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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

Reliable Deniable Communication: Hiding Messages in Noise

Pak HouChe

MayankBakshi

SidharthJaggi

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

Bob’s Decoder

BSC(pb)

T

Message

Trans. Status


Alice’s Encoder

M

Bob’s Decoder

BSC(pb)

T

Message

Trans. Status

BSC(pw)

Willie’s (Best) Estimator




Hypothesis testing2
Hypothesis Testing

  • Want:

  • Known: for opt. estimator


Hypothesis testing3
Hypothesis Testing

  • Want:

  • Known: for opt. estimator

  • , (w.h.p.)


Bash goeckel towsley 1
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.


This work
This work

No shared secret

BSC(pb)

pb < pw

BSC(pw)




Main theorems
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


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



Theorem 3 reliability
Theorem 3 – Reliability

  • Random codebook ( i.i.d. ) )

  • minimum distance decoder

  • For ,


logarithm of

# binary vectors

0

n


log(# vectors)

n

0


log(# vectors)


log(# codewords)


log(# vectors)

n

0


Theorem 3 – Deniability proof sketch

  • Recall: want to show


Theorem 3 – Deniability proof sketch

  • Recall: want to show



Theorem 3 – Deniability proof sketch

!!!


Theorem 3 – Deniability proof sketch

!!!


Theorem 3 – Deniability proof sketch

with high probability


Theorem 3 deniability proof sketch1
Theorem 3 – Deniability proof sketch

logarithm of

# vectors

0

n


Theorem 3 deniability proof sketch2
Theorem 3 – Deniability proof sketch

logarithm of

# vectors

0

n


Theorem 3 – Deniability proof sketch

# codewords of “type”


Theorem 3 – Deniability proof sketch


Theorem 3 – Deniability proof sketch


Theorem 3 – Deniability proof sketch


Theorem 3 – Deniability proof sketch


Theorem 3 – Deniability proof sketch

  • w.p.


Theorem 3 – Deniability proof sketch

  • w.p.

  • close to w.p.

  • , w.h.p.


Theorem 4
Theorem 4

logarithm of

# codewords

0

n


Theorem 41
Theorem 4

Too fewcodewords

=> Not deniable

logarithm of

# codewords

0

n


Summary
Summary

1/2

  • Thm 1 & 2 Converse

    • (Upper Bound)

  • Thm 3 Achievability

  • Thm 4 Lower Bound

0

1/2


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