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1/13 Secrecy Codes for Wireless Control Systems Anastasios Tsiamis, Konstantinos Gatsis, George J. Pappas University of Pennsylvania July 13, 2018

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Page 1: Secrecy Codes for Wireless Control Systemsiot.stanford.edu/nsf-final/slides/sitp-nsf-final-codes.pdf2/13 Secrecy Issues in the Internet of Things I Interconnected sensors and actuators

1/13

Secrecy Codes for Wireless Control Systems

Anastasios Tsiamis, Konstantinos Gatsis, George J. Pappas

University of Pennsylvania

July 13, 2018

Page 2: Secrecy Codes for Wireless Control Systemsiot.stanford.edu/nsf-final/slides/sitp-nsf-final-codes.pdf2/13 Secrecy Issues in the Internet of Things I Interconnected sensors and actuators

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Secrecy Issues in the Internet of Things

I Interconnected sensors and actuators.

I Communication over wireless networks.

The wireless medium may be compromised.

I Broadcast nature.

I Eavesdroppers may intercept sensitive data about the physicalsystem.

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Eavesdropping attacks in Dynamical Systems

Dynamical System

ENC

Sensor

ChannelDEC

User

Eavesdropper

GoalI Protect dynamical state information, e.g. position, velocity.

I Design secrecy codes.

ChallengesI Tradeoff between security and code complexity.

ApproachI Can we exploit model knowledge/physics for secrecy?

Page 4: Secrecy Codes for Wireless Control Systemsiot.stanford.edu/nsf-final/slides/sitp-nsf-final-codes.pdf2/13 Secrecy Issues in the Internet of Things I Interconnected sensors and actuators

3/13

Eavesdropping attacks in Dynamical Systems

Dynamical System

ENC

Sensor

ChannelDEC

User

Eavesdropper

GoalI Protect dynamical state information, e.g. position, velocity.

I Design secrecy codes.

ChallengesI Tradeoff between security and code complexity.

ApproachI Can we exploit model knowledge/physics for secrecy?

Page 5: Secrecy Codes for Wireless Control Systemsiot.stanford.edu/nsf-final/slides/sitp-nsf-final-codes.pdf2/13 Secrecy Issues in the Internet of Things I Interconnected sensors and actuators

3/13

Eavesdropping attacks in Dynamical Systems

Dynamical System

ENC

Sensor

ChannelDEC

User

Eavesdropper

GoalI Protect dynamical state information, e.g. position, velocity.

I Design secrecy codes.

ChallengesI Tradeoff between security and code complexity.

ApproachI Can we exploit model knowledge/physics for secrecy?

Page 6: Secrecy Codes for Wireless Control Systemsiot.stanford.edu/nsf-final/slides/sitp-nsf-final-codes.pdf2/13 Secrecy Issues in the Internet of Things I Interconnected sensors and actuators

3/13

Eavesdropping attacks in Dynamical Systems

Dynamical System

ENC

Sensor

ChannelDEC

User

Eavesdropper

GoalI Protect dynamical state information, e.g. position, velocity.

I Design secrecy codes.

ChallengesI Tradeoff between security and code complexity.

ApproachI Can we exploit model knowledge/physics for secrecy?

Page 7: Secrecy Codes for Wireless Control Systemsiot.stanford.edu/nsf-final/slides/sitp-nsf-final-codes.pdf2/13 Secrecy Issues in the Internet of Things I Interconnected sensors and actuators

4/13

Previous work

Encryption

I Generic tool applied in practice. J. Katz and Y. Lindell. 2014

I Adversary should have bounded computational capabilities.

I Communication/computation overheads.

Physical layer security

I Information theoretic tools. A. D. Wyner. 1975, M. Wiese et al. 2016

I Provable guarantees.

I Requires eavesdropper’s channel model.

Our approach: State-Secrecy Codes

I Exploit the system dynamics.

I New tradeoff between code complexity and security.

I Simple and fast.

I Strong security guarantees about the current state.

Related work

I Codes for several types of linear systems

A. Tsiamis et al. CDC 2017, ACC 2018, CDC 2018

I Non-coding approach

A. S. Leong et al. IFAC 2017, CDC 2017

A. Tsiamis et al. IFAC 2017

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4/13

Previous work

Encryption

I Generic tool applied in practice. J. Katz and Y. Lindell. 2014

I Adversary should have bounded computational capabilities.

I Communication/computation overheads.

Physical layer security

I Information theoretic tools. A. D. Wyner. 1975, M. Wiese et al. 2016

I Provable guarantees.

I Requires eavesdropper’s channel model.

