Information Hiding Problems: Hiding Capacity and Key Design

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Ira Byron Hudson
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1 Iformatio Hidig Problems: Hidig Capacity ad Key Desig Joseph. O Sulliva Electroic Systems ad Sigals Research Laboratory Departmet of Electrical Egieerig Washigto Uiversity i St. Louis Iformatio Hidig Problems Game-Theory Formulatios Eamples Costraits Hidig Capacity Spectrum of problems Private Key Public Coclusios

2 J.. O Sulliva ITW 00 0/4/0 Iformatio Hidig Problems M S Ecoder- Ifo Hider ttac Chael Y Decoder ˆ M K Covertet Key S i K i are pairwise i.i.d.; Source Sets of allowable iformatio hidig ad attac chaels: ad Rate R Ecoder f Decoder Probability of Error: P e R R m P Y K m f S K m

3 J.. O Sulliva ITW 00 0/4/0 Iformatio Hidig Problems M S Ecoder- Ifo Hider ttac Chael Y Decoder ˆ M K Private Game: K = S Public Game: K idepedet of S Rage i betwee: K V S V quatifies iformatio provided about S by K Key selectio: Fi V vary K

4 J.. O Sulliva ITW 00 0/4/0 Iformatio Hidig Games M S Ecoder- Ifo Hider ttac Chael Y Decoder ˆ M K Fi sets of allowable iformatio hidig ad attac chaels: ad Capacity Game: Determie maimal achievable rate R hidig capacity C Mouli ad O Sulliva; Cohe ad Lapidoth; Merhav ad Someh- Baruch; Che Worell ad Barro Error Epoet Game: Determie maimum error epoet for each value of rate R ER Merhav ad Someh-Baruch Other Games: idetificatio detectio ad estimatio figerpritig Mouli et al.; Merhav ad Steiberg; etc

5 J.. O Sulliva ITW 00 0/4/0 Iformatio Hidig Costraits Ecoded data idepedet of covertet Message Ecoder M Source P S Source Ecoder ttac Decoder

6 Stegaography J.. O Sulliva ITW 00 0/4/0 - hidig iformatio so that its presece is udetectable Ecoded data eed ot be idepedet of covertet. Message Ecoder Source P S Source Ecoder Detectio Suppose the attacer simply wats to detect the presece or absece of a hidde message. If D P P S 0 the perfect hidig is achieved. Otherwise the error rate is determied by D P P S.

7 Issues i Embeddig J.. O Sulliva ITW 00 0/4/0 Message Source Ecoder ttac Decoder

8 Message J.. O Sulliva ITW 00 0/4/0 Iformatio Hidig Costraits S Trasparecy or uobtrusiveess: S ad similar mea w.p. ep. boud E[ d S ] D P[ d S D ] 0 S P[ d Source Ecoder ttac Decoder S D S ] e S

9 J.. O Sulliva ITW 00 0/4/0 Eample Implemetatio Issues Trasform Model coefficiets i trasform domai Group coefficiets accordig to margials Iformatio embeddig i coefficiets Perceptually most sigificat Iverse trasform Radomized codig Embeddig Iverse Trasform

10 J.. O Sulliva ITW 00 0/4/0 ttac Chael Costraits ttac Chael Costraits Source Ecoder ttac Decoder Message Robustess: ad Y similar mea w.p. ep. boud S ] [ D Y d E e D Y d P D Y d P ] [ 0 ] [

11 J.. O Sulliva ITW 00 0/4/0 ttac Chael Costraits Message S Source Ecoder ttac - Iadequacy of E[ d Y ] D

12 J.. O Sulliva ITW 00 0/4/0 rbitrary Varyig Chael Result Message S Source Ecoder ttac - If a deletio attac is allowed with probability bouded away from zero the the hidig capacity is zero.

13 J.. O Sulliva ITW 00 0/4/0 ttac Chael Costraits ttac Chael Costraits Mouli ad O Sulliva: mea Memoryless attacs: Bloc-memoryless: Probability oe or large deviatios bouds L i il i L i il L L i i i y y y y e D Y d P D Y d P ] [ 0 ] [ ] [ D Y d E

14 J.. O Sulliva ITW 00 0/4/0 ttac Chael Costraits For may applicatios deletio attacs are used Prisoer or subversive commuicatio For other applicatios deletio is uacceptable Uauthorized use or acquisitio of itellectual property Traitor problems Mathematical models may ot match reality

15 J.. O Sulliva ITW 00 0/4/0 Game Theory View cowledge iformatio will be hidde cowledge eistece of adversary Publish hidig strategy cosistet with stadard approaches to cryptography Need for secret ey for radomized codig Need for ecodig robustess agaist broad families of attacs Need for decoder to adapt to or be robust with respect to attacs

16 J.. O Sulliva ITW 00 0/4/0 Iformatio Hidig Iformatio Hidig Codig Theorems Codig Theorems Public Game: Private Game: Other: Gaussia squared error game: Public ad private games have equal capacity Where ; ; mi ma ; mi ma ; ; mi ma K S U I K Y U I C S Y I C S U I Y U I C

17 J.. O Sulliva ITW 00 0/4/0 Defiitios fiite sets U is a auiliary radom variable over a set of ow cardiality : : D y d q y y s p s u q D s d s p s u s u s u

18 J.. O Sulliva ITW 00 0/4/0 Payoff Fuctio Payoff Fuctio Properties Properties Set is cove for every Set is cove Cove i Cocave i pus Cove i pus Key Desig: Cove i ps ; ; y s u p s u p s u K S U I K Y U I J

19 J.. O Sulliva ITW 00 0/4/0 Payoff Fuctio Relatioship to Chiag ad Cover ISIT 00 Uified view of chael codig with state iformatio ad source codig with side iformatio at the decoder Iformatio available at decoder iformatio available at ecoder I U; Y K I U; S K I U; Y K I U; S K

20 J.. O Sulliva ITW 00 0/4/0 Equal Capacity i Public ad Private Games Barro Che ad Worell 00. If the ** that achieve capacity are such that U Y S is a Marov chai ad the resultig joit distributio o SY is the same as i the public game the the values of the public ad private games are equal. C ma mi I U; Y I U; S

21 J.. O Sulliva ITW 00 0/4/0 Key Desig Issues Key Desig Issues Primary roles of ey: Provide radomizatio of ecodig strategy ecoder-decoder commo radomess Iform decoder about covertet Iformatio: K V S Marov Chai v v V S U I v V Y U I v p v p K S U I K Y U I v s u s u ] ; ; [ ; ;

22 J.. O Sulliva ITW 00 0/4/0 Commets o Keys ribtrary ey K implies select V=fK. Last epasio emphasizes IU;YV-IU;SV Suppose V V S. Let V = f K ad V = f K ad assume the margials o K ad K are idetical. The the capacity of the game with K is at least the capacity of the game with K.

23 J.. O Sulliva ITW 00 0/4/0 Further Implemetatio Issues Distributios o sources Images video voice music Optio: base models o successful compressio algorithms Model real attacs Malicious beig uaticipated Cut-out of itellectual property; edited photos Figerpritig for traitor problems Collusio attacs out of m

24 J.. O Sulliva ITW 00 0/4/0 Related Emergig pplicatios Upgrades of legacy commuicatio systems Worell Ramchadra Pradha et al. Legacy system defies covertet Digital upgrade is ecoded data Importace of Gaussia view DC-IM etc.

25 J.. O Sulliva ITW 00 0/4/0 Coclusios Reviewed capacity results i iformatio hidig games Reviewed some roles of eys For more iformatio o Our results see Mouli ad O Sulliva Error epoet games see Merhav ad Someh-Baruch Gaussia games see Cohe ad Lapidoth lso: Worell Ramchadra Steiberg several special issues cofereces etc.

The Center for Security Technologies Academic Issues in Homeland Security

The Center for Security Technologies Academic Issues in Homeland Security The Ceter for Security Techologies Academic Issues i Homelad Security Joseph A. O Sulliva Professor of Electrical Egieerig Director of the Electroic Systems ad Sigals Research Laboratory Associate Director