OUTLINE! SaTC - 15 June Basic Architecture of a Communication System. U s. coder c. coder 0. SaTC - 15 June 2016

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1 Game heoretic Approach to Information Security AMER BAȘAR ECE, CAS, CSL, II, and MechSE, UIUC SaC Workshop University of Wisconsin, Madison June 5-7, 26 OULINE! Fundamental problem in information transmission / communication Intervention by adversary(ies) Role of ame theory Some classes of information security ames and their solutions Other settins of adversarial intervention Conclusions / References Classical Communication Settin he fundamental problem of communication is that of reproducin at one point (destination) either eactly or approimately a messae selected at another point (), iven the cost of transmission. Classical Communication Settin he fundamental problem of communication is that of reproducin at one point (destination) either eactly or approimately a messae selected at another point (), iven the cost of transmission. U Y s. coder c. coder channel c. decoder s. decoder U U s. coder c. coder Y channel c. decoder s. decoder What information to send U U s. coder c. coder Y channel c. decoder s. decoder How to send it U U s. coder c. coder Y channel c. decoder s. decoder Prob (Y=y U =u ) U Classical Communication Settin, w ~ independent random variables u, u are real valued variables J(, h) = E [ Q(, u, u ), h ] J * = min min J(, h)

2 Classical Communication Settin, w ~ independent random variables u, u are real valued actions J(, h) = E [ Q(, u, u ), h ] Standard distortion measure: J * = min min J(, γ ) Q(, u, u ) = k (u ) 2 (u - ) 2 A multi-channel etension or with k= & SaC E[(u - 5 June 26 ) 2 ] α v λ w y 2 h u u λn λ i s are nonzero constants (ains);, v, w i s are independent random variables y y n v A multi-channel etension u = (v) λ w y 2 h u u λn Distortion: Q(, u, u ) = k (u ) 2 (u - ) 2 y y n u = h(y,..,y n ) y i = λ I (v) w i v Multiple Serial Decision Units u w. h. w m- y m h m u m ~ N(, σ 2 ), w i ~ N(, σ w2 ), v ~ N(, σ v2 ) J(, h [,m] ) = E [ Q(, u, u [,m] ), h [,m] ] Q(, u, u [,m] ) = (u m ) 2 Σ m i= (u i- ) 2 Source (S) A multi-sensor transmission w 2 n n 2 z Receiver h y Desin {(,, n ), h} to minimize a distortion at receiver, with w i, z noises u Multi-aent networked systems as raphs Network is a connected raph Nodes are aents / dynamic systems /mobile Links are one of three types of connections SaC%&%5%June%26% Multi-aent networked systems as raphs Links are one of three types of connections: Communication Collaboration Physical! Layered raphs SaC%&%5%June%26% Intrusion/Intervention by an Adversary Passive attack Eavesdroppin (on transmission a passive attack) Active attacks Jammin (communication channels) Denial of service Messae distortion (by flippin bits active attack) Node capture and clonin (physically capturin sensor nodes, replicatins the nodes, and deployin into the network) Some nodes could be adversarial: jammin communication interruptin collaboration breakin physical links Leads to a ame situation! Conflic4n%interests% %between%mul4ple%% coopera4ve%as%well%as% non&coopera4ve%aents% SaC%&%5%June%26%

3 Aerial Jammin Attack on the CommNet of a team of UAVs he jammer wants to maimize the time for which communication can be jammed. he two UAVs want to minimize the time for which communication remains jammed. Back to Classical Settin but with v is the jammin sinal enerated by the adversary (J) Back to Classical Settin but with Q: What is known about the capabilities, information access, and objectives of J? Back to Classical Settin but with Back to Classical Settin but with Back to Classical Settin but with Q: What is known about the capabilities, information access, and objectives of J? For eample: E[v 2 ] α Q: What is known about the capabilities, information access, and objectives of J? J has access to some information, I J, on and u! v = μ(i J ) Lookin for policies ( (, h), μ ) Standard distortion measure Q IJ (, u, u, v) = k (u ) 2 (u - ) 2 with J s constraint E[v 2 ] α or Q IJ (, u, u, v) = k (u ) 2 (u - ) 2 k J v 2 possibly randomized Back to Classical Settin but with R(, h, μ) := E[Q IJ (, u, u, v) (, h), μ ] J has access to some information, I J, on and u! v = μ(i J ) Lookin for policies ( (, h), μ ) possibly randomized Back to Classical Settin but with R(, h, μ) := E[Q IJ (, u, u, v) (, h),,μ ] R is what the system cares about and hence a reasonable approach is inf (, h) sup μ R(, h, μ) =: R* (UV of ZSG) If J behaves differently, then system does no worse than R* usin the same policy pair. Upper and lower values, Saddle Point, and Nonzero-sum Games inf (, h) sup μ R(, h, v μ) w=: R* (UV of ZSG) Lower value (LV) is: sup μ inf (, h) R(, h, μ) R* If equal, then there is value, and possibility of SP: A triple (*, h*, μ*) such that R(*, h*, μ) R(*, h*, μ*) R(, h, μ*) for all, h, μ

