A New Approach to Lossy Compression and Applications to Security - PowerPoint PPT Presentation

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 transmission/channel coding 3 security/cryptography data compression 4 rate-distortion based 4 information-theoretic 7 5 secrecy security 5 joint source-channel coding data transmission 3 6 traditional 6 2 information-theoretic secrecy 7 joint source-channel information-theoretic secrecy 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 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

Looking through the engineering glass X M Y Encoder Decoder X : data source M : encoded message (used for storage or transmission) Y : reconstructed data encoder/decoder: data encoding methods such as JPEG, MP3, MP4 objective: ( size ( M ) , distance ( X , Y )) E. C. Song (Princeton University) Rising Star November 9, 2015 4 / 12

Information theory X n Y n M Encoder f n Decoder g 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

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

Perfect secrecy K ∈ [ 1 : 2 nR 0 ] M ∈ [ 1 : 2 nR ] X n Decoder g n ˆ Encoder f n X n Eavesdropper Theorem (Shannon) A rate pair ( R , R 0 ) is achievable under perfect secrecy if and only if R ≥ H ( X ) , R 0 ≥ H ( X ) . E. C. Song (Princeton University) Rising Star November 9, 2015 7 / 12

What if we reduce key size? not perfect secrecy how “imperfect”? 1 n H ( 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

Rate-distortion based secrecy K ∈ [ 1 : 2 nR 0 ] M ∈ [ 1 : 2 nR ] X n Decoder g n Y n Encoder f n P Z n | M Z n Average distortion for the legitimate receiver: E [ d b ( X n , Y n )] ≤ D b Minimum average distortion for the eavesdropper: E [ d e ( X n , Z n )] ≥ D e min P Zn | M 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 K ∈ [ 2 nR 0 ] t = 1 , ..., n M ∈ [ 2 nR ] X n Y n Encoder f n Decoder g n Eavesdropper Z n X t − 1 Average distortion for the legitimate receiver: E [ d b ( X n , Y n )] ≤ D b Minimum average distortion for the eavesdropper: E [ d e ( X n , Z n )] ≥ D e min { P Zt | MXt − 1 } n t = 1 E. C. Song (Princeton University) Rising Star November 9, 2015 11 / 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