Our approach: State-Secrecy Codes

I Exploit the system dynamics.

I New tradeoff between code complexity and security.

I Simple and fast.

I Strong security guarantees about the current state.

Related work

I Codes for several types of linear systems

A. Tsiamis et al. CDC 2017, ACC 2018, CDC 2018

I Non-coding approach

A. S. Leong et al. IFAC 2017, CDC 2017

A. Tsiamis et al. IFAC 2017

Page 9: Secrecy Codes for Wireless Control Systemsiot.stanford.edu/nsf-final/slides/sitp-nsf-final-codes.pdf2/13 Secrecy Issues in the Internet of Things I Interconnected sensors and actuators

4/13

Previous work

Encryption

I Generic tool applied in practice. J. Katz and Y. Lindell. 2014

I Adversary should have bounded computational capabilities.

I Communication/computation overheads.

Physical layer security

I Information theoretic tools. A. D. Wyner. 1975, M. Wiese et al. 2016

I Provable guarantees.

I Requires eavesdropper’s channel model.

Our approach: State-Secrecy Codes

I Exploit the system dynamics.

I New tradeoff between code complexity and security.

I Simple and fast.

I Strong security guarantees about the current state.

Related work

I Codes for several types of linear systems

A. Tsiamis et al. CDC 2017, ACC 2018, CDC 2018

I Non-coding approach

A. S. Leong et al. IFAC 2017, CDC 2017

A. Tsiamis et al. IFAC 2017

Page 10: Secrecy Codes for Wireless Control Systemsiot.stanford.edu/nsf-final/slides/sitp-nsf-final-codes.pdf2/13 Secrecy Issues in the Internet of Things I Interconnected sensors and actuators

4/13

Previous work

Our approach: State-Secrecy Codes

I Exploit the system dynamics.

I New tradeoff between code complexity and security.

I Simple and fast.

I Strong security guarantees about the current state.

Related work

I Codes for several types of linear systems

A. Tsiamis et al. CDC 2017, ACC 2018, CDC 2018

I Non-coding approach

A. S. Leong et al. IFAC 2017, CDC 2017

A. Tsiamis et al. IFAC 2017

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5/13

Model

System

Sensor &Encoder

User

Eavesdropper

xk zk

γu,k

γe,k

x̂u,k

x̂e,k

ACK

Linear System

I state xk; e.g. position and velocity at time k

xk+1 = Axk + wk+1, wk : Gaussian process noise

Sensor and encoder

I zk encoded version of state xk.

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5/13

Model

System

Sensor &Encoder

User

Eavesdropper

xk zk

γu,k

γe,k

x̂u,k

x̂e,k

ACK

Linear System

I state xk; e.g. position and velocity at time k

xk+1 = Axk + wk+1, wk : Gaussian process noise

Sensor and encoder

I zk encoded version of state xk.

Page 13: Secrecy Codes for Wireless Control Systemsiot.stanford.edu/nsf-final/slides/sitp-nsf-final-codes.pdf2/13 Secrecy Issues in the Internet of Things I Interconnected sensors and actuators

5/13

Model

System

Sensor &Encoder

User

Eavesdropper

xk zk

γu,k

γe,k

x̂u,k

x̂e,k

ACK

ChannelI Packet drop channels:

I Message either received intact or dropped.

I γu,k = 1: message zk received.

I γu,k = 0: message zk dropped.

I Acknowledgment signals available.

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5/13

Model

System

Sensor &Encoder

User

Eavesdropper

xk zk

γu,k

γe,k

x̂u,k

x̂e,k

ACK

Decoders: Minimum Mean Square Error Estimators

I Information sets:

Iu,k = {Received messages zk}Ie,k = {Intercepted messages zk,User’s outcomes γu,k}

I Estimation:

x̂u,k minimizes E(‖xk − x̂u,k‖2 |Iu,k)

Pu,k user mmse covariance given Iu,k

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5/13

Model

System

Sensor &Encoder

User

Eavesdropper

xk zk

γu,k

γe,k

x̂u,k

x̂e,k

ACK

Decoders: Minimum Mean Square Error Estimators

I Information sets:

Iu,k = {Received messages zk}Ie,k = {Intercepted messages zk,User’s outcomes γu,k}

I Estimation:

x̂u,k minimizes E(‖xk − x̂u,k‖2 |Iu,k)

Pu,k user mmse covariance given Iu,k

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Problem: Secrecy

Secrecy

Find a coding scheme such that:

I Eavesdropper’s minimum mean square error (mmse) forthe current state is maximum asymptotically.

