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A New Approach to Lossy Compression and Applicationsto Security
Eva C. Song
Department of Electrical EngineeringPrinceton University
Joint work with: Paul Cuff and H. Vincent Poor
November 9, 2015
Overview
security
data compression
data transmission
1
23
45
6
7
1 compression/source coding2 transmission/channel coding3 security/cryptography4 rate-distortion based
information-theoreticsecrecy
5 joint source-channel coding6 traditional
information-theoretic secrecy7 joint source-channel
information-theoreticsecrecy
E. C. Song (Princeton University) Rising Star November 9, 2015 2 / 12
Lossy compression
Low compression (high quality) JPEG High compression (low quality) JPEG
tradeoff between compression and qualitycommon in: audio, video, images, streaming, etcpopular technique: MP3, JPEG, MPEG-4, etcgood for data storage and transmission
E. C. Song (Princeton University) Rising Star November 9, 2015 3 / 12
Looking through the engineering glass
Encoder DecoderX M Y
X : data sourceM: encoded message (used for storage or transmission)Y : reconstructed dataencoder/decoder: data encoding methods such as JPEG, MP3, MP4objective: (size(M), distance(X ,Y ))
E. C. Song (Princeton University) Rising Star November 9, 2015 4 / 12
Information theory
Encoder fn Decoder gn
X n M Y n
Assumption 1 (general): known source distributionAssumption 2 (a bit less general and this work)
I i.i.d. source distributionI large n
E. C. Song (Princeton University) Rising Star November 9, 2015 5 / 12
My contribution
Invented compressor: Likelihood EncoderAchieves best rate-distortion:
I point-to-point lossy compressionI multiuser lossy compressionI SECURITY
E. C. Song (Princeton University) Rising Star November 9, 2015 6 / 12
Perfect secrecy
X n Encoder fn Decoder gn X̂ 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
What if we reduce key size?
not perfect secrecyhow “imperfect”?1nH(X n|M) < H(X )
I hard to interpretI 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
Rate-distortion based secrecy
X n Encoder fn Decoder gn Y n
K ∈ [1 : 2nR0 ]
PZn|M Zn
M ∈ [1 : 2nR ]
Average distortion for the legitimate receiver:
E[db(X n,Y n)] ≤ Db
Minimum average distortion for the eavesdropper:
minPZn|M
E [de(X n,Zn)] ≥ De
Conclusion: secrecy is almost FREE!
E. C. Song (Princeton University) Rising Star November 9, 2015 9 / 12
Really FREE?
assumption: one attempt!one-bit secrecy
E. C. Song (Princeton University) Rising Star November 9, 2015 10 / 12
Secure source coding with causal disclosure
X n Encoder fn Decoder gn Y n
K ∈ [2nR0 ]
Eavesdropper Zn
X t−1
t = 1, ..., nM ∈ [2nR ]
Average distortion for the legitimate receiver:
E [db(X n,Y n)] ≤ Db
Minimum average distortion for the eavesdropper:
min{PZt |MXt−1}nt=1
E [de(X n,Zn)] ≥ De
E. C. Song (Princeton University) Rising Star November 9, 2015 11 / 12
About causal disclosure
Fully generalizes Shannon cipher systemCorresponding 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
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