligiblity -based Security Framework

1. Modeling Ad-hoc Rushing Attack in aNegligiblity-based Security Framework Jiejun Kong, *Xiaoyan Hong, #Mario Gerla Scalable Network Technologies *Computer Science Department #Computer Science Department Los Angeles University of Alabama, Tuscaloosa University of California, Los Angeles jkong@scalable-networks.com, hxy@cs.ua.edu, gerla@cs.ucla.eduACM WiSe’06September 29, 2006. Los Angeles, California

2. Notion: Security as a “landslide” game • Played by the guard and the adversary • Proposal can be found as early as Shannon’s 1949 paper • Not a 50%-50% chance game, which is too good for the adversary • The notion has been used in modern crypto since 1970s • Based on NP-complexity • The guard wins the game with 1 - negligible probability • The adversary wins the game with negligible probability • The asymptotic notion of “negligible” applies to one-way function (encryption, one-way hash), pseudorandom generator, zero-knowledge proof, ……AND this time ……secure routing

3. Insecure Secure(Ambiguous area) The Asymptotic Cryptography Model The “negligible” line(sub-polynomial line) • Security can be achieved by a polynomial-bounded guard against a polynomial-bounded adversary Probability of security breach 1 2 # of key bits (key length) 128

4. Insecure Secure(Ambiguous area) Our Asymptotic Network Security Model The “negligible” line(sub-polynomial line) • Conforming to the classic notion of security The “exponential” line Probability of network security breach Network metric (e.g., # of nodes -- network scale)

5. Definition: A function m: NR is negligible, if for every positive integer c and all sufficiently large x’s (i.e., there exists Nc>0, for all x>Nc), Negligible := (Asymptotic) Sub-Polynomial • Consistent with computational cryptography’s asymptotic notion of “negligible / sub-polynomial” • is negligible by definition x is key length in computational cryptox is network metric (e.g., # of nodes) in network security

6. Problem Statement • Secure routing problems are not solved • Rushing attacks, wormhole attacks, etc. are threatening mobile wireless networks • Secure routing lacks formal modeling • More generally, foundation of network security is unknown • The connection between network scale and network security is unknown

7. Forwarding in Wireless Networks E(Aforward) • Area defined by intersection of 2 or more transmission circles • Node redundancy is common in wireless ad hoc networks • In the E(Aforward), expectation size of the forwarding area, there are usually more than 1 “good” or “bad” nodes inside

8. RREQ RREP Rushing Attack [Hu,Perrig,Johnson 2003] • RREQ forwarding • Rushing attackers disobey delay (MAC/routing/queuing) requirements& w/ higher prob., are placed on RREP / DATA path • Low-cost: feasible as long as capable of intercepting & forwarding dest source

9. Mobile network model • Divides the entire network area A into large number n of very small tiles (i.e., possible “positions”) • A node’s presence probability p at each tile is small Follows a spatial binomial distributionB(n,p) • When n is large and p is small, B(n,p) is approximately a spatial Poisson point distribution with rate r1 • If there are N mobile nodes, use r1 as the average PDF rN= N·r1 • The probability of exactly k nodes in an area A’

10. r1in Random Way Point model [Bettstetter et al.] a=1000

11. In our stochastic model, r1is arbitrary If in certain area the node’s stochastic presence PDF is 0, then this area should not be counted in the entire network area A • No matter what the mobility model is, there is a stochastic PDF for node’s probabilistic presence at each position

12. Modeling adversarial presence • q : percentage of non-cooperative network members (e.g., probability of node selfishness & intrusion) • 3 random variables • x :number of nodes in the forwarding community area • y: number of cooperative nodes • z: number of non-cooperative nodes

13. Integral and differential not a problem: Rushing Attack is Low-cost & Severe ! • Per-hop success prob. of node-to-node routing is negligiblewith respect to network scale Nunder rushing attack • Per-hop failure prob. of node-to-node ad hoc routing schemes is unfortunately 1 - negligible(N) • As illustrated later, this means rushing attack makes legacy node-to-node routing schemes fall into negativeRP • Negative RP: success/yes probability is negligible, severe problem! • RP: failure/no probability is negligible

14. …progress … • Secure routing problems are not solved • Rushing attacks, wormhole attacks, etc. are threatening mobile wireless networks • Secure routing lacks formal modeling • More generally, foundation of network security is unknown • The connection between network scale and network security is unknown

15. Terminology • Las Vegas algo.  Always correct, probably fast • Monte-Carlo algo.  Always fast, probably correct with 1-side error • Today’s focus • Atlantic City algo. (or Monte-Carlo w/ 2-side) Always fast, probably correct with 2-side error