I User’s mmse is optimal.

Assumptions

I Public A.

I Passive eavesdropper.

I Eavesdropper knows model, coding scheme, acknowledgments.

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State-Secrecy Code

Coding Scheme

zk = xk − Lk−tkxtk

tk: the most recent message received at the user

I Matrix L depends on the dynamical system’s model.

I Choice of L: makes zk less correlated to xk for the eavesdropper.

I ACKs: user and sensor agree on tk.

I Fast and simple.

I Can be used along with encryption.

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Example

Code

zk = xk − Lk−tkxtk

Encoder User Eavesdropper

x0

x0 x0

x1 − Lx0 −x2 − L2x0 −x3 − Lx2 − x3 − Lx2x4 − L2x2 x4 − L2x2

I User decodes by adding.

I Eavesdropper decodes initially.

I Eavesdropper cannot decode for k > 2.

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8/13

Example

Code

zk = xk − Lk−tkxtk

Encoder User Eavesdropper

x0 x0

x0

x1 − Lx0 −x2 − L2x0 −x3 − Lx2 − x3 − Lx2x4 − L2x2 x4 − L2x2

I User decodes by adding.

I Eavesdropper decodes initially.

I Eavesdropper cannot decode for k > 2.

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8/13

Example

Code

zk = xk − Lk−tkxtk

Encoder User Eavesdropper

x0 x0

x0

x1 − Lx0

−x2 − L2x0 −x3 − Lx2 − x3 − Lx2x4 − L2x2 x4 − L2x2

I User decodes by adding.

I Eavesdropper decodes initially.

I Eavesdropper cannot decode for k > 2.

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8/13

Example

Code

zk = xk − Lk−tkxtk

Encoder User Eavesdropper

x0 x0

x0

x1 − Lx0 −

x2 − L2x0 −x3 − Lx2 − x3 − Lx2x4 − L2x2 x4 − L2x2

I User decodes by adding.

I Eavesdropper decodes initially.

I Eavesdropper cannot decode for k > 2.

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8/13

Example

Code

zk = xk − Lk−tkxtk

Encoder User Eavesdropper

x0 x0

x0

x1 − Lx0 −x2 − L2x0

−x3 − Lx2 − x3 − Lx2x4 − L2x2 x4 − L2x2

I User decodes by adding.

I Eavesdropper decodes initially.

I Eavesdropper cannot decode for k > 2.

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8/13

Example

Code

zk = xk − Lk−tkxtk

Encoder User Eavesdropper

x0 x0

x0

x1 − Lx0 −x2 − L2x0 x2 − L2x0

−x3 − Lx2 − x3 − Lx2x4 − L2x2 x4 − L2x2

I User decodes by adding.

I Eavesdropper decodes initially.

I Eavesdropper cannot decode for k > 2.

Page 24: Secrecy Codes for Wireless Control Systemsiot.stanford.edu/nsf-final/slides/sitp-nsf-final-codes.pdf2/13 Secrecy Issues in the Internet of Things I Interconnected sensors and actuators

8/13

Example

Code

zk = xk − Lk−tkxtk

Encoder User Eavesdropper

x0 x0

x0

x1 − Lx0 −x2 − L2x0 x2 − L2x0

x3 − Lx2

− x3 − Lx2x4 − L2x2 x4 − L2x2

I User decodes by adding.

I Eavesdropper decodes initially.

I Eavesdropper cannot decode for k > 2.

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8/13

Example

Code

zk = xk − Lk−tkxtk

Encoder User Eavesdropper

x0 x0

x0

x1 − Lx0 −x2 − L2x0 x2 − L2x0

x3 − Lx2 −

x3 − Lx2x4 − L2x2 x4 − L2x2

I User decodes by adding.

I Eavesdropper decodes initially.

I Eavesdropper cannot decode for k > 2.

Page 26: Secrecy Codes for Wireless Control Systemsiot.stanford.edu/nsf-final/slides/sitp-nsf-final-codes.pdf2/13 Secrecy Issues in the Internet of Things I Interconnected sensors and actuators

8/13

Example

Code

zk = xk − Lk−tkxtk

Encoder User Eavesdropper

x0 x0

x0

x1 − Lx0 −x2 − L2x0 x2 − L2x0

x3 − Lx2 −

x3 − Lx2

x4 − L2x2

x4 − L2x2

I User decodes by adding.

I Eavesdropper decodes initially.

I Eavesdropper cannot decode for k > 2.

