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Paul Cuff THE SOURCE CODING SIDE OF SECRECY TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.: AA.

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Presentation on theme: "Paul Cuff THE SOURCE CODING SIDE OF SECRECY TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.: AA."— Presentation transcript:

1 Paul Cuff THE SOURCE CODING SIDE OF SECRECY TexPoint fonts used in EMF. Read the TexPoint manual before you delete this box.: AA

2 Game Theoretic Secrecy Motivating Problem Mixed Strategy Non-deterministic Requires random decoder Dual to wiretap channel Encoder Communication leakage Eavesdropping Zero-sum Repeated Game Player 1 Player 2 State

3 Main Topics of this Talk Achievability Proof Techniques: 1.Pose problems in terms of existence of joint distributions 2.Relax Requirements to “close in total variation” 3.Main Tool --- Reverse Channel Encoder 4.Easy Analysis of Optimal Adversary

4 Restate Problem---Example 1 (RD Theory) Can we design: such that Does there exists a distribution: StandardExistence of Distributions fg

5 Restate Problem---Example 2 (Secrecy) Can we design: such that Does there exists a distribution: StandardExistence of Distributions fg Eve Score [Cuff 10]

6 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 p 1. How? Property 1:

7 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 p 1. Why? Property 2 (bounded functions):

8 Summary Achievability Proof Techniques: 1.Pose problems in terms of existence of joint distributions 2.Relax Requirements to “close in total variation” 3.Main Tool --- Reverse Channel Encoder 4.Easy Analysis of Optimal Adversary Secrecy Example:For arbitrary ², does there exist a distribution satisfying:

9 Cloud Overlap Lemma Previous Encounters Wyner, used divergence Han-Verdú, general channels, used total variation Cuff 08, 09, 10, provide simple proof and utilize for secrecy encoding P X|U (x|u) Memoryless Channel

10 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 = (J a, J s ), and ignore J s for now) Construct a joint distribution between the source X n and the information J a (revealed to the Adversary) using a memoryless channel. P X|U (x|u) Memoryless Channel

11 Simple Analysis This encoder yields a very simple analysis and convenient properties 1.If |J a | is large enough, then X n will be nearly i.i.d. in total variation 2.Performance: P X|U (x|u) Memoryless Channel

12 Summary Achievability Proof Techniques: 1.Pose problems in terms of existence of joint distributions 2.Relax Requirements to “close in total variation” 3.Main Tool --- Reverse Channel Encoder 4.Easy Analysis of Optimal Adversary


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