16. RP (1-run): not this one! Polynomial-time If correct answer is FAILURE/NO, it always returns FAILURE/NO If correct answer is SUCCESS/YES, it returns SUCCESS/YES with probability ½+(x); but may return FAILURE/NO otherwise RP(n-runs): today’s pick! Polynomial-time If correct answer is FAILURE/NO, it always returns FAILURE/NO If correct answer is SUCCESS/YES, it returns SUCCESS/YES with probability 1-(½)n; but may return FAILURE/NO RP:Randomized Polynomial-time X

17. deviation bound (x) (x) (x) (x) (x) (x) deviation bound poly(x) A Generic Family of Random Algorithmswith Invariant Deviation (x)(This is proven in Theorem 2) the ideal line(can be foundby Las Vegasalgorithms)

18. Turing Machine (TM) • Deterministic TM • At most 1 move for each transition state • Non-deterministic TM & Probabilistic TM • Can be represented by DTM + random tape j y t M q Add a random tape to hold coin-tosses for probabilistic Turing Machines

19. # # # # # # # # # # # # # Old place replaced by blank tape RREQ j j RREP y y y y t t t t M M M M q q q q On-demand route discovery starts # # # # # # # # # # # # # Route successfully established whenRREP is received after poly(N) steps Routing in Probabilistic Turing Machinewith GVG oracle • # of possible node positions < O(poly(n)) • Every node is only a “puppet” tape carrier --- The randomized state is maintained by an oracle, the Global Virtual God • Node communication, mobility and the environmental randomness are simulated by GVG in random tape Modeling mobility

20. Community Based Security (CBS) • Community-to-community forwarding (not node-to-node) • Turn the table • Now the forwarding failure becomes negligible (x) • Rushing attack becomes ineffective • Ideally, stay in GVG-RP (i.e., with (x)forwarding failure) for polynomial routing steps (wrt. network scale N)

21. …progress … • Secure routing problems are not solved • Rushing attacks, wormhole attacks, etc. are threatening mobile wireless networks • Secure routing lacks formal modeling • More generally, foundation of network security is unknown • The connection between network scale and network security is unknown

22. Connecting a few Theories Stochastic Mobility Analysis & Spatial Poisson Processes Probabilistic Complexity Theory RP & BPP requires discovery of negligibility

23. Summary • Initiative • Some problems (wrt. foundations of network security) are based on randomized algorithms and probabilistic complexity theory • This paper’s contributions • Devises the GVG oracle to translate wireless networking problems into randomized algorithms • Algorithms/Protocols in GVG-RP are asymptotically invariant • (x) failure probability at each step  (x) failure probability over polynomial steps • In a closed spaceA(2-d network area or 3-d network volume) where nodes follow spatial Poisson point distribution and with non-zero PDF • Routing protocols based on local community coordination are in RP • In contrast, legacy routing protocols based on node-to-node coordination are in negative RP They are severely vulnerable to low-cost routing attacks (rushing attack) • Detailed protocol design is available, though not a perfect implementation • Jiejun Kong, Xiaoyan Hong, Yunjung Yi, Joon-Sang Park, Mario Gerla, “A Secure Ad-hoc Routing Approach using Localized Self-healing Communities,” pp.254-265, ACM MOBIHOC, May 25-28, 2005. • Open challenges • Applications in other network security domains • Foundations of network security

24. Thank you! Questions?

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26. PROTOCERATOPS ERA: Late Cretaceous ( Santonian - Campanian85.8 - 71.3 Ma ). SIZE: Length 2m. Height 75cm. Weight 1.4 tonnes. TOROSAURUS ERA: Late Cretaceous ( Maastrichtian71.3 - 65 Ma ). SIZE: Length 7.6 m. Weight 7 - 8 tonnes. ALLOSAURUS ERA: Late Jurassic ( Kimmeridgian 154.1 - 150.7 Ma ). SIZE: Length 10 - 12 m. Weight 1 - 1.7 tonnes. TYRANNOSAURUS ERA: Late Cretaceous ( Campanian - Maastrichtian 83.5 - 65 Ma ). SIZE: Length 12-14 m. Height 5m. Weight 4.5 - 7 tonnes. Why does size matter? • When competition is about physical power in body (network of cells): right before the “Cretaceous-Tertiary (K-T) extinction” event, the dinosaurs were of their largest size

27. Why does size matter? (cont’d) • When competition is about intelligence in networks of neuron: cranial capacity and complexity         

28. BPP (1-run) Polynomial-time On either case, will give correct answer with probability ½+(x)(i.e., give incorrect answer otherwise) BPP(n-runs) Polynomial-time On either case, will give correct answer with probability 1-e-n/24(i.e., give incorrect answer otherwise) Prove by Chernoff’s bound BPP:Bounded-error Probabilistic Polynomial-time

29. r1 • Inspired by Bettstetter et al.’s work • For any mobility model (random walk, random way point), Bettstetter et al. have shown thatr1 is computable following • For example, in random way point model in a square network area of size a£a defined by -a/2·x· a/2 and -a/2·y· a/2 • r1 is “location dependent”, yet computable in NS2 & QualNet given any area A’(using finite element method)