The Source Coding Side of Secrecy TexPoint fonts used in EMF Read the TexPoint manual before you delete this box A A Game Theoretic Secrecy Motivating Problem Mixed Strategy Nondeterministic ID: 559025
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Slide1
Paul Cuff
The Source Coding Side of Secrecy
TexPoint fonts used in EMF.
Read the TexPoint manual before you delete this box.:
A
ASlide2
Game Theoretic Secrecy
Motivating Problem
Mixed Strategy
Non-deterministic
Requires randomdecoderDual to wiretap channel
Encoder
Communication
leakage
Eavesdropping
Zero-sum
Repeated
Game
Player 1
Player 2
StateSlide3
Main Topics of this Talk
Achievability Proof Techniques:
Pose
problems in terms of
existence of joint distributionsRelax Requirements to
“close in total variation”
Main Tool --- Reverse Channel EncoderEasy Analysis of Optimal AdversarySlide4
Restate Problem---Example 1 (RD Theory)
Can we design:
such that
Does there exists a distribution:
Standard
Existence of Distributions
f
gSlide5
Restate Problem---Example 2 (Secrecy)
Can we design:
such that
Does there exists a distribution:
Standard
Existence of Distributions
f
g
Eve
Score
[Cuff 10]Slide6
Tricks with Total Variation
Technique
Find a distribution
p
1 that is easy to analyze and satisfies the relaxed constraints.Construct p
2 to satisfy the hard constraints while maintaining small total variation distance to
p1.
How?
Property 1:Slide7
Tricks with Total Variation
Technique
Find a distribution
p
1 that is easy to analyze and satisfies the relaxed constraints.Construct p
2 to satisfy the hard constraints while maintaining small total variation distance to
p1.
Why?
Property 2 (bounded functions):Slide8
Summary
Achievability Proof Techniques:
Pose
problems in terms of
existence of joint distributionsRelax Requirements to “close in total variation”
Main Tool --- Reverse Channel Encoder
Easy Analysis
of Optimal AdversarySecrecy Example: For arbitrary
², does there exist a distribution satisfying:Slide9
Cloud Overlap Lemma
Previous EncountersWyner
, 75 --- used divergence
Han-
Verdú, 93 --- general channels, used total variationCuff 08, 09, 10, 11 --- provide simple proof and utilize for secrecy encoding
P
X|U
(
x|u
)
Memoryless
ChannelSlide10
Reverse Channel Encoder
For simplicity, ignore the key K, and consider
J
a
to be the part of the message that the adversary obtains. (i.e. J = (Ja,
Js), and ignore
Js for now)Construct a joint distribution between the source Xn
and the information Ja (revealed to the Adversary) using a memoryless channel.
P
X|U
(
x|u
)
Memoryless
ChannelSlide11
Simple Analysis
This encoder yields a very simple analysis and convenient properties
If |
J
a
| is large enough, then X
n will be nearly i.i.d. in total variationPerformance:
P
X|U
(
x|u
)
Memoryless
ChannelSlide12
Summary
Achievability Proof Techniques:
Pose
problems in terms of
existence of joint distributionsRelax Requirements to
“close in total variation”Main Tool ---
Reverse Channel EncoderEasy Analysis of Optimal Adversary