paul cuff electrical engineering princeton university causal secrecy: an informed eavesdropper
TRANSCRIPT
![Page 1: PAUL CUFF ELECTRICAL ENGINEERING PRINCETON UNIVERSITY Causal Secrecy: An Informed Eavesdropper](https://reader030.vdocument.in/reader030/viewer/2022032702/56649ca75503460f9496a34b/html5/thumbnails/1.jpg)
PAUL CUFFELECTRICAL ENGINEERING
PRINCETON UNIVERSITY
Causal Secrecy:An Informed Eavesdropper
![Page 2: PAUL CUFF ELECTRICAL ENGINEERING PRINCETON UNIVERSITY Causal Secrecy: An Informed Eavesdropper](https://reader030.vdocument.in/reader030/viewer/2022032702/56649ca75503460f9496a34b/html5/thumbnails/2.jpg)
Main Idea
Secrecy for distributed systems
Limit the adversaries “useful” information
Node A
Node BMessageInformation
Action
Adversary
Distributed System
Attack
![Page 3: PAUL CUFF ELECTRICAL ENGINEERING PRINCETON UNIVERSITY Causal Secrecy: An Informed Eavesdropper](https://reader030.vdocument.in/reader030/viewer/2022032702/56649ca75503460f9496a34b/html5/thumbnails/3.jpg)
Communication in Distributed Systems
“Smart Grid”
Image from http://www.solarshop.com.au
![Page 4: PAUL CUFF ELECTRICAL ENGINEERING PRINCETON UNIVERSITY Causal Secrecy: An Informed Eavesdropper](https://reader030.vdocument.in/reader030/viewer/2022032702/56649ca75503460f9496a34b/html5/thumbnails/4.jpg)
Perfectly Private Communication
Vernam Cipher (1917) Key Sequence: 001011… Information: 101100…
One Time Pad Random Secret Key [Mauborgne]
Shannon [1949 paper] One time pad is necessary and sufficient for perfect
secrecy.
XOR 100111…
![Page 5: PAUL CUFF ELECTRICAL ENGINEERING PRINCETON UNIVERSITY Causal Secrecy: An Informed Eavesdropper](https://reader030.vdocument.in/reader030/viewer/2022032702/56649ca75503460f9496a34b/html5/thumbnails/5.jpg)
Obtaining Secret Key
Secret Key Generation Key extracted from correlated observations and public
communication. [Gacs-Korner 73, Maurer 93, Ahlswede-Csiszar 93]
Quantum Key Distribution Key exchanged using entangled photos. Secrecy
verifiable. [Bennett-Brassard 84]
Public Key Distribution Key obtained by public communication is intractable
to compute by a third party. [Diffie-Hellman, Merkle 76]
![Page 6: PAUL CUFF ELECTRICAL ENGINEERING PRINCETON UNIVERSITY Causal Secrecy: An Informed Eavesdropper](https://reader030.vdocument.in/reader030/viewer/2022032702/56649ca75503460f9496a34b/html5/thumbnails/6.jpg)
Creating Secure Channels
Physical Layer Security Use Channel Noise to Create Private Channel
Wyner’s Wiretap Channel [Wyner 75]
![Page 7: PAUL CUFF ELECTRICAL ENGINEERING PRINCETON UNIVERSITY Causal Secrecy: An Informed Eavesdropper](https://reader030.vdocument.in/reader030/viewer/2022032702/56649ca75503460f9496a34b/html5/thumbnails/7.jpg)
Focus of Talk
What do we do with Secrecy Resources?