4 Upper and lower values, Saddle Point, and Nonzero-sum Games SP: A triple (*, v h*, μ*) w such that R(*, h*, μ) R(*, h*, μ*) y h R(, h, u μ*) for all, h, μ If J is known to have a different objective, say maimizin R J, not fully alined with R, then a NZSG! Nash equilibrium: R(*, h*, μ*) R(, h, μ*) R J (*, h*, μ) R J (*, h*, μ*) Back to Classical Settin with Jammer ake as distortion measure Q IJ (, u, u, v) = k (u ) 2 (u - ) 2 k J v 2 and assume ~ N(, σ 2 ), w ~ N(, σ w2 ) hen, there eists a SP, with the worstcase v comprised of two additive terms: (i) rv linearly correlated with I J Back to Classical Settin with Jammer And ake the as minimizin distortion measure and h are linear in their Q IJ (, respective u, u, v) = information, k (u ) 2 (uand - ) could 2 k J v 2 also and involve assume a discrete ~ N(, σrv 2 ), dictatin w ~ N(, which σ w2 ) of hen, multiple there solutions eists a SP, & R with should the pick worstcase v comprised requires of two clean additive side channel terms: (coordination or (i) a rv sinalin linearly mechanism). correlated with I J Back to Classical Settin with Jammer In And ake some the as reions minimizin distortion of the measure and parameter h are linear space, in the SP their Qenables IJ (, respective u, the u, v) pair = information, k(, (uh), ) 2 with (uand proper - ) could 2 k J v 2 randomization also involve assume a discrete and ~ N(, coordination, σrv 2 ), dictatin w ~ to N(, neutralize which σ w2 ) J of hen, so multiple that there it discards/disreards solutions eists a SP, & R with should the its pick worstcase v comprised and requires injects of two clean additive independent side channel terms: information (coordination noise or (i) a rv sinalin into linearly the channel. mechanism. correlated with I J Back to Classical Settin with Jammer (J) Solutions And ake the as minimizin distortion and techniques measure and etend h are linear to vector in -valued their Q IJ (, respective s, u, u, v) multiple = information, k (u ) channels, 2 (uand - ) could multiple 2 k J v 2 jammers, also and involve assume and a some discrete ~ N(, classes σrv 2 ), dictatin of on-gaussian ~ N(, which σ w2 ) distributions. of hen, multiple there solutions eists a SP, & R with should the pick worstcase v comprised requires of two clean additive side channel terms: (coordination or (i) a rv sinalin linearly mechanism. correlated with I J Bansal & B (JOA 89); Akyol, Rose, B (I 5) Refs: B (I 83); B&Wu (I 85); B&Wu (JOA 86); adversary controlin some nodes Source (S) w n Nodes m,..,n controled by adversaries, injectin sinals m,, n to maimize distortion at receiver. 2 µ n 2 z Receiver h y u adversary controlin some nodes (2) Sensor policies: i = i (sw i ), i=,,m Adversary policies: j =µ j (sw i ), j=m,, n Receiver policy: u = h(y), y=σ i i Σ j j z Distortion measure: Q SJ (s, { i }, u, { j }) = = (u -s) 2 kσ i ( i ) 2 k J Σ j ( j ) 2 Zero-sum ame: R(, h, μ) := := E[Q SJ (s, { i }, u, { j }) ({ i }, h),,{{μ j } ] adversary controlin some nodes (3) Lookin for a SP solution for R(, h, μ) with (, h) as minimizers, and μ as maimizer, with each i possibly randomized, and likewise each μ j, with also coordination amon the m sensors and the receiver, and likewise amon the n-m adversaries. adversary controlin some nodes (4) Solution (Akyol, Rose, B (ISI 3)): With all statistics Gaussian, the best for sensors is to use randomized linear transformations for i s, and share the randomization information with the receiver. For the adversaries, SP solution dictates Gaussian j s, correlated across them With lack of coordination amon adversaries, the system benefits, i.e. R is lower.