Page 27: Secrecy Codes for Wireless Control Systemsiot.stanford.edu/nsf-final/slides/sitp-nsf-final-codes.pdf2/13 Secrecy Issues in the Internet of Things I Interconnected sensors and actuators

8/13

Example

Code

zk = xk − Lk−tkxtk

Encoder User Eavesdropper

x0 x0

x0

x1 − Lx0 −x2 − L2x0 x2 − L2x0

x3 − Lx2 −

x3 − Lx2

x4 − L2x2 x4 − L2x2

x4 − L2x2

I User decodes by adding.

I Eavesdropper decodes initially.

I Eavesdropper cannot decode for k > 2.

Page 28: Secrecy Codes for Wireless Control Systemsiot.stanford.edu/nsf-final/slides/sitp-nsf-final-codes.pdf2/13 Secrecy Issues in the Internet of Things I Interconnected sensors and actuators

8/13

Example

Code

zk = xk − Lk−tkxtk

Encoder User Eavesdropper

x0 x0 x0

x1 − Lx0 − x1 − Lx0x2 − L2x0 x2 − L2x0 −x3 − Lx2 − x3 − Lx2x4 − L2x2 x4 − L2x2 x4 − L2x2

I User decodes by adding.

I Eavesdropper decodes initially.

I Eavesdropper cannot decode for k > 2.

Page 29: Secrecy Codes for Wireless Control Systemsiot.stanford.edu/nsf-final/slides/sitp-nsf-final-codes.pdf2/13 Secrecy Issues in the Internet of Things I Interconnected sensors and actuators

8/13

Example

Code

zk = xk − Lk−tkxtk

Encoder User Eavesdropper

x0 x0 x0

x1 − Lx0 − x1 − Lx0x2 − L2x0 x2 − L2x0 −x3 − Lx2 − x3 − Lx2x4 − L2x2 x4 − L2x2 x4 − L2x2

I User decodes by adding.

I Eavesdropper decodes initially.

I Eavesdropper cannot decode for k > 2.

Page 30: Secrecy Codes for Wireless Control Systemsiot.stanford.edu/nsf-final/slides/sitp-nsf-final-codes.pdf2/13 Secrecy Issues in the Internet of Things I Interconnected sensors and actuators

8/13

Example

Code

zk = xk − Lk−tkxtk

Encoder User Eavesdropper

x0 x0 x0

x1 − Lx0 − x1 − Lx0x2 − L2x0 x2 −x3 − Lx2 − x3 − Lx2x4 − L2x2 x4 − L2x2 x4 − L2x2

I User decodes by adding.

I Eavesdropper decodes initially.

I Eavesdropper cannot decode for k > 2.

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8/13

Example

Code

zk = xk − Lk−tkxtk

Encoder User Eavesdropper

x0 x0 x0

x1 − Lx0 − x1 − Lx0x2 − L2x0 x2 −x3 − Lx2 − x3 − Lx2x4 − L2x2 x4 x4 − L2x2

I User decodes by adding.

I Eavesdropper decodes initially.

I Eavesdropper cannot decode for k > 2.

Page 32: Secrecy Codes for Wireless Control Systemsiot.stanford.edu/nsf-final/slides/sitp-nsf-final-codes.pdf2/13 Secrecy Issues in the Internet of Things I Interconnected sensors and actuators

8/13

Example

Code

zk = xk − Lk−tkxtk

Encoder User Eavesdropper

x0 x0 x0

x1 − Lx0 − x1

x2 − L2x0 x2 −x3 − Lx2 − x3 − Lx2x4 − L2x2 x4 x4 − L2x2

I User decodes by adding.

I Eavesdropper decodes initially.

I Eavesdropper cannot decode for k > 2.

Page 33: Secrecy Codes for Wireless Control Systemsiot.stanford.edu/nsf-final/slides/sitp-nsf-final-codes.pdf2/13 Secrecy Issues in the Internet of Things I Interconnected sensors and actuators

8/13

Example

Code

zk = xk − Lk−tkxtk

Encoder User Eavesdropper

x0 x0 x0

x1 − Lx0 − x1

x2 − L2x0 x2 −x3 − Lx2 − x3 − Lx2, x3 =?

x4 − L2x2 x4 x4 − L2x2, x4 =?

I User decodes by adding.

I Eavesdropper decodes initially.

I Eavesdropper cannot decode for k > 2.

Page 34: Secrecy Codes for Wireless Control Systemsiot.stanford.edu/nsf-final/slides/sitp-nsf-final-codes.pdf2/13 Secrecy Issues in the Internet of Things I Interconnected sensors and actuators

8/13

Example

Code

zk = xk − Lk−tkxtk

Encoder User Eavesdropper

x0 x0 x0

x1 − Lx0 − x1

x2 − L2x0 x2 −x3 − Lx2 − x3 − Lx2, x3 =?

x4 − L2x2 x4 x4 − L2x2, x4 =?

