Reliable Deniable Communication: Hiding Messages from Noise

1. Reliable Deniable Communication: Hiding Messages from Noise Institute of Network Coding The Chinese University of Hong Kong Pak HouChe Joint Work with SidharthJaggi, MayankBakshi and MadhiJafariSiavoshani

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

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

4. Model Alice’s Encoder M T t

5. Model Alice’s Encoder M Bob’s Decoder BSC(pb) T Message Trans. Status

6. Model Alice’s Encoder M Bob’s Decoder BSC(pb) T Message Trans. Status

7. Model Alice’s Encoder M Bob’s Decoder BSC(pb) T Message Trans. Status BSC(pw) Willie’s Estimator

8. Model Alice’s Encoder M Bob’s Decoder BSC(pb) T Message Trans. Status BSC(pw) Willie’s Estimator

9. Model Alice’s Encoder M Bob’s Decoder BSC(pb) T Message Trans. Status Asymmetry pb < pw BSC(pw) Willie’s Estimator

10. Prior Work Shared secret ([1] Bash, Goeckel & Towsley) Alice Bob Willie [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 Alice Bob Asymmetry pb < pw Willie

12. Hypothesis Testing

13. Hypothesis Testing

14. Hypothesis Testing

15. Hypothesis Testing

16. Intuition

17. Intuition

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

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

20. Theorem 2 & 3 1/2 pb>pw 0 1/2

21. Theorem 2 & 3 1/2 0 1/2

22. Theorem 2 & 3 pw=1/2 1/2 0 1/2

23. Theorem 2 & 3 1/2 0 1/2

24. Theorem 2 & 3 1/2 0 1/2

25. Theorem 2 & 3 1/2 pb=1/2 0 1/2

26. Theorem 2 & 3 1/2 0 1/2

27. Theorem 2 & 3 1/2 0 1/2

28. Theorem 2 & 3 1/2 0 1/2

29. Theorem 2 & 3 1/2 pw>pb 0 1/2

30. Theorem 2 & 3 1/2 0 1/2

31. Theorem 2 & 3 1/2 Achievable region 0 1/2

32. Theorem 3 – Proof Idea • Recall: want to show

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

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

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

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

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

38. Theorem 3 – Proof Idea Logarithm of # codewords

39. Theorem 3 – Proof Idea • Recall: want to show

40. Theorem 3 – Proof Idea !!!

41. Theorem 3 – Proof Idea !!!

42. Theorem 3 – Proof Idea • Chernoffbound is weak • Other concentration inequality

43. Theorem 3 – Proof Idea

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

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

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

47. Theorem 3 – Sketch Proof # codewords of “type”

48. Theorem 3 – Sketch Proof

49. Theorem 3 – Sketch Proof

50. Theorem 3 – Sketch Proof • w.p.