Reliable deniable communication hiding messages in noise
Sponsored Links
This presentation is the property of its rightful owner.
1 / 42

Reliable Deniable Communication: Hiding Messages in Noise PowerPoint PPT Presentation


  • 54 Views
  • Uploaded on
  • Presentation posted in: General

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.

Download Presentation

Reliable Deniable Communication: Hiding Messages in Noise

An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -

Presentation Transcript


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


Hypothesis Testing


Hypothesis Testing

  • Want:


Hypothesis Testing

  • Want:

  • Known: for opt. estimator


Hypothesis Testing

  • Want:

  • Known: for opt. estimator

  • , (w.h.p.)


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

No shared secret

BSC(pb)

pb < pw

BSC(pw)


Intuition


Intuition


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 2 (Converse)

  • ,if

  • if


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

log(# vectors)

n

0


Theorem 3 – Deniability proof sketch

!!!


Theorem 3 – Deniability proof sketch

!!!


Theorem 3 – Deniability proof sketch

with high probability


Theorem 3 – Deniability proof sketch

logarithm of

# vectors

0

n


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

logarithm of

# codewords

0

n


Theorem 4

Too fewcodewords

=> Not deniable

logarithm of

# codewords

0

n


Summary

1/2

  • Thm 1 & 2 Converse

    • (Upper Bound)

  • Thm 3 Achievability

  • Thm 4 Lower Bound

0

1/2


  • Login