Secrecy Codes for Wireless Control...
Transcript of Secrecy Codes for Wireless Control...
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Secrecy Codes for Wireless Control Systems
Anastasios Tsiamis, Konstantinos Gatsis, George J. Pappas
University of Pennsylvania
July 13, 2018
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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.
![Page 3: 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.](https://reader030.fdocuments.us/reader030/viewer/2022041022/5ed33d483908c161e04f3ee3/html5/thumbnails/3.jpg)
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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.](https://reader030.fdocuments.us/reader030/viewer/2022041022/5ed33d483908c161e04f3ee3/html5/thumbnails/4.jpg)
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.](https://reader030.fdocuments.us/reader030/viewer/2022041022/5ed33d483908c161e04f3ee3/html5/thumbnails/5.jpg)
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.](https://reader030.fdocuments.us/reader030/viewer/2022041022/5ed33d483908c161e04f3ee3/html5/thumbnails/6.jpg)
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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 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.](https://reader030.fdocuments.us/reader030/viewer/2022041022/5ed33d483908c161e04f3ee3/html5/thumbnails/7.jpg)
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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 8: 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.](https://reader030.fdocuments.us/reader030/viewer/2022041022/5ed33d483908c161e04f3ee3/html5/thumbnails/8.jpg)
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.](https://reader030.fdocuments.us/reader030/viewer/2022041022/5ed33d483908c161e04f3ee3/html5/thumbnails/9.jpg)
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.](https://reader030.fdocuments.us/reader030/viewer/2022041022/5ed33d483908c161e04f3ee3/html5/thumbnails/10.jpg)
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
![Page 11: 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.](https://reader030.fdocuments.us/reader030/viewer/2022041022/5ed33d483908c161e04f3ee3/html5/thumbnails/11.jpg)
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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 12: 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.](https://reader030.fdocuments.us/reader030/viewer/2022041022/5ed33d483908c161e04f3ee3/html5/thumbnails/12.jpg)
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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.](https://reader030.fdocuments.us/reader030/viewer/2022041022/5ed33d483908c161e04f3ee3/html5/thumbnails/13.jpg)
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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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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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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
![Page 16: 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.](https://reader030.fdocuments.us/reader030/viewer/2022041022/5ed33d483908c161e04f3ee3/html5/thumbnails/16.jpg)
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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.
![Page 19: 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.](https://reader030.fdocuments.us/reader030/viewer/2022041022/5ed33d483908c161e04f3ee3/html5/thumbnails/19.jpg)
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.
![Page 20: 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.](https://reader030.fdocuments.us/reader030/viewer/2022041022/5ed33d483908c161e04f3ee3/html5/thumbnails/20.jpg)
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.
![Page 21: 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.](https://reader030.fdocuments.us/reader030/viewer/2022041022/5ed33d483908c161e04f3ee3/html5/thumbnails/21.jpg)
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.
![Page 22: 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.](https://reader030.fdocuments.us/reader030/viewer/2022041022/5ed33d483908c161e04f3ee3/html5/thumbnails/22.jpg)
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.](https://reader030.fdocuments.us/reader030/viewer/2022041022/5ed33d483908c161e04f3ee3/html5/thumbnails/24.jpg)
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 25: 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.](https://reader030.fdocuments.us/reader030/viewer/2022041022/5ed33d483908c161e04f3ee3/html5/thumbnails/25.jpg)
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.](https://reader030.fdocuments.us/reader030/viewer/2022041022/5ed33d483908c161e04f3ee3/html5/thumbnails/26.jpg)
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.](https://reader030.fdocuments.us/reader030/viewer/2022041022/5ed33d483908c161e04f3ee3/html5/thumbnails/27.jpg)
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.](https://reader030.fdocuments.us/reader030/viewer/2022041022/5ed33d483908c161e04f3ee3/html5/thumbnails/28.jpg)
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.](https://reader030.fdocuments.us/reader030/viewer/2022041022/5ed33d483908c161e04f3ee3/html5/thumbnails/29.jpg)
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.](https://reader030.fdocuments.us/reader030/viewer/2022041022/5ed33d483908c161e04f3ee3/html5/thumbnails/30.jpg)
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.
![Page 31: 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.](https://reader030.fdocuments.us/reader030/viewer/2022041022/5ed33d483908c161e04f3ee3/html5/thumbnails/31.jpg)
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.](https://reader030.fdocuments.us/reader030/viewer/2022041022/5ed33d483908c161e04f3ee3/html5/thumbnails/32.jpg)
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.](https://reader030.fdocuments.us/reader030/viewer/2022041022/5ed33d483908c161e04f3ee3/html5/thumbnails/33.jpg)
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.](https://reader030.fdocuments.us/reader030/viewer/2022041022/5ed33d483908c161e04f3ee3/html5/thumbnails/34.jpg)
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.](https://reader030.fdocuments.us/reader030/viewer/2022041022/5ed33d483908c161e04f3ee3/html5/thumbnails/35.jpg)
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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.](https://reader030.fdocuments.us/reader030/viewer/2022041022/5ed33d483908c161e04f3ee3/html5/thumbnails/36.jpg)
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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
![Page 37: 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.](https://reader030.fdocuments.us/reader030/viewer/2022041022/5ed33d483908c161e04f3ee3/html5/thumbnails/37.jpg)
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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.](https://reader030.fdocuments.us/reader030/viewer/2022041022/5ed33d483908c161e04f3ee3/html5/thumbnails/38.jpg)
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.](https://reader030.fdocuments.us/reader030/viewer/2022041022/5ed33d483908c161e04f3ee3/html5/thumbnails/39.jpg)
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.](https://reader030.fdocuments.us/reader030/viewer/2022041022/5ed33d483908c161e04f3ee3/html5/thumbnails/40.jpg)
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.](https://reader030.fdocuments.us/reader030/viewer/2022041022/5ed33d483908c161e04f3ee3/html5/thumbnails/41.jpg)
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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?
![Page 42: 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.](https://reader030.fdocuments.us/reader030/viewer/2022041022/5ed33d483908c161e04f3ee3/html5/thumbnails/42.jpg)
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?
![Page 43: 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.](https://reader030.fdocuments.us/reader030/viewer/2022041022/5ed33d483908c161e04f3ee3/html5/thumbnails/43.jpg)
13/13
Thank you!