![Page 8: PAUL CUFF ELECTRICAL ENGINEERING PRINCETON UNIVERSITY Causal Secrecy: An Informed Eavesdropper](https://reader030.vdocument.in/reader030/viewer/2022032702/56649ca75503460f9496a34b/html5/thumbnails/8.jpg)
Example: Communication Limited Control
Adversary
00101110010010111
Signal (sensor)Communication
Signal (control)
Attack Signal
![Page 9: PAUL CUFF ELECTRICAL ENGINEERING PRINCETON UNIVERSITY Causal Secrecy: An Informed Eavesdropper](https://reader030.vdocument.in/reader030/viewer/2022032702/56649ca75503460f9496a34b/html5/thumbnails/9.jpg)
Example: Feedback Stabilization
“Data Rate Theorem” [Wong-Brockett 99, Baillieul 99]
Controller
Dynamic System
EncoderDecoder10010011011010101101010100101101011
SensorAdversary
Feedback
![Page 10: PAUL CUFF ELECTRICAL ENGINEERING PRINCETON UNIVERSITY Causal Secrecy: An Informed Eavesdropper](https://reader030.vdocument.in/reader030/viewer/2022032702/56649ca75503460f9496a34b/html5/thumbnails/10.jpg)
Isolate Communication Component
Schematic
Assumption Adversary knows everything about the system except
the keyRequirement
The decipherer accurately reconstructs the information
Public Channel
Key Key
Source Signal Output Signal
Adversary
![Page 11: PAUL CUFF ELECTRICAL ENGINEERING PRINCETON UNIVERSITY Causal Secrecy: An Informed Eavesdropper](https://reader030.vdocument.in/reader030/viewer/2022032702/56649ca75503460f9496a34b/html5/thumbnails/11.jpg)
Equivocation
Equivocation:Not an operationally defined quantityBounds:
List decoding Additional information needed for decryption
Not concerned with structure
![Page 12: PAUL CUFF ELECTRICAL ENGINEERING PRINCETON UNIVERSITY Causal Secrecy: An Informed Eavesdropper](https://reader030.vdocument.in/reader030/viewer/2022032702/56649ca75503460f9496a34b/html5/thumbnails/12.jpg)
Coordination
Don’t want Adversary to Coordinate Many ways to define this.
Establish a Pay-off function Min-max game between communication system and
adversary.
![Page 13: PAUL CUFF ELECTRICAL ENGINEERING PRINCETON UNIVERSITY Causal Secrecy: An Informed Eavesdropper](https://reader030.vdocument.in/reader030/viewer/2022032702/56649ca75503460f9496a34b/html5/thumbnails/13.jpg)
Competitive Distributed System
Node A Node BMessage
Key
Information Action
Adversary
Attack
Encoder:
System payoff: .
Decoder:
Adversary:
![Page 14: PAUL CUFF ELECTRICAL ENGINEERING PRINCETON UNIVERSITY Causal Secrecy: An Informed Eavesdropper](https://reader030.vdocument.in/reader030/viewer/2022032702/56649ca75503460f9496a34b/html5/thumbnails/14.jpg)
Zero-Sum Game
Value obtained by system:Objective
Maximize payoff
Node A Node BMessage
Key
Information Action
Adversary
Attack
![Page 15: PAUL CUFF ELECTRICAL ENGINEERING PRINCETON UNIVERSITY Causal Secrecy: An Informed Eavesdropper](https://reader030.vdocument.in/reader030/viewer/2022032702/56649ca75503460f9496a34b/html5/thumbnails/15.jpg)
Secrecy-Distortion Literature
[Yamamoto 97]: Cause an eavesdropper to have high reconstruction
distortion Replace payoff (π) with distortion
[Yamamoto 88]: No secret key Lossy compression
![Page 16: PAUL CUFF ELECTRICAL ENGINEERING PRINCETON UNIVERSITY Causal Secrecy: An Informed Eavesdropper](https://reader030.vdocument.in/reader030/viewer/2022032702/56649ca75503460f9496a34b/html5/thumbnails/16.jpg)
Secrecy is Too Easy
Consider a binary, uniform, memoryless source (i.e. random bits)
Use a “one-bit pad”
Adversary can narrow the source sequence to two complementary sequences “Perfect Secrecy:” No good reconstruction
![Page 17: PAUL CUFF ELECTRICAL ENGINEERING PRINCETON UNIVERSITY Causal Secrecy: An Informed Eavesdropper](https://reader030.vdocument.in/reader030/viewer/2022032702/56649ca75503460f9496a34b/html5/thumbnails/17.jpg)
INFORMATION THEORETIC RATE REGIONS
PROVABLE SECRECY
Theoretical Results
![Page 18: PAUL CUFF ELECTRICAL ENGINEERING PRINCETON UNIVERSITY Causal Secrecy: An Informed Eavesdropper](https://reader030.vdocument.in/reader030/viewer/2022032702/56649ca75503460f9496a34b/html5/thumbnails/18.jpg)
Lossless TransmissionGeneral Reward Function
Simplex interpretation Linear program
Hamming Distortion
Common Information Secret Key
Two Categories of Results
![Page 19: PAUL CUFF ELECTRICAL ENGINEERING PRINCETON UNIVERSITY Causal Secrecy: An Informed Eavesdropper](https://reader030.vdocument.in/reader030/viewer/2022032702/56649ca75503460f9496a34b/html5/thumbnails/19.jpg)
General Payoff Function
No requirement for lossless transmission.
