Reliable Deniable Communication: Hiding Messages from Noise Pak Hou Che Joint Work with Sidharth Jaggi, Mayank Bakshi and Madhi Jafari Siavoshani Institute of Network Coding The Chinese University of Hong Kong

Introduction Is Alice talking to someone? Alice Willie Bob

Introduction Is Alice talking to someone? Alice Willie Bob Goal: decode message Goal: detect Alice’s status Goal: transmit reliably & deniably

Model M T Alice’s Encoder

Model M T BSC(p b ) Alice’s Encoder Bob’s Decoder

Model M T BSC(p b ) Alice’s Encoder Bob’s Decoder

Model M T BSC(p b ) Alice’s Encoder Bob’s Decoder BSC(p w ) Willie’s Estimator

Model M T BSC(p b ) Alice’s Encoder Bob’s Decoder BSC(p w ) Willie’s Estimator

Model M T BSC(p b ) Alice’s Encoder Bob’s Decoder BSC(p w ) Willie’s Estimator Asymmetry p b < p w

Prior Work AliceBob Willie Shared secret ([1] Bash, Goeckel & Towsley) [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.

Our Case AliceBob Willie Asymmetry p b < p w

Hypothesis Testing Willie’s Estimation Alice’s Transmit Status

Hypothesis Testing Willie’s Estimation Alice’s Transmit Status

Hypothesis Testing Willie’s Estimation Alice’s Transmit Status

Hypothesis Testing Willie’s Estimation Alice’s Transmit Status

Intuition

Theorem 1 (high deniability => low weight codewords)

Theorem 2 & 3 (Converse & achievability for reliable & deniable comm.)

Theorem 2 & 3 0 1/2 p b >p w

Theorem 2 & 3 0 1/2

Theorem 2 & 3 0 1/2 p w =1/2

Theorem 2 & 3 0 1/2

Theorem 2 & 3 0 1/2

Theorem 2 & 3 0 1/2 p b =1/2

Theorem 2 & 3 0 1/2

Theorem 2 & 3 0 1/2

Theorem 2 & 3 0 1/2

Theorem 2 & 3 0 1/2 p w >p b

Theorem 2 & 3 0 1/2

Theorem 2 & 3 0 1/2

Theorem 3 – Proof Idea

0n logarithm of # codewords

Theorem 3 – Proof Idea 0n logarithm of # codewords

Theorem 3 – Proof Idea 0n logarithm of # codewords Too few codewords => Not deniable (Thm4)

Theorem 3 – Proof Idea 0n logarithm of # codewords

Theorem 3 – Proof Idea 0n logarithm of # codewords

Theorem 3 – Proof Idea Logarithm of # codewords

Theorem 3 – Proof Idea

0n logarithm of # codewords

Theorem 3 – Proof Idea 0n logarithm of # codewords

Theorem 3 – Proof Idea 0n logarithm of # codewords

Theorem 3 – Sketch Proof

Summary 0 1/2

Summary 0 1/2