5 SI with Privacy Constraints (also a ame but not ZS), θ u Common cost: J R (, h) = E{(u ) 2 } Privacy constraint: J (, h) = E{(θ E[θ y]) 2 } D P (*) Find S that minimizes J R (, h S ) st (*) holds, where h S = h() minimizes J R (, h) uniquely for all. Soft Watermarkin Game Watermark U Y U Encoder Attacker Decoder (,S) µ h(y) S Sinal Constraints: E{((,S) S) 2 } P E E{(Y U ) 2 } P A Distortion: E{h(Y) ) 2 }! R(,h; µ) UV is: inf inf h sup µ R(,h; µ) With, S, Gaussian, worst-case µ is affine- Soft Watermarkin Game Gaussian -- (Mıhçak, Akyol, B, Lanbort 26) Watermark U Y U Encoder Attacker Decoder (,S) µ h(y) S Sinal Constraints: E{((,S) S) 2 } P E E{(Y U ) 2 } P A Distortion: E{h(Y) ) 2 }! R(,h; µ) UV is: inf inf h sup µ R(,h; µ) Denial of Service Attack (Gupta, Nayyar, Lanbort, B; CDC 2) v J R γ u y γ u ransmitter () observes and decides whether to transmit or not Jammer (J) observes s action and decides whether to deny service or not Both actions incur cost (inactions do not) Receiver (R) incurs no cost if transmission is unblocked; otherwise cost is var( 2 ) Denial of Service Attack (Gupta, Nayyar, Lanbort, B; CDC 2) v J R γ u y γ u If ransmitter uses stratey () observes ϒ, ϒ() = and α, decides α= or, whether to transmit or not and J blocks w.p. p, then cost to -R: Jammer (J) observes s action and decides J(ϒ,p) = E[ c whether to deny {α=} d service {v=b} (- or not est ) 2 ] to Both be minimized actions incur by cost and maimized by J Receiver (R) incurs no cost if transmission Best unblocked; responses otherwise are of cost the is threshold var( 2 ) type Best responses min J(ϒ,)! α * = if 2 > c min J(ϒ,)! α * = if d > c for < p <, min J(ϒ,p)! α * = if 2 > Δ p := (c-pd) / (-p) p * = if E [ 2 α = ] > d = if E [ 2 α = ] < d (,) if E [ 2 α = ] = d An equivalent ame and its SP solution Multi-stae version with limits on frequency of blockin Multi-stae version with limits on frequency of blockin (2) Oriinal dynamic ame with asymmetric information is now a static ame (with symmetric information) in Δ (threshold) & p Admits a SP, where Δ and p could take inner values (finite non-zero Δ, and proper mied for J) Source { t } i.i.d. zero-mean Gaussian N-stae additive cost, but J can block M < N times J knows all past actions, and current action of knows all past actions, and past and present values of output State s t (common information): # blockins Oriinal dynamic ame with asymmetric information can be lifted to one with symmetric information, and results of static ame applied iteratively, but now also by keepin track of s t SP solution is aain of the threshold type, with Δ t and p t now dependin on s t. Etension to correlated outputs..

6 Intrusion Detection (IDS) Intrusion Detection (IDS) Intrusion Detection (IDS) Interaction between attacker(s) and the IDS is modeled as a non-cooperative ame Interaction between attacker(s) and the IDS is modeled as a non-cooperative ame A sensor network is introduced as a third, fictitious player, with a fied probability distribution for each attack type Interaction between attacker(s) and the IDS is modeled as a non-cooperative ame A sensor network is introduced as a third, fictitious player, with a fied probability distribution for each attack type Output of the sensor network is measurement to IDS, based on which it decides on the presence (or not) of an attack and its type Intrusion Detection (IDS) Interaction between attacker(s) and the IDS is modeled as a non-cooperative ame A sensor network is introduced as a third, fictitious player, with a fied probability distribution for each attack type Output of the sensor network is measurement to IDS, based on which it decides on the presence (or not) of an attack and its type Payoffs to attacker(s) and IDS for each triple of actions Finite or infinite (continuous-kernel) NZS ames dependin on whether # actions is finite or not. Finite or infinite (continuous-kernel) NZS ames dependin on whether # actions is finite or not. As a finite ame, there is a NE in mied strateies: worst probabilistic attacker behavior and correspondin best IDS stratey Finite or infinite (continuous-kernel) NZS ames dependin on whether # actions is finite or not. As a finite ame, there is a NE in mied strateies: worst probabilistic attacker behavior and correspondin best IDS stratey As a continuous-kernel ame, there eists a unique NE under some mild conditions Finite or infinite (continuous-kernel) NZS ames dependin on whether # actions is finite or not. As a finite ame, there is a NE in mied strateies: worst probabilistic attacker behavior and correspondin best IDS stratey As a continuous-kernel ame, there eists a unique NE under some mild conditions If payoffs are completely conflictin (zero-sum), there eist saddle-point solutions A Finite Security Game in Etensive Form (sinle subsystem, sinle detectable threat)

7 Selected References o Network Security Concepts o Security Games (SGs) Network Security: A Decision and Game- heoretic Approach (Alpcan, B, CUP, 2) Game theory meets network security and privacy (Manshei, Zhu, Alpcan, B, Hubau; ACM Survey, 2) A hierarchical security architecture for the smart rid (Zhu, B; in Hossain, Han, Poor, edts, Smart Grid Communications and Networkin, CUP, 22) Hybrid learnin in stochastic ames and its applications in network security (Zhu, B; in Lewis, Liu, edts, Computational Intellience Series, IEEE 2) Game heory in Wireless and Comm Nets (Han, Niyato, Saad, B, Hjorunes; CUP, Oct 2) Deterministic SGs Stochastic SGs SGs w information limitations o Decision Makin for Network Security Security risk-manaement Re allocation for security Usability, trust, and privacy o Security Attack and Intrusion Detection hanks!! Machine learnin for intrusion and anomaly detection Hypothesis testin for attack detection