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Reliable Deniable Communication: Hiding Messages in Noise

Reliable Deniable Communication: Hiding Messages in Noise. Pak Hou Che Mayank Bakshi Sidharth Jaggi. The Chinese University of Hong Kong. The Institute of Network Coding. Alice. Bob. Reliability. Alice. Bob. Reliability. Deniability. Willie (the Warden). Alice’s Encoder. M. T.

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Reliable Deniable Communication: Hiding Messages in Noise

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  1. Reliable Deniable Communication: Hiding Messages in Noise Pak HouChe MayankBakshi SidharthJaggi The Chinese University of Hong Kong The Institute of Network Coding

  2. Alice Bob Reliability

  3. Alice Bob Reliability Deniability Willie (the Warden)

  4. Alice’s Encoder M T t

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

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

  7. Hypothesis Testing

  8. Hypothesis Testing • Want:

  9. Hypothesis Testing • Want: • Known: for opt. estimator

  10. Hypothesis Testing • Want: • Known: for opt. estimator • , (w.h.p.)

  11. Bash, Goeckel & Towsley [1] Shared secret bits AWGN channels Capacity = bits [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.

  12. This work No shared secret BSC(pb) pb < pw BSC(pw)

  13. Intuition

  14. Intuition

  15. Main Theorems • Theorem 1 • Deniability  low weight codewords • Theorem 2 • Converse of reliability • Theorem 3 • Achievability (reliability & deniability) • Theorem 4 • Trade-off between deniability & size of codebook

  16. Theorem 1 (wt(c.w.))(high deniability => low weight codewords)

  17. Theorem 2 (Converse) • , if • if

  18. Theorem 3 – Reliability • Random codebook ( i.i.d. ) ) • minimum distance decoder • For ,

  19. logarithm of # binary vectors 0 n

  20. log(# vectors) n 0

  21. log(# vectors)

  22. log(# codewords)

  23. log(# vectors) n 0

  24. Theorem 3 – Deniability proof sketch • Recall: want to show

  25. Theorem 3 – Deniability proof sketch • Recall: want to show

  26. Theorem 3 – Deniability proof sketch log(# vectors) n 0

  27. Theorem 3 – Deniability proof sketch !!!

  28. Theorem 3 – Deniability proof sketch !!!

  29. Theorem 3 – Deniability proof sketch with high probability

  30. Theorem 3 – Deniability proof sketch logarithm of # vectors 0 n

  31. Theorem 3 – Deniability proof sketch logarithm of # vectors 0 n

  32. Theorem 3 – Deniability proof sketch # codewords of “type”

  33. Theorem 3 – Deniability proof sketch

  34. Theorem 3 – Deniability proof sketch

  35. Theorem 3 – Deniability proof sketch

  36. Theorem 3 – Deniability proof sketch

  37. Theorem 3 – Deniability proof sketch • w.p.

  38. Theorem 3 – Deniability proof sketch • w.p. • close to w.p. • , w.h.p.

  39. Theorem 4 logarithm of # codewords 0 n

  40. Theorem 4 Too fewcodewords => Not deniable logarithm of # codewords 0 n

  41. Summary 1/2 • Thm 1 & 2 Converse • (Upper Bound) • Thm 3 Achievability • Thm 4 Lower Bound 0 1/2

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