1. Information Hiding & Digital Watermarking Tri Van Le

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

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

4. Broken Cryptosystems (I) Merkle Hellman 1978-1984 Iterated Knapsack 1978-1984 Lu-Lee 1979-1980 Merlke Hellman Merlke Hellman Lu-Lee Adiga Shankar 1985-1988 Adigar Shankar Nieder- reiter 1986-1988 Neiderreiter Goodman McAuly 1984-1988 Goodman McAuly Pieprzyk 1985-1988 Pieprzyk Chor Rivest 1988-1998 Chor Rivest Okamoto 1986-1987 Okamoto 1987-1988 Okamoto

5. Broken Cryptosystems (II) Matsumoto Imai 1983-1984 Cade 1985-1986 Yagisawa 1985-1986 Matsumoto Imai CadeYasigawa TMKIF 1986-1985 Tsujii, Itoh Matsumoto Kurosama Fujioka Luccio Mazzone 1980-1981 Luccio Mazzone Kravitz Reed 1982-1982 Kravitz Reed Rao Nam 1986-1988 Rao Nam Low Degree CG 1982 High Degree CG 1988 Rivest Adleman Dertouzos 1978-1987 Rivest Adleman Dertouzos Krawczyk Boyar

6. Broken Cryptosystems (III) Ong Schnorr 1983-1984 Ong Schorr Ong Schnorr Shamir 1984-1985 Ong Schorr Shamir Okamoto Shiraishi 1985-1985 Okamoto Shiraishi

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

8. 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

9. 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

10. Broken Schemes (I)

11. Broken Schemes (II)

12. Broken Schemes (III)

13. Broken Schemes (IV)

14. 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

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

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

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

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

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

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

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

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

23. 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

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

25. Thank you Questions? More details?

26. 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

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

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

29. 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.

30. 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.

31. 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