Any payoff function π(x,y,z)Any source distribution
(i.i.d.)
Adversary:
![Page 20: PAUL CUFF ELECTRICAL ENGINEERING PRINCETON UNIVERSITY Causal Secrecy: An Informed Eavesdropper](https://reader030.vdocument.in/reader030/viewer/2022032702/56649ca75503460f9496a34b/html5/thumbnails/20.jpg)
Payoff-Rate Function
Maximum achievable average payoff
Markov relationship:
Theorem:
![Page 21: PAUL CUFF ELECTRICAL ENGINEERING PRINCETON UNIVERSITY Causal Secrecy: An Informed Eavesdropper](https://reader030.vdocument.in/reader030/viewer/2022032702/56649ca75503460f9496a34b/html5/thumbnails/21.jpg)
Unlimited Public Communication
Maximum achievable average payoff
Conditional common information:
Theorem (R=∞):
![Page 22: PAUL CUFF ELECTRICAL ENGINEERING PRINCETON UNIVERSITY Causal Secrecy: An Informed Eavesdropper](https://reader030.vdocument.in/reader030/viewer/2022032702/56649ca75503460f9496a34b/html5/thumbnails/22.jpg)
Competitive Distributed System
Node A Node BMessage
Key
Information Action
Adversary
Attack
Encoder:
System payoff: .
Decoder:
Adversary:
![Page 23: PAUL CUFF ELECTRICAL ENGINEERING PRINCETON UNIVERSITY Causal Secrecy: An Informed Eavesdropper](https://reader030.vdocument.in/reader030/viewer/2022032702/56649ca75503460f9496a34b/html5/thumbnails/23.jpg)
Zero-Sum Game
Value obtained by system:Objective
Maximize payoff
Node A Node BMessage
Key
Information Action
Adversary
Attack
![Page 24: PAUL CUFF ELECTRICAL ENGINEERING PRINCETON UNIVERSITY Causal Secrecy: An Informed Eavesdropper](https://reader030.vdocument.in/reader030/viewer/2022032702/56649ca75503460f9496a34b/html5/thumbnails/24.jpg)
Theorem:
[Cuff 10]
Lossless Case
Require Y=X Assume a payoff function
Related to Yamamoto’s work [97] Difference: Adversary is more capable with more
information
Also required:
![Page 25: PAUL CUFF ELECTRICAL ENGINEERING PRINCETON UNIVERSITY Causal Secrecy: An Informed Eavesdropper](https://reader030.vdocument.in/reader030/viewer/2022032702/56649ca75503460f9496a34b/html5/thumbnails/25.jpg)
Binary-Hamming Case
Binary Source:Hamming DistortionNaïve approach
Random hashing or time-sharingOptimal approach
Reveal excess 0’s or 1’s to condition the hidden bits
0 1 0 0 1 0 0 0 0 1
* * 0 0 * * 0 * 0 *
Source
Public message
(black line)
(orange line)
![Page 26: PAUL CUFF ELECTRICAL ENGINEERING PRINCETON UNIVERSITY Causal Secrecy: An Informed Eavesdropper](https://reader030.vdocument.in/reader030/viewer/2022032702/56649ca75503460f9496a34b/html5/thumbnails/26.jpg)
Linear Program on the Simplex
Constraint:
Minimize:
Maximize:
U will only have mass at a small subset of points (extreme points)
![Page 27: PAUL CUFF ELECTRICAL ENGINEERING PRINCETON UNIVERSITY Causal Secrecy: An Informed Eavesdropper](https://reader030.vdocument.in/reader030/viewer/2022032702/56649ca75503460f9496a34b/html5/thumbnails/27.jpg)
Linear Program on the Simplex
![Page 28: PAUL CUFF ELECTRICAL ENGINEERING PRINCETON UNIVERSITY Causal Secrecy: An Informed Eavesdropper](https://reader030.vdocument.in/reader030/viewer/2022032702/56649ca75503460f9496a34b/html5/thumbnails/28.jpg)
Summary
Information available to Adversary is key consideration No use of “equivocation” Coordination ability extracted by considering
competitive game.