1. Reliable Deniable Communication: Hiding Messages from Noise Pak Hou Che Joint Work with Sidharth Jaggi, Mayank Bakshi and Madhi Jafari Siavoshani Institute of Network Coding The Chinese University of Hong Kong

2. Introduction Is Alice talking to someone? Alice Willie Bob

3. Introduction Is Alice talking to someone? Alice Willie Bob Goal: decode message Goal: detect Alice’s status Goal: transmit reliably & deniably

4. Model M T Alice’s Encoder

5. Model M T BSC(p b ) Alice’s Encoder Bob’s Decoder

6. Model M T BSC(p b ) Alice’s Encoder Bob’s Decoder

7. Model M T BSC(p b ) Alice’s Encoder Bob’s Decoder BSC(p w ) Willie’s Estimator

8. Model M T BSC(p b ) Alice’s Encoder Bob’s Decoder BSC(p w ) Willie’s Estimator

9. Model M T BSC(p b ) Alice’s Encoder Bob’s Decoder BSC(p w ) Willie’s Estimator Asymmetry p b < p w

10. Prior Work AliceBob Willie Shared secret ([1] Bash, Goeckel & Towsley) [1] B. A. Bash, D. Goeckel and D. Towsley, “Square root law for communication with low probability of detection on AWGN channels,” in Proceedings of the IEEE International Symposium on Information Theory (ISIT), 2012, pp. 448–452.

11. Our Case AliceBob Willie Asymmetry p b < p w

12. Hypothesis Testing Willie’s Estimation Alice’s Transmit Status

13. Hypothesis Testing Willie’s Estimation Alice’s Transmit Status

14. Hypothesis Testing Willie’s Estimation Alice’s Transmit Status

15. Hypothesis Testing Willie’s Estimation Alice’s Transmit Status

16. Intuition

18. Theorem 1 (high deniability => low weight codewords)

19. Theorem 2 & 3 (Converse & achievability for reliable & deniable comm.)

20. Theorem 2 & 3 0 1/2 p b >p w

21. Theorem 2 & 3 0 1/2

22. Theorem 2 & 3 0 1/2 p w =1/2

23. Theorem 2 & 3 0 1/2

24. Theorem 2 & 3 0 1/2

25. Theorem 2 & 3 0 1/2 p b =1/2

26. Theorem 2 & 3 0 1/2

27. Theorem 2 & 3 0 1/2

28. Theorem 2 & 3 0 1/2

29. Theorem 2 & 3 0 1/2 p w >p b

30. Theorem 2 & 3 0 1/2

31. Theorem 2 & 3 0 1/2

32. Theorem 3 – Proof Idea

33. 0n logarithm of # codewords

34. Theorem 3 – Proof Idea 0n logarithm of # codewords

35. Theorem 3 – Proof Idea 0n logarithm of # codewords Too few codewords => Not deniable (Thm4)

36. Theorem 3 – Proof Idea 0n logarithm of # codewords

37. Theorem 3 – Proof Idea 0n logarithm of # codewords

38. Theorem 3 – Proof Idea Logarithm of # codewords

39. Theorem 3 – Proof Idea

44. 0n logarithm of # codewords

45. Theorem 3 – Proof Idea 0n logarithm of # codewords

46. Theorem 3 – Proof Idea 0n logarithm of # codewords

47. Theorem 3 – Sketch Proof

54. Summary 0 1/2

55. Summary 0 1/2