Critical eventWhen the user receives while the eavesdropper misses:

γu,k = 1, γe,k = 0, for some k

Damages the eavesdropper (here for k = 2).

Page 35: Secrecy Codes for Wireless Control Systemsiot.stanford.edu/nsf-final/slides/sitp-nsf-final-codes.pdf2/13 Secrecy Issues in the Internet of Things I Interconnected sensors and actuators

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Secrecy guarantees

Theorem 1: Secrecy

If the critical event occurs at time k0 secrecy is achieved:

I Eavesdropper’s mmse is asymptotically maximum:

Pe,k → maximum value

I User’s mmse remains optimal:

Pu,k = 0, when user receives. (γu,k = 1)

I One occurrence of the critical event is sufficient.(user receives and eavesdropper fails to intercept at some time k.)

I Condition holds for most packet dropping channels.

Page 36: Secrecy Codes for Wireless Control Systemsiot.stanford.edu/nsf-final/slides/sitp-nsf-final-codes.pdf2/13 Secrecy Issues in the Internet of Things I Interconnected sensors and actuators

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Simulation scenario

z

y

φ

I Linearized dynamics, planar quadrotor

I Hovers around target point (0, 0, 0)

I State is position and velocity

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11/13

Simulation scenario

0 50 100 150 200 250 300 350 400

z es

timat

ion

-1

-0.5

0

0.5

1

UserEavesdropperTrue state

I Height estimation

I Critical event occurs at time k = 47

I Eavesdropper gets confused about the state; trivial estimatexe = 0

I User’s estimation remains accurate

Page 38: Secrecy Codes for Wireless Control Systemsiot.stanford.edu/nsf-final/slides/sitp-nsf-final-codes.pdf2/13 Secrecy Issues in the Internet of Things I Interconnected sensors and actuators

11/13

Simulation scenario

0 50 100 150 200 250 300 350 400

z es

timat

ion

-1

-0.5

0

0.5

1

UserEavesdropperTrue state

I Height estimation

I Critical event occurs at time k = 47

I Eavesdropper gets confused about the state; trivial estimatexe = 0

I User’s estimation remains accurate

Page 39: Secrecy Codes for Wireless Control Systemsiot.stanford.edu/nsf-final/slides/sitp-nsf-final-codes.pdf2/13 Secrecy Issues in the Internet of Things I Interconnected sensors and actuators

11/13

Simulation scenario

0 50 100 150 200 250 300 350 400

z es

timat

ion

-1

-0.5

0

0.5

1

UserEavesdropperTrue state

I Height estimation

I Critical event occurs at time k = 47

I Eavesdropper gets confused about the state; trivial estimatexe = 0

I User’s estimation remains accurate

Page 40: Secrecy Codes for Wireless Control Systemsiot.stanford.edu/nsf-final/slides/sitp-nsf-final-codes.pdf2/13 Secrecy Issues in the Internet of Things I Interconnected sensors and actuators

11/13

Simulation scenario

0 50 100 150 200 250 300 350 400

z es

timat

ion

-1

-0.5

0

0.5

1

UserEavesdropperTrue state

I Height estimation

I Critical event occurs at time k = 47

I Eavesdropper gets confused about the state; trivial estimatexe = 0

I User’s estimation remains accurate

Page 41: Secrecy Codes for Wireless Control Systemsiot.stanford.edu/nsf-final/slides/sitp-nsf-final-codes.pdf2/13 Secrecy Issues in the Internet of Things I Interconnected sensors and actuators

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Conclusion

Summary

I We can exploit the dynamical system model/physics for secrecy.

I Codes specialized for dynamical systems.

I Simple and fast, strong guarantees for the current state.

I Secrecy guarantees for several types of linear systems.

Future Work

I How to defend against active eavesdroppers?

I How can we combine codes with encryption efficiently?

I How can we apply the codes in closed-loop control systems?

I How can we protect past states?

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12/13

Conclusion

Summary

I We can exploit the dynamical system model/physics for secrecy.

I Codes specialized for dynamical systems.

I Simple and fast, strong guarantees for the current state.

I Secrecy guarantees for several types of linear systems.

Future Work

I How to defend against active eavesdroppers?

I How can we combine codes with encryption efficiently?

I How can we apply the codes in closed-loop control systems?

I How can we protect past states?

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13/13

Thank you!