Reliable deniable communication hiding messages in noise
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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

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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


Reliable deniable communication hiding messages in noise 2622039

Alice

Bob

Reliability


Reliable deniable communication hiding messages in noise 2622039

Alice

Bob

Reliability

Deniability

Willie

(the Warden)


Reliable deniable communication hiding messages in noise 2622039

Alice’s Encoder

M

T

t


Reliable deniable communication hiding messages in noise 2622039

Alice’s Encoder

M

Bob’s Decoder

BSC(pb)

T

Message

Trans. Status


Reliable deniable communication hiding messages in noise 2622039

Alice’s Encoder

M

Bob’s Decoder

BSC(pb)

T

Message

Trans. Status

BSC(pw)

Willie’s (Best) Estimator


Hypothesis testing

Hypothesis Testing


Hypothesis testing1

Hypothesis Testing

  • Want:


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)


Intuition

Intuition


Intuition1

Intuition


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 2 converse

Theorem 2 (Converse)

  • ,if

  • if


Theorem 3 reliability

Theorem 3 – Reliability

  • Random codebook ( i.i.d. ) )

  • minimum distance decoder

  • For ,


Reliable deniable communication hiding messages in noise 2622039

logarithm of

# binary vectors

0

n


Reliable deniable communication hiding messages in noise 2622039

log(# vectors)

n

0


Reliable deniable communication hiding messages in noise 2622039

log(# vectors)


Reliable deniable communication hiding messages in noise 2622039

log(# codewords)


Reliable deniable communication hiding messages in noise 2622039

log(# vectors)

n

0


Reliable deniable communication hiding messages in noise 2622039

Theorem 3 – Deniability proof sketch

  • Recall: want to show


Reliable deniable communication hiding messages in noise 2622039

Theorem 3 – Deniability proof sketch

  • Recall: want to show


Theorem 3 deniability proof sketch

Theorem 3 – Deniability proof sketch

log(# vectors)

n

0


Reliable deniable communication hiding messages in noise 2622039

Theorem 3 – Deniability proof sketch

!!!


Reliable deniable communication hiding messages in noise 2622039

Theorem 3 – Deniability proof sketch

!!!


Reliable deniable communication hiding messages in noise 2622039

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


Reliable deniable communication hiding messages in noise 2622039

Theorem 3 – Deniability proof sketch

# codewords of “type”


Reliable deniable communication hiding messages in noise 2622039

Theorem 3 – Deniability proof sketch


Reliable deniable communication hiding messages in noise 2622039

Theorem 3 – Deniability proof sketch


Reliable deniable communication hiding messages in noise 2622039

Theorem 3 – Deniability proof sketch


Reliable deniable communication hiding messages in noise 2622039

Theorem 3 – Deniability proof sketch


Reliable deniable communication hiding messages in noise 2622039

Theorem 3 – Deniability proof sketch

  • w.p.


Reliable deniable communication hiding messages in noise 2622039

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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