Reliable Deniable Communication: Hiding Messages in Noise

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Reliable Deniable Communication: Hiding Messages in Noise

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Reliable Deniable Communication: Hiding Messages in Noise

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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

T

t

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

- Want:

- Want:
- Known: for opt. estimator

- Want:
- Known: for opt. estimator
- , (w.h.p.)

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.

No shared secret

BSC(pb)

pb < pw

BSC(pw)

- 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

- ,if
- if

- 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

log(# vectors)

n

0

Theorem 3 – Deniability proof sketch

!!!

Theorem 3 – Deniability proof sketch

!!!

Theorem 3 – Deniability proof sketch

with high probability

logarithm of

# vectors

0

n

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.

logarithm of

# codewords

0

n

Too fewcodewords

=> Not deniable

logarithm of

# codewords

0

n

1/2

- Thm 1 & 2 Converse
- (Upper Bound)

- Thm 3 Achievability
- Thm 4 Lower Bound

0

1/2