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A New Approach to Lossy Compression and Applications to Security Eva C. Song Department of Electrical Engineering Princeton University Joint work with: Paul Cuff and H. Vincent Poor November 9, 2015 Overview 1 compression/source coding 1 2

SLIDE 1

A New Approach to Lossy Compression and Applications to Security

Eva C. Song

Department of Electrical Engineering Princeton University Joint work with: Paul Cuff and H. Vincent Poor

November 9, 2015

SLIDE 2

Overview

security data compression data transmission 1 2 3 4 5 6 7

1 compression/source coding 2 transmission/channel coding 3 security/cryptography 4 rate-distortion based

information-theoretic secrecy

5 joint source-channel coding 6 traditional

information-theoretic secrecy

7 joint source-channel

information-theoretic secrecy

E. C. Song (Princeton University)

Rising Star November 9, 2015 2 / 12

SLIDE 3

Lossy compression

Low compression (high quality) JPEG High compression (low quality) JPEG

tradeoff between compression and quality common in: audio, video, images, streaming, etc popular technique: MP3, JPEG, MPEG-4, etc good for data storage and transmission

E. C. Song (Princeton University)

Rising Star November 9, 2015 3 / 12

SLIDE 4

Looking through the engineering glass

Encoder Decoder X M Y X: data source M: encoded message (used for storage or transmission) Y : reconstructed data encoder/decoder: data encoding methods such as JPEG, MP3, MP4

bjective: (size(M), distance(X, Y ))
E. C. Song (Princeton University)

Rising Star November 9, 2015 4 / 12

SLIDE 5

Information theory

Encoder fn Decoder gn X n M Y n Assumption 1 (general): known source distribution Assumption 2 (a bit less general and this work)

◮ i.i.d. source distribution ◮ large n

E. C. Song (Princeton University)

Rising Star November 9, 2015 5 / 12

SLIDE 6

My contribution

Invented compressor: Likelihood Encoder Achieves best rate-distortion:

◮ point-to-point lossy compression ◮ multiuser lossy compression ◮ SECURITY

E. C. Song (Princeton University)

Rising Star November 9, 2015 6 / 12

SLIDE 7

Perfect secrecy

X n Encoder fn Decoder gn ˆ X n K ∈ [1 : 2nR0] Eavesdropper M ∈ [1 : 2nR]

Theorem (Shannon)

A rate pair (R, R0) is achievable under perfect secrecy if and only if R ≥ H(X), R0 ≥ H(X).

E. C. Song (Princeton University)

Rising Star November 9, 2015 7 / 12

SLIDE 8

What if we reduce key size?

not perfect secrecy how “imperfect”?

1 nH(X n|M) < H(X)

◮ hard to interpret ◮ what can the eavesdropper do with the information?

more practical metric for secrecy

E. C. Song (Princeton University)

Rising Star November 9, 2015 8 / 12

SLIDE 9

Rate-distortion based secrecy

X n Encoder fn Decoder gn Y n K ∈ [1 : 2nR0] PZ n|M Z n M ∈ [1 : 2nR] Average distortion for the legitimate receiver: E[db(X n, Y n)] ≤ Db Minimum average distortion for the eavesdropper: min

PZn|M

E [de(X n, Z n)] ≥ De Conclusion: secrecy is almost FREE!

E. C. Song (Princeton University)

Rising Star November 9, 2015 9 / 12

SLIDE 10

Really FREE?

assumption: one attempt!

ne-bit secrecy
E. C. Song (Princeton University)

Rising Star November 9, 2015 10 / 12

SLIDE 11

Secure source coding with causal disclosure

X n Encoder fn Decoder gn Y n K ∈ [2nR0] Eavesdropper Z n X t−1 t = 1, ..., n M ∈ [2nR] Average distortion for the legitimate receiver: E [db(X n, Y n)] ≤ Db Minimum average distortion for the eavesdropper: min

{PZt |MXt−1}n

t=1

E [de(X n, Z n)] ≥ De

E. C. Song (Princeton University)

Rising Star November 9, 2015 11 / 12

SLIDE 12

About causal disclosure

Fully generalizes Shannon cipher system Corresponding setting under noisy broadcast channels (physical layer) More about our work: http://www.princeton.edu/~csong

E. C. Song (Princeton University)

Rising Star November 9, 2015 12 / 12