Information Hiding & Digital Watermarking Tri Van Le

Outlines Some history State of the art Research goals Possible approaches Research plan

Cryptography in the 80s Beginning time of open research A lot of schemes proposed Most of them soon broken

Broken Cryptosystems (I) Merkle Hellman Iterated Knapsack Lu-Lee Merlke Hellman Merlke Hellman Lu-Lee Adiga Shankar Adigar Shankar Nieder- reiter Neiderreiter Goodman McAuly Goodman McAuly Pieprzyk Pieprzyk Chor Rivest Chor Rivest Okamoto Okamoto Okamoto

Broken Cryptosystems (II) Matsumoto Imai Cade Yagisawa Matsumoto Imai CadeYasigawa TMKIF Tsujii, Itoh Matsumoto Kurosama Fujioka Luccio Mazzone Luccio Mazzone Kravitz Reed Kravitz Reed Rao Nam Rao Nam Low Degree CG 1982 High Degree CG 1988 Rivest Adleman Dertouzos Rivest Adleman Dertouzos Krawczyk Boyar

Broken Cryptosystems (III) Ong Schnorr Ong Schorr Ong Schnorr Shamir Ong Schorr Shamir Okamoto Shiraishi Okamoto Shiraishi

Proven Secure Cryptosystems (I) Shannon’s work (1949) –Mathematical proof of security –Information theoretic secrecy Enemy with unlimited power –Can compute any desired function

Proven Secure Cryptosystems (II) Rabin (81), Goldwasser & Micali (82) –Mathematical proof of security –Computational secrecy Enemy with limited time and space –Can run in polynomial time –Can use polynomial space

Information Hiding (state of the art) Similar to that of cryptography in 80s –Many schemes were proposed –Most of them were broken Use heuristic security –Subjective measurements –Assume very specific enemy

Broken Schemes (I)

Broken Schemes (II)

Broken Schemes (III)

Broken Schemes (IV)

Research Goals Fundamental way –Systematic research –Same as Shannon and Goldwasser’s work What have been done –Covert channels –Anonymous communications What are the properties

Fundamental Models Unconditional hiding –Unlimited enemy Statistical hiding –Polynomial samples Computational hiding –Polynomial time

What have been done Covert channels Anonymous communications Information hiding –Steganography –Digital watermarking

Covert Channels Leakage information (e.g. viruses) –Disk space –CPU load Subliminal channels –Digital signatures –Encryption schemes –Cryptographic malwares

Covert Computations Computation inside computations –Secret design calculations inside a factoring computation –Secret physics simulations inside a cryptographic software or devices

Anonymous Communications MIX Networks –Electronic voting –Anonymous communication Onion Routings –Limited anonymous communication Blind signatures –Digital cash

Information Hiding Steganography –Invisible inks –Small dots –Letters Digital watermarking –Common lossy compressions –Common signal processing operations

Information Hiding Hiding property –Output must look like the cover Secrecy –No partial information on input message Authenticity –Hard to compute valid output

Our Approaches Arbitrary key –Steganography, watermarking Restricted key –Protection of key materials Key = Ciphertext –Secret sharing

Research Plan To understand information hiding –Perfect hiding (done) Necessary and sufficient conditions Computational complexity results Constructions of prefect secure schemes Constructions of schemes with non-reliability –Computational hiding (under research) Conventional constructions Public key schemes

Research Plan Other aspects –Replacing privacy by authenticity Extra problem –Robustness against modifications

Thank you Questions? More details?

Approaches Arbitrary key distribution –E: K  M  C –K: key space –M: message space –C: cover space Requires –E(k,m) is distributed accordingly to P cover

Approaches Restricted key distribution –c = E(k,m) –k is distributed accordingly to P K –c is distributed accordingly to P Cover

Approaches Key = Ciphertext –S: M  C  C –(k 1,k 2 ) = S(m) Requires –k 1 and k 2 distributed accordingly to P Cover

Models Perfect hiding –P c = P cover –Ciphertext distributes exactly as P cover Statistical Hiding –|P c - P cover | is a negligible function Negligible function –f(n) 0 and n>N d.

Models Computational Hiding –P c and P cover are P-time indistinguishable –For all P-time P.T.M. M:  Prob(M(P c )=1) - Prob(M(P cover )=1)  is negligible.

Examples Quadratic residues –n = pq –S 1 = {x 2 |x in Z n * } –S 2 = {x|x in Z n * and J(x)=1} Decision Diffie-Hellman –U 1 = (g, g a, g b, g ab ) mod p –U 2 = (g, g a, g b, g